Engineering symbols glossary

Every symbol the MechanixCalc calculators print — what it is called, what it means, its SI and Imperial units, and the tools that use it. Engineering standards reuse letters: the same symbol can mean a speed in one tool and an exponent in another, so those are listed first. Each tool's field help (the ⓘ next to an input) links here.

Same symbol, different meaning (38)

Read the label and the unit next to the field, not the letter alone. Where two meanings would sit on the same tool, the on-screen label carries a subscript to tell them apart (no calculation changes).

n
- Axial / moment ratio (Eurocode 3) — Steel Sections
- Rotational speed — Shaft Keys, Power Screw, Journal Bearings, Cylindrical Gears +17
- Load-introduction factor — Bolted Joints
- Number of items — Bolted Joints, Pipe & Flange Reference, Steel Sections, O-Ring & Seals +9
- Polytropic / isentropic exponent — Compressor Analysis, Hydraulic Accumulator
P
- Pitch — Ball Screws, Roller Chain Drive, Belt & Pulley, Steel Sections +3
- Power — Motor Sizing & VFD, Shaft Couplings, Cylindrical Gears, Bevel & Worm Gears +7
- Equivalent dynamic load (bearings, guides) — Bearing Analysis, Linear Guide Life, Ball Screws
- Axial (column) load — Column Buckling
- Pressure — Hydraulic Cylinders, Pressure Vessels, Pump & Fan Selection, Compressor Analysis +6
a
- Centre distance — Cylindrical Gears, Bevel & Worm Gears, Planetary Gears
- Weld throat — Weld Design
- Position / side length — Beam Deflection, Shaft Analysis, Torsion of Sections, Flywheel & Inertia +3
- Acceleration — Cam & Follower, Pneumatics, Vibration Analysis, Hydraulic Cylinders
f
- Frequency — Shaft Couplings, Beam Deflection, Cam & Follower, Torsion of Sections +5
- Feed per revolution — Machining Parameters
- Darcy friction factor — Pipe Flow, Hydraulic Accumulator, Pump & Fan Selection
- Friction coefficient / factor — Conveyor Belt, Journal Bearings, Pneumatics
m
- Axial / moment ratio (Eurocode 3) — Steel Sections
- Module — Cylindrical Gears, Bevel & Worm Gears, Planetary Gears, Slewing Rings
- Mass — Hydraulic Cylinders, Cam & Follower, Flywheel & Inertia, Conveyor Belt +4
- S-N (Wöhler) slope exponent — Weld Design, Fatigue Analysis
N
- Rotational speed — Shaft Keys, Power Screw, Journal Bearings, Cylindrical Gears +17
- Axial force — Steel Sections, Torsion of Sections
- Number of items — Bolted Joints, Pipe & Flange Reference, Steel Sections, O-Ring & Seals +9
- Number of cycles — Fatigue Analysis, Cylindrical Gears, Hydraulic Accumulator, Wire Rope & Lifting +4
p
- Contact / bearing pressure — Shaft Keys, Clutches & Brakes, Power Screw, Press Fits +5
- Pitch — Ball Screws, Roller Chain Drive, Belt & Pulley, Steel Sections +3
- Life exponent — Linear Guide Life, Bearing Analysis, Ball Screws
- Pressure — Hydraulic Cylinders, Pressure Vessels, Pump & Fan Selection, Compressor Analysis +6
Q
- Quality (resonance) factor — Vibration Analysis
- Load (slewing rings, hoists) — Slewing Rings, Wire Rope & Lifting
- Flow rate — Hydraulic Cylinders, Pipe & Flange Reference, Journal Bearings, Conveyor Belt +6
- Heat flow / duty — Heat Exchanger, Roller Chain Drive, O-Ring & Seals, Thermal Analysis +2
S
- Allowable stress — Pressure Vessels, Pipe Stress
- Safety factor — Motor Sizing & VFD, Bolted Joints, Hydraulic Cylinders, Linear Guide Life +28
- Stroke / travel — Hydraulic Cylinders, Ball Screws, Pneumatics, Springs
- Sommerfeld number — Journal Bearings
T
- Period — Beam Deflection, Vibration Analysis
- Torque — Motor Sizing & VFD, Shaft Keys, Shaft Couplings, Clutches & Brakes +9
- Tool life — Machining Parameters
- Temperature — Pressure Vessels, Clutches & Brakes, Ball Screws, Press Fits +8
α
- Coefficient of thermal expansion — Bolted Joints, Press Fits, Thermal Analysis, Pipe Stress +1
- Pressure / contact angle — Cylindrical Gears, Bevel & Worm Gears, Cam & Follower, Bearing Analysis +1
- Wrap angle — Belt & Pulley, Roller Chain Drive, Conveyor Belt
- Angular acceleration — Slewing Rings, Flywheel & Inertia
ε
- Strain — Sheet Metal
- Absolute roughness — Pipe Flow
- Eccentricity ratio (journal bearing) — Journal Bearings
- Heat-exchanger effectiveness — Heat Exchanger
C
- Centre distance (belts, chains) — Belt & Pulley, Roller Chain Drive
- Basic dynamic load rating — Bearing Analysis, Linear Guide Life, Slewing Rings, Ball Screws
- Capacitance — Dust Collection
I
- Second moment of area — Beam Deflection, Column Buckling, Steel Sections, Pipe & Flange Reference +4
- Mass moment of inertia — Motor Sizing & VFD, Slewing Rings, Torsion of Sections, Flywheel & Inertia +4
- Electric current — Motor Sizing & VFD, Weld Design
k
- Bolt-circle diameter (flanges) — Pipe & Flange Reference
- Stiffness / spring rate — Shaft Couplings, Cam & Follower, Wire Rope & Lifting, Torsion of Sections +6
- S-N (Wöhler) slope exponent — Weld Design, Fatigue Analysis
W
- Section modulus — Pipe & Flange Reference, Beam Deflection, Steel Sections, Torsion of Sections +3
- Width — O-Ring & Seals, Sheet Metal, Pipe Stress
- Load / force — Power Screw, Journal Bearings, Conveyor Belt, Wire Rope & Lifting +1
η
- Utilisation ratio (Eurocode 3) — Steel Sections
- Efficiency — Motor Sizing & VFD, Hydraulic Cylinders, Slewing Rings, Ball Screws +15
- Dynamic viscosity — Pipe & Flange Reference, Journal Bearings, Pump & Fan Selection, Pipe Flow +1
λ
- Slenderness — Column Buckling, Steel Sections, Hydraulic Cylinders, Pneumatics
- Lead angle — Ball Screws, Power Screw
- Darcy friction factor — Pipe Flow, Hydraulic Accumulator, Pump & Fan Selection
φ
- Pressure / contact angle — Cylindrical Gears, Bevel & Worm Gears, Cam & Follower, Bearing Analysis +1
- Phase / twist angle — Rotor Dynamics, Vibration Analysis, Torsion of Sections
- Joint load factor — Bolted Joints
e
- Eccentricity / edge distance — Column Buckling, Weld Design, Vibration Analysis, Rotor Dynamics +3
- Load factors (ISO 281) — Bearing Analysis
E
- Young's modulus — Bolted Joints, Hydraulic Cylinders, Beam Deflection, Fatigue Analysis +15
- Energy — Hydraulic Accumulator, Clutches & Brakes, Dust Collection, Flywheel & Inertia
G
- Shear modulus — Torsion of Sections, Springs, Shaft Analysis
- Balance quality grade — Rotor Dynamics, Vibration Analysis
h
- Head — Pump & Fan Selection, Pipe Flow
- Film heat-transfer coefficient — Heat Exchanger
i
- Radius of gyration — Pipe & Flange Reference
- Transmission ratio — Motor Sizing & VFD, Belt & Pulley, Cylindrical Gears, Planetary Gears +1
J
- Polar moment / torsion constant — Torsion of Sections, Steel Sections, Column Buckling, Weld Design +1
- Mass moment of inertia — Motor Sizing & VFD, Slewing Rings, Torsion of Sections, Flywheel & Inertia +4
K
- Effective-length factor — Column Buckling
- Bulk modulus — Pipe Flow
q
- Notch sensitivity — Fatigue Analysis, Press Fits, Shaft Analysis
- Heat flux — Clutches & Brakes
R
- Radius — Pressure Vessels, Cam & Follower, Flywheel & Inertia, Roller Chain Drive +2
- Specific gas constant — Compressor Analysis
Re
- Yield strength (EN/ISO) — Shaft Analysis, Press Fits, Steel Sections, Weld Design
- Reynolds number — Pipe Flow, Heat Exchanger, Pump & Fan Selection, Dust Collection
s
- Stroke / travel — Hydraulic Cylinders, Ball Screws, Pneumatics, Springs
- Slip (induction motor) — Motor Sizing & VFD
U
- Overall heat-transfer coefficient — Heat Exchanger
- Voltage — Weld Design, Motor Sizing & VFD
V
- Volume — Hydraulic Accumulator, Pneumatics, Compressor Analysis, Dust Collection
- Voltage — Weld Design, Motor Sizing & VFD
Z
- Section modulus — Pipe & Flange Reference, Beam Deflection, Steel Sections, Torsion of Sections +3
- Number of items — Bolted Joints, Pipe & Flange Reference, Steel Sections, O-Ring & Seals +9
β
- Helix angle — Cylindrical Gears, Planetary Gears
- Cam rise / dwell angle — Cam & Follower
δ
- Deflection / interference — Beam Deflection, Shaft Analysis, Springs, Vibration Analysis +4
- Pitch-cone angle — Bevel & Worm Gears
μ
- Friction coefficient — Bolted Joints, Clutches & Brakes, Slewing Rings, Power Screw +8
- Dynamic viscosity — Pipe & Flange Reference, Journal Bearings, Pump & Fan Selection, Pipe Flow +1
ν
- Poisson's ratio — Press Fits, Flywheel & Inertia, Pressure Vessels, Thermal Analysis +5
- Kinematic viscosity — Journal Bearings, Cylindrical Gears, Roller Chain Drive, Bearing Analysis +1
ρ
- Density — Pipe & Flange Reference, Belt & Pulley, Flywheel & Inertia, Pump & Fan Selection +9
- Radius of curvature — Cam & Follower

Subscripts added where both meanings share a screen

Bolted Joints: bolt count vs VDI 2230 load-introduction factor n → label Bolts n_b
Steel Sections: bolt count vs axial ratio n = N_Ed/N_pl,Rd → label Number of Bolts n_b
Machining Parameters: spindle speed n vs Taylor exponent → label Taylor exponent n_T (default 0.40 coated carbide)
Machining Parameters: spindle speed n vs Taylor exponent → label Taylor n_T (tool material)
Pneumatics: cylinder stroke S vs vacuum-gripper safety factor → label Safety Factor SF
Pipe Stress: B31.3 weld strength-reduction factor W vs expansion-loop width → label Loop Width W_loop
O-Ring & Seals: O-ring groove width W vs ASME gasket bolt load → label Governing Force W_m
Conveyor Belt: ISO 5048 friction coefficient f vs allowable sag ratio → label Sag Factor f_sag
Hydraulic Accumulator: Darcy friction factor f vs cycle frequency → label Cycle frequency f_cyc
Dust Collection: volumetric flow Q vs electrostatic charge generation → label Charge Generation Q_ch (nC/s)

Stress & strength

Symbol	Name, meaning and tools	SI	Imperial
σ	Normal stressForce per unit area acting normal to a section; tension positive, compression negative.SI MPa (N/mm²) · Imperial ksi / psiBolted Joints Mohr's Circle Beam Deflection Fatigue Analysis Pressure Vessels Column Buckling Press Fits Flywheel & Inertia Thermal Analysis Torsion of Sections Weld Design Shaft Analysis Pipe Stress Sheet Metal Steel Sections	MPa (N/mm²)	ksi / psi
σ_a, σ_m	Alternating / mean stressHalf the stress range and the average of the cycle — the two inputs of every mean-stress (Goodman, Gerber, Haigh) check.SI MPa · Imperial ksiFatigue Analysis Shaft Analysis Torsion of Sections Springs Bolted Joints Weld Design	MPa	ksi
τ	Shear stressForce per unit area acting in the plane of a section (torsion, transverse shear, key and spline shear).SI MPa · Imperial ksi / psiMohr's Circle Shaft Keys Shaft Couplings Beam Deflection Fatigue Analysis Slewing Rings Power Screw Belt & Pulley Torsion of Sections Springs Weld Design Shaft Analysis Bolted Joints	MPa	ksi / psi
σ_vm	Von Mises equivalent stressSingle equivalent stress combining normal and shear components (distortion-energy criterion), compared with the yield strength.SI MPa · Imperial ksiBolted Joints Mohr's Circle Fatigue Analysis Power Screw Press Fits Flywheel & Inertia Torsion of Sections Weld Design Shaft Analysis Pipe Stress	MPa	ksi
p	Contact / bearing pressureSurface pressure between two bodies — key flank, fit interface, nut thread, journal, clutch lining, Hertz contact.SI MPa (N/mm²) · Imperial psi / ksiShaft Keys Clutches & Brakes Power Screw Press Fits Journal Bearings Cam & Follower Mechanism Actuator Sizing Tolerance Stack-up Bolted Joints	MPa (N/mm²)	psi / ksi
Rp0.2 (R_p0,2)	0.2 % proof strengthStress at 0.2 % plastic strain — the yield figure of EN/ISO material standards for metals without a sharp yield point.SI MPa · Imperial ksiBolted Joints Shaft Analysis Sheet Metal	MPa	ksi
Rm (R_m)	Tensile strength (EN/ISO)Maximum engineering stress in a tensile test; the EN/ISO name for the ultimate tensile strength.SI MPa · Imperial ksiBolted Joints Clutches & Brakes Press Fits Bevel & Worm Gears Torsion of Sections Springs Shaft Analysis Sheet Metal	MPa	ksi
Re (ReH)	Yield strength (EN/ISO)Upper yield strength ReH of EN 10025 / EN 10083 steels — the EN name for Sy.SI MPa · Imperial ksiShaft Analysis Press Fits Steel Sections Weld Design	MPa	ksi
Sy (S_y, fy)	Yield strengthStress at which the material starts to deform plastically (fy in Eurocode 3, Sy in Shigley/ASME).SI MPa · Imperial ksiBolted Joints Hydraulic Cylinders Pipe & Flange Reference Mohr's Circle Shaft Keys Shaft Couplings Beam Deflection Fatigue Analysis Pressure Vessels Column Buckling Power Screw Press Fits Steel Sections Cylindrical Gears Flywheel & Inertia Thermal Analysis Torsion of Sections Springs Weld Design Shaft Analysis Pipe Stress Sheet Metal	MPa	ksi
Sut (S_u)	Ultimate tensile strengthMaximum engineering stress before fracture (Shigley/ASME notation; Rm in EN/ISO).SI MPa · Imperial ksiBolted Joints Mohr's Circle Beam Deflection Fatigue Analysis Pressure Vessels Torsion of Sections Springs Shaft Analysis Pipe Stress Sheet Metal	MPa	ksi
Se (S_e)	Endurance limitFully reversed stress amplitude a part survives indefinitely (corrected by the Marin factors k_a … k_e).SI MPa · Imperial ksiFatigue Analysis Torsion of Sections Springs Shaft Analysis Press Fits	MPa	ksi
S	Allowable stressCode allowable stress of a material at temperature (ASME VIII, B31.3: S, S_A, S_E, S_L).SI MPa · Imperial ksi / psiPressure Vessels Pipe Stress	MPa	ksi / psi
ε	StrainRelative elongation (dimensionless); ε₁ / ε₂ are the major and minor strains of a forming limit check.SI — (mm/mm) · Imperial — (in/in)Sheet Metal	— (mm/mm)	— (in/in)

Safety & load factors

Symbol	Name, meaning and tools	SI	Imperial
SF (S)	Safety factorCapacity divided by demand; ≥ the required minimum passes. Each tool says which capacity (yield, fatigue, buckling, slip …).SI — · Imperial —Motor Sizing & VFD Bolted Joints Hydraulic Cylinders Linear Guide Life Mohr's Circle Shaft Keys Shaft Couplings Beam Deflection Fatigue Analysis Pressure Vessels Clutches & Brakes Slewing Rings Ball Screws Column Buckling Power Screw Press Fits Steel Sections Cam & Follower Belt & Pulley Roller Chain Drive Flywheel & Inertia Conveyor Belt Mechanism Actuator Sizing Hydraulic Accumulator Wire Rope & Lifting Torsion of Sections Springs Weld Design Shaft Analysis Rotor Dynamics Pipe Stress Pneumatics	—	—
S_H	Pitting (contact) safety factorISO 6336-2 / ISO 10300 safety factor against flank pitting.SI — · Imperial —Cylindrical Gears Bevel & Worm Gears Planetary Gears Slewing Rings	—	—
S_F	Bending safety factor (gears) / yield safety factor (bolts)ISO 6336-3 tooth-root bending safety factor; in VDI 2230 S_F is the safety factor against bolt yield.SI — · Imperial —Cylindrical Gears Bevel & Worm Gears Planetary Gears Bolted Joints	—	—
s₀	Static safety factor (rolling bearings)Static load rating divided by the static equivalent load, C₀ / P₀ (ISO 76).SI — · Imperial —Bearing Analysis Slewing Rings Linear Guide Life Ball Screws	—	—
n_s, n_f	Static / fatigue safety factor (Shigley)Shigley's notation: n_s against yield, n_f against fatigue (Goodman/Gerber).SI — · Imperial —Shaft Analysis Fatigue Analysis Springs	—	—
K_A	Application factorMultiplies the nominal load for the driving and driven machines' shock (ISO 6336, DIN 3990, ISO 10300).SI — · Imperial —Cylindrical Gears Bevel & Worm Gears Planetary Gears Slewing Rings Shaft Keys Shaft Analysis Shaft Couplings	—	—
K_V	Dynamic factorInternal dynamic load of the mesh from pitch-line velocity and gear quality (ISO 6336-1).SI — · Imperial —Cylindrical Gears Bevel & Worm Gears Planetary Gears	—	—
K_γ	Mesh load-sharing factorUnequal load sharing between planets (ISO 6336 / AGMA 6123).SI — · Imperial —Planetary Gears	—	—
α_A	Tightening factorVDI 2230 ratio of maximum to minimum assembly preload for the tightening method.SI — · Imperial —Bolted Joints	—	—
Kt	Theoretical stress-concentration factorPeak elastic stress at a notch divided by the nominal stress (geometry only).SI — · Imperial —Mohr's Circle Shaft Keys Fatigue Analysis Press Fits Torsion of Sections Shaft Analysis	—	—
Kf	Fatigue notch factorEffective fatigue stress concentration, Kf = 1 + q·(Kt − 1).SI — · Imperial —Shaft Keys Fatigue Analysis Press Fits Shaft Analysis	—	—
q	Notch sensitivityHow much of Kt a material feels in fatigue (0 … 1).SI — · Imperial —Fatigue Analysis Press Fits Shaft Analysis	—	—
k_a … k_e	Marin factorsSurface, size, load, temperature and reliability corrections of the endurance limit (Shigley).SI — · Imperial —Shaft Analysis Torsion of Sections Fatigue Analysis	—	—
η	Utilisation ratio (Eurocode 3)Eurocode 3 interaction / utilisation (η ≤ 1 passes) — NOT an efficiency.SI — · Imperial —Steel Sections	—	—
n, m	Axial / moment ratio (Eurocode 3)Eurocode 3 ratios n = N_Ed / N_pl,Rd and m = M_Ed / M_Rd.SI — · Imperial —Steel Sections	—	—

Material properties

Symbol	Name, meaning and tools	SI	Imperial
E	Young's modulusElastic modulus in tension/compression (steel ≈ 200–210 GPa).SI GPa / MPa · Imperial Msi / ksiBolted Joints Hydraulic Cylinders Beam Deflection Fatigue Analysis Pressure Vessels Column Buckling Press Fits Steel Sections Belt & Pulley Conveyor Belt Pipe Flow Thermal Analysis Wire Rope & Lifting Shaft Analysis Pipe Stress Sheet Metal Flywheel & Inertia Springs Torsion of Sections	GPa / MPa	Msi / ksi
G	Shear modulusElastic modulus in shear, G = E / (2(1 + ν)) (steel ≈ 79–81 GPa).SI GPa · Imperial MsiTorsion of Sections Springs Shaft Analysis	GPa	Msi
ν	Poisson's ratioLateral contraction per unit axial strain (steel ≈ 0.3).SI — · Imperial —Press Fits Flywheel & Inertia Pressure Vessels Thermal Analysis Mohr's Circle Beam Deflection Steel Sections Cam & Follower Cylindrical Gears	—	—
ρ	DensityMass per unit volume.SI kg/m³ · Imperial lb/ft³Pipe & Flange Reference Belt & Pulley Flywheel & Inertia Pump & Fan Selection Compressor Analysis Pipe Flow Shaft Analysis Pipe Stress Shaft Couplings Beam Deflection Conveyor Belt Rotor Dynamics Heat Exchanger	kg/m³	lb/ft³
α	Coefficient of thermal expansionStrain per degree of temperature change.SI 1/K (×10⁻⁶/°C, µm/m·K) · Imperial 1/°F (×10⁻⁶/°F)Bolted Joints Press Fits Thermal Analysis Pipe Stress Ball Screws	1/K (×10⁻⁶/°C, µm/m·K)	1/°F (×10⁻⁶/°F)
μ	Friction coefficientRatio of friction force to normal force at a contact (thread, head, fit, lining, pulley).SI — · Imperial —Bolted Joints Clutches & Brakes Slewing Rings Power Screw Press Fits Cam & Follower Conveyor Belt O-Ring & Seals Belt & Pulley Mechanism Actuator Sizing Tolerance Stack-up Bearing Analysis	—	—

Geometry

Symbol	Name, meaning and tools	SI	Imperial
d	DiameterDiameter of a shaft, bolt, wire, pipe bore or rolling element (d₁, d₂, d_m … qualify which).SI mm · Imperial inBolted Joints Shaft Keys Shaft Analysis Bearing Analysis Springs Press Fits Pipe Flow Pump & Fan Selection Ball Screws Power Screw Wire Rope & Lifting Shaft Couplings Torsion of Sections O-Ring & Seals Hydraulic Cylinders Pipe & Flange Reference Journal Bearings Cylindrical Gears Machining Parameters	mm	in
D	Outer / pitch / drum diameterOuter diameter of a hub, ring or bearing, the mean coil diameter of a spring, or a drum / sheave diameter.SI mm · Imperial inBearing Analysis Springs Press Fits Wire Rope & Lifting Pressure Vessels Pipe Stress Hydraulic Cylinders Journal Bearings Slewing Rings Dust Collection	mm	in
L	LengthSpan, length, grip or engagement length — the label says which.SI mm / m · Imperial in / ftBolted Joints Hydraulic Cylinders Shaft Keys Shaft Couplings Beam Deflection Pressure Vessels Ball Screws Column Buckling Press Fits Steel Sections Journal Bearings Cam & Follower Bevel & Worm Gears Belt & Pulley Flywheel & Inertia Conveyor Belt Pump & Fan Selection Pipe Flow Thermal Analysis Wire Rope & Lifting Torsion of Sections Springs Weld Design Shaft Analysis Pipe Stress Pneumatics Heat Exchanger GD&T Sheet Metal	mm / m	in / ft
t	Thickness / timeWall or sheet thickness in geometry panels; time in motion panels (t_acc, t_start).SI mm / s · Imperial in / sPressure Vessels Pipe Stress Sheet Metal Weld Design Column Buckling Steel Sections Motor Sizing & VFD Conveyor Belt Flywheel & Inertia Clutches & Brakes	mm / s	in / s
b	Face widthTooth or belt face width, or a section width.SI mm · Imperial inCylindrical Gears Bevel & Worm Gears Planetary Gears Slewing Rings Belt & Pulley Beam Deflection Shaft Keys	mm	in
a	Centre distanceDistance between gear (or pulley) axes.SI mm · Imperial inCylindrical Gears Bevel & Worm Gears Planetary Gears	mm	in
a	Weld throatEffective throat thickness of a fillet weld (a ≈ 0.707·s).SI mm · Imperial inWeld Design	mm	in
a	Position / side lengthLoad position along a span, or a section side (beams, shaft, torsion, flywheel, buckling).SI mm · Imperial inBeam Deflection Shaft Analysis Torsion of Sections Flywheel & Inertia Column Buckling Sheet Metal Bolted Joints	mm	in
C	Centre distance (belts, chains)Distance between pulley or sprocket axes.SI mm · Imperial inBelt & Pulley Roller Chain Drive	mm	in
m	ModuleGear tooth size, m = d / z (mm per tooth).SI mm · Imperial in (= 25.4 / DP)Cylindrical Gears Bevel & Worm Gears Planetary Gears Slewing Rings	mm	in (= 25.4 / DP)
z	Number of teethTooth count of a gear, sprocket, pulley or cutter (z₁ pinion, z₂ wheel).SI — · Imperial —Slewing Rings Cylindrical Gears Bevel & Worm Gears Belt & Pulley Roller Chain Drive Planetary Gears Machining Parameters	—	—
x	Profile shift coefficientAddendum modification in multiples of the module (ISO 21771).SI — · Imperial —Cylindrical Gears	—	—
p (P)	PitchThread, chain, belt, screw or bolt pitch (P for an ISO thread; p_b, p₁ …).SI mm · Imperial inBall Screws Roller Chain Drive Belt & Pulley Steel Sections Bolted Joints Power Screw Heat Exchanger	mm	in
I	Second moment of areaBending stiffness of a section (area moment of inertia).SI mm⁴ / cm⁴ · Imperial in⁴Beam Deflection Column Buckling Steel Sections Pipe & Flange Reference Weld Design Pipe Stress Hydraulic Cylinders Torsion of Sections	mm⁴ / cm⁴	in⁴
J	Polar moment / torsion constantTorsional stiffness of a section (J = πd⁴/32 for a solid round).SI mm⁴ · Imperial in⁴Torsion of Sections Steel Sections Column Buckling Weld Design Shaft Analysis	mm⁴	in⁴
Z (W)	Section modulusI / c — bending stress σ = M / Z (W_el, W_pl in Eurocode 3).SI mm³ / cm³ · Imperial in³Pipe & Flange Reference Beam Deflection Steel Sections Torsion of Sections Weld Design Shaft Analysis Pipe Stress	mm³ / cm³	in³
λ	SlendernessEffective length over radius of gyration (λ̄ non-dimensional in EC3).SI — · Imperial —Column Buckling Steel Sections Hydraulic Cylinders Pneumatics	—	—
λ	Lead angleHelix angle of a screw thread, tan λ = P_h / (π·d₂).SI ° · Imperial °Ball Screws Power Screw	°	°
K	Effective-length factorColumn end-condition factor, L_e = K·L (Euler / Johnson).SI — · Imperial —Column Buckling	—	—
α (φ)	Pressure / contact angleGear pressure angle (20° standard), cam pressure angle or bearing contact angle. The bevel tool also prints it as φ.SI ° · Imperial °Cylindrical Gears Bevel & Worm Gears Cam & Follower Bearing Analysis Planetary Gears	°	°
α	Wrap angleAngle of belt, chain or conveyor-belt contact on the small pulley / drive pulley.SI ° · Imperial °Belt & Pulley Roller Chain Drive Conveyor Belt	°	°
β	Helix angleGear helix angle at the reference cylinder.SI ° · Imperial °Cylindrical Gears Planetary Gears	°	°
δ	Deflection / interferenceDeflection of a beam, shaft or spring; the diametral interference of a press fit.SI mm / µm · Imperial inBeam Deflection Shaft Analysis Springs Vibration Analysis Press Fits Wire Rope & Lifting Bearing Analysis Shaft Couplings	mm / µm	in
δ	Pitch-cone angleBevel gear pitch-cone angle (δ₁ pinion, δ₂ wheel).SI ° · Imperial °Bevel & Worm Gears	°	°
ρ	Radius of curvatureLocal radius of curvature of a cam surface or tooth flank (ρ_min).SI mm · Imperial inCam & Follower	mm	in
R (r)	RadiusRadius of a shell, flywheel, bend, roller or pitch circle — the label says which.SI mm · Imperial inPressure Vessels Cam & Follower Flywheel & Inertia Roller Chain Drive Sheet Metal Bevel & Worm Gears	mm	in
R_e	Outer cone distanceBevel gear outer cone distance (ISO 23509).SI mm · Imperial inBevel & Worm Gears	mm	in
e	Eccentricity / edge distanceLoad eccentricity (columns, welds, bolt groups, rotors) or a bolt edge / end distance e₁, e₂ (EC3).SI mm · Imperial inColumn Buckling Weld Design Vibration Analysis Rotor Dynamics Steel Sections Belt & Pulley Bolted Joints	mm	in
ε	Absolute roughnessPipe wall roughness height used in the Colebrook friction factor.SI mm · Imperial inPipe Flow	mm	in
k	Bolt-circle diameter (flanges)EN 1092-1 flange bolt-circle diameter.SI mm · Imperial inPipe & Flange Reference	mm	in
i	Radius of gyration√(I / A); sets slenderness.SI mm · Imperial inPipe & Flange Reference	mm	in
W	WidthGroove, sheet or loop width (W_loop on the pipe-stress tool).SI mm / m · Imperial in / ftO-Ring & Seals Sheet Metal Pipe Stress	mm / m	in / ft
n (N, Z)	Number of itemsA count — bolts (n_b), coils, starts, rope parts, isolators, passes, splines, friction faces, rolling elements (Z).SI — · Imperial —Bolted Joints Pipe & Flange Reference Steel Sections O-Ring & Seals Springs Ball Screws Wire Rope & Lifting Vibration Analysis Heat Exchanger Shaft Keys Clutches & Brakes Slewing Rings Bearing Analysis	—	—

Motion & speed

Symbol	Name, meaning and tools	SI	Imperial
n (N)	Rotational speedRevolutions per minute (n₁ driver, n₂ driven; N in ISO 281 / AGMA style pages).SI rpm (min⁻¹) · Imperial rpmShaft Keys Power Screw Journal Bearings Cylindrical Gears Belt & Pulley Roller Chain Drive Bearing Analysis Machining Parameters Compressor Analysis Shaft Couplings Ball Screws Cam & Follower Pump & Fan Selection Flywheel & Inertia Shaft Analysis O-Ring & Seals Rotor Dynamics Vibration Analysis Motor Sizing & VFD Bevel & Worm Gears Slewing Rings	rpm (min⁻¹)	rpm
ω	Angular velocityω = 2π·n / 60.SI rad/s · Imperial rad/sMotor Sizing & VFD Shaft Couplings Beam Deflection Clutches & Brakes Slewing Rings Journal Bearings Cam & Follower Flywheel & Inertia Torsion of Sections Shaft Analysis Bearing Analysis Rotor Dynamics Vibration Analysis	rad/s	rad/s
α	Angular accelerationRate of change of angular velocity.SI rad/s² · Imperial rad/s²Slewing Rings Flywheel & Inertia	rad/s²	rad/s²
v	VelocityLinear speed — belt, chain, rope, piston, flow, cutting or sliding speed.SI m/s · Imperial ft/s (ft/min)Hydraulic Cylinders Cam & Follower Belt & Pulley Roller Chain Drive Conveyor Belt Pipe Flow Wire Rope & Lifting Weld Design Dust Collection O-Ring & Seals Heat Exchanger Machining Parameters Pneumatics	m/s	ft/s (ft/min)
a	AccelerationLinear acceleration (a_max of a cam follower, handling acceleration, peak vibration acceleration).SI m/s² · Imperial ft/s² (g)Cam & Follower Pneumatics Vibration Analysis Hydraulic Cylinders	m/s²	ft/s² (g)
f	FrequencyCycles per second — natural, excitation or chatter frequency (f_n, f₁, f_exc).SI Hz · Imperial HzShaft Couplings Beam Deflection Cam & Follower Torsion of Sections Vibration Analysis Machining Parameters Springs Rotor Dynamics Conveyor Belt	Hz	Hz
f	Feed per revolutionTool advance per spindle revolution.SI mm/rev · Imperial in/revMachining Parameters	mm/rev	in/rev
ζ	Damping ratioFraction of critical damping.SI — · Imperial —Cam & Follower Rotor Dynamics Vibration Analysis Machining Parameters	—	—
T	PeriodTime for one cycle, T = 1 / f.SI s · Imperial sBeam Deflection Vibration Analysis	s	s
φ	Phase / twist anglePhase angle of a response, or angle of twist of a shaft (torsion).SI ° / rad · Imperial ° / radRotor Dynamics Vibration Analysis Torsion of Sections	° / rad	° / rad
s (S)	Stroke / travelStroke of a cylinder, screw or spring travel.SI mm · Imperial inHydraulic Cylinders Ball Screws Pneumatics Springs	mm	in
s	Slip (induction motor)Relative speed lag of the rotor, s = (n_s − n) / n_s.SI — (%) · Imperial — (%)Motor Sizing & VFD	— (%)	— (%)
G	Balance quality gradeISO 21940-11 permissible residual unbalance as e·ω (G 2.5, G 6.3 …).SI mm/s · Imperial mm/sRotor Dynamics Vibration Analysis	mm/s	mm/s
Q	Quality (resonance) factorAmplification at resonance, Q = 1 / (2ζ).SI — · Imperial —Vibration Analysis	—	—
β	Cam rise / dwell angleCam rotation angle over which the follower rises (β) or dwells (β_d).SI ° · Imperial °Cam & Follower	°	°
i	Transmission ratioSpeed ratio driver : driven.SI — · Imperial —Motor Sizing & VFD Belt & Pulley Cylindrical Gears Planetary Gears Roller Chain Drive	—	—

Forces, torque & power

Symbol	Name, meaning and tools	SI	Imperial
F	ForceA force (F_a axial, F_r radial, F_t tangential, F_M preload …).SI N / kN · Imperial lbf / kipBolted Joints Bearing Analysis Cylindrical Gears Bevel & Worm Gears Shaft Analysis Slewing Rings Ball Screws Springs Hydraulic Cylinders Shaft Keys Press Fits Beam Deflection Column Buckling Weld Design Pneumatics Linear Guide Life	N / kN	lbf / kip
Fa, Fr, Ft	Axial / radial / tangential loadForce components along the axis, towards the axis and along the pitch circle.SI N / kN · Imperial lbfBolted Joints Slewing Rings Ball Screws Cylindrical Gears Bevel & Worm Gears Conveyor Belt Thermal Analysis Shaft Analysis Bearing Analysis Shaft Keys Belt & Pulley Roller Chain Drive Planetary Gears	N / kN	lbf
T (M_t)	TorqueTwisting moment.SI N·m · Imperial lbf·ft / lbf·inMotor Sizing & VFD Shaft Keys Shaft Couplings Clutches & Brakes Press Fits Cylindrical Gears Flywheel & Inertia Torsion of Sections Weld Design Shaft Analysis Slewing Rings Bevel & Worm Gears Planetary Gears	N·m	lbf·ft / lbf·in
T₁, T₂	Belt / rope tensionTight-side and slack-side tension of a belt or conveyor belt.SI N / kN · Imperial lbfBelt & Pulley Conveyor Belt	N / kN	lbf
M	Bending momentMoment about a section's neutral axis.SI N·m · Imperial lbf·ftBeam Deflection Shaft Analysis Steel Sections Slewing Rings Weld Design Pipe Stress Fatigue Analysis	N·m	lbf·ft
P	PowerMechanical power, P = T·ω.SI kW · Imperial hpMotor Sizing & VFD Shaft Couplings Cylindrical Gears Bevel & Worm Gears Belt & Pulley Roller Chain Drive Torsion of Sections Conveyor Belt Pump & Fan Selection Compressor Analysis Planetary Gears	kW	hp
P	Equivalent dynamic load (bearings, guides)Single load giving the same life as the real combination, P = X·Fr + Y·Fa (ISO 281).SI N / kN · Imperial lbfBearing Analysis Linear Guide Life Ball Screws	N / kN	lbf
P	Axial (column) loadCompressive load on a column; P_cr is the critical (buckling) load.SI N / kN · Imperial lbf / kipColumn Buckling	N / kN	lbf / kip
Q	Load (slewing rings, hoists)Equivalent bearing load of a slewing ring; lifted load of a hoist.SI kN · Imperial kip / lbfSlewing Rings Wire Rope & Lifting	kN	kip / lbf
W	Load / forceAxial load on a screw, radial load on a journal, rope working load, gasket bolt load W_m.SI N / kN · Imperial lbfPower Screw Journal Bearings Conveyor Belt Wire Rope & Lifting O-Ring & Seals	N / kN	lbf
N	Axial forceNormal force in a member (N_Ed in Eurocode 3).SI kN · Imperial kipSteel Sections Torsion of Sections	kN	kip
k	Stiffness / spring rateForce per unit deflection (k_T torsional per radian).SI N/mm (N·m/rad) · Imperial lbf/in (lbf·in/rad)Shaft Couplings Cam & Follower Wire Rope & Lifting Torsion of Sections Springs Rotor Dynamics Vibration Analysis Machining Parameters Bolted Joints Bearing Analysis	N/mm (N·m/rad)	lbf/in (lbf·in/rad)
J (I)	Mass moment of inertiaRotational inertia about an axis (J_load, J_motor; I on flywheel, couplings, mechanism pages).SI kg·m² · Imperial lb·ft²Motor Sizing & VFD Slewing Rings Torsion of Sections Flywheel & Inertia Shaft Couplings Mechanism Actuator Sizing Clutches & Brakes Rotor Dynamics	kg·m²	lb·ft²
m	MassMass of a moving part, load or rotor.SI kg · Imperial lbHydraulic Cylinders Cam & Follower Flywheel & Inertia Conveyor Belt Rotor Dynamics Pneumatics Vibration Analysis Belt & Pulley	kg	lb
φ (Φ)	Joint load factorVDI 2230 share of the axial working load that reaches the bolt (Φ_n = n·φ).SI — · Imperial —Bolted Joints	—	—
n	Load-introduction factorVDI 2230 position of the load introduction in the clamped parts (0 … 1).SI — · Imperial —Bolted Joints	—	—
η	EfficiencyOutput power divided by input power (mesh, drive, pump, fan, screw, motor).SI — (%) · Imperial — (%)Motor Sizing & VFD Hydraulic Cylinders Slewing Rings Ball Screws Power Screw Cylindrical Gears Bevel & Worm Gears Roller Chain Drive Planetary Gears Flywheel & Inertia Conveyor Belt Mechanism Actuator Sizing Pump & Fan Selection Compressor Analysis Hydraulic Accumulator Wire Rope & Lifting Weld Design Dust Collection Pneumatics	— (%)	— (%)
E	EnergyStored, dissipated or ignition energy (E_heat, MIE).SI J / kJ · Imperial ft·lbf / BTUHydraulic Accumulator Clutches & Brakes Dust Collection Flywheel & Inertia	J / kJ	ft·lbf / BTU

Life & fatigue

Symbol	Name, meaning and tools	SI	Imperial
C (C_a)	Basic dynamic load ratingLoad a bearing / guide / screw carries for 10⁶ revolutions (or 50 / 100 km) at 90 % reliability.SI kN · Imperial lbfBearing Analysis Linear Guide Life Slewing Rings Ball Screws	kN	lbf
C₀	Basic static load ratingStatic load producing the permissible permanent deformation (ISO 76).SI kN · Imperial lbfBearing Analysis Linear Guide Life Slewing Rings Ball Screws	kN	lbf
L10	Basic rating lifeLife reached by 90 % of identical bearings, in 10⁶ revolutions (ISO 281).SI 10⁶ rev · Imperial 10⁶ revBearing Analysis Slewing Rings Ball Screws Linear Guide Life Shaft Analysis Journal Bearings	10⁶ rev	10⁶ rev
L10h	Rating life in hoursL10 converted to operating hours at the stated speed.SI h · Imperial hBearing Analysis Slewing Rings Ball Screws Shaft Analysis	h	h
p	Life exponentExponent of the load-life law L = (C/P)^p — 3 for ball, 10/3 for roller contact.SI — · Imperial —Linear Guide Life Bearing Analysis Ball Screws	—	—
X, Y, e	Load factors (ISO 281)Radial and axial load factors of P = X·Fr + Y·Fa; e is the Fa/Fr switch point.SI — · Imperial —Bearing Analysis	—	—
N (N_f)	Number of cyclesLoad cycles applied, or the cycles to failure N_f at a stress level.SI cycles · Imperial cyclesFatigue Analysis Cylindrical Gears Hydraulic Accumulator Wire Rope & Lifting Pipe Stress Pressure Vessels Shaft Analysis Weld Design	cycles	cycles
k (m)	S-N (Wöhler) slope exponentSlope of the S-N curve, N·Δσ^m = constant (m = 3 / 5 for welds, EN 1993-1-9).SI — · Imperial —Weld Design Fatigue Analysis	—	—
n_T, C_T	Taylor tool-life exponent / constantTaylor's law V_c·T^n = C — the exponent n_T and the constant C_T.SI — / m/min · Imperial — / ft/minMachining Parameters	— / m/min	— / ft/min
T	Tool lifeMinutes of cutting until the wear criterion.SI min · Imperial minMachining Parameters	min	min

Fluids & pressure

Symbol	Name, meaning and tools	SI	Imperial
p (P)	PressureFluid or gas pressure (gauge or absolute — the label says which). Several fluid tools print it as capital P.SI bar / kPa / MPa · Imperial psiHydraulic Cylinders Pressure Vessels Pump & Fan Selection Compressor Analysis Pipe Flow Hydraulic Accumulator Pipe Stress O-Ring & Seals Pneumatics Journal Bearings	bar / kPa / MPa	psi
Δp	Pressure dropPressure loss across a pipe, filter, valve or exchanger.SI bar / kPa · Imperial psiPipe & Flange Reference Roller Chain Drive Pipe Flow Hydraulic Accumulator Dust Collection Pneumatics Heat Exchanger Pump & Fan Selection	bar / kPa	psi
Q	Flow rateVolumetric (or mass, Q_m) flow.SI m³/h / L/min / m³/s · Imperial gpm / cfmHydraulic Cylinders Pipe & Flange Reference Journal Bearings Conveyor Belt Pump & Fan Selection Compressor Analysis Pipe Flow Hydraulic Accumulator Dust Collection Pneumatics	m³/h / L/min / m³/s	gpm / cfm
μ (η)	Dynamic viscosityShear stress per shear rate of a fluid.SI Pa·s (mPa·s = cP) · Imperial cP / lb·s/ft²Pipe & Flange Reference Journal Bearings Pump & Fan Selection Pipe Flow Dust Collection	Pa·s (mPa·s = cP)	cP / lb·s/ft²
ν	Kinematic viscosityDynamic viscosity divided by density (ISO VG grades at 40 °C).SI mm²/s (cSt) · Imperial cSt / SUSJournal Bearings Cylindrical Gears Roller Chain Drive Bearing Analysis Pump & Fan Selection	mm²/s (cSt)	cSt / SUS
Re	Reynolds numberInertial over viscous forces, Re = ρ·v·d / μ; laminar below ≈ 2300 in pipes.SI — · Imperial —Pipe Flow Heat Exchanger Pump & Fan Selection Dust Collection	—	—
f (λ)	Darcy friction factorPipe friction factor of Darcy-Weisbach, Δp = f·(L/d)·ρv²/2.SI — · Imperial —Pipe Flow Hydraulic Accumulator Pump & Fan Selection	—	—
f	Friction coefficient / factorArtificial friction coefficient of a conveyor (ISO 5048), Petroff friction coefficient of a journal, seal friction of a cylinder.SI — · Imperial —Conveyor Belt Journal Bearings Pneumatics	—	—
NPSH	Net positive suction headAbsolute suction head above vapour pressure — available (NPSHa) vs required (NPSHr).SI m · Imperial ftPump & Fan Selection Pipe Flow	m	ft
H (h)	HeadPressure expressed as a height of liquid column (H pump head, h_f friction loss).SI m · Imperial ftPump & Fan Selection Pipe Flow	m	ft
n (κ)	Polytropic / isentropic exponentExponent of p·Vⁿ = const (κ for the isentropic case).SI — · Imperial —Compressor Analysis Hydraulic Accumulator	—	—
V	VolumeGas, receiver or vessel volume (V₀ precharge volume).SI L / m³ · Imperial in³ / ft³ / galHydraulic Accumulator Pneumatics Compressor Analysis Dust Collection	L / m³	in³ / ft³ / gal
R	Specific gas constantR = R_universal / M (air 287 J/(kg·K)).SI J/(kg·K) · Imperial ft·lbf/(lb·°R)Compressor Analysis	J/(kg·K)	ft·lbf/(lb·°R)
K	Bulk modulusFluid stiffness; with E and the wall it sets the pressure-wave speed a.SI GPa / MPa · Imperial psiPipe Flow	GPa / MPa	psi
ε	Eccentricity ratio (journal bearing)Journal eccentricity over radial clearance (0 … 1).SI — · Imperial —Journal Bearings	—	—
S	Sommerfeld numberDimensionless journal-bearing characteristic.SI — · Imperial —Journal Bearings	—	—
h_min	Minimum film thicknessSmallest oil-film gap in a journal bearing.SI µm · Imperial in (µin)Journal Bearings	µm	in (µin)

Heat & temperature

Symbol	Name, meaning and tools	SI	Imperial
T (ϑ)	TemperatureAbsolute or Celsius temperature (T_op, T_amb, T₁ inlet …).SI °C / K · Imperial °F / °RPressure Vessels Clutches & Brakes Ball Screws Press Fits Roller Chain Drive Compressor Analysis Hydraulic Accumulator Pipe Stress Pneumatics Heat Exchanger Journal Bearings Thermal Analysis	°C / K	°F / °R
ΔT	Temperature differenceTemperature rise or difference (thermal growth, coolant rise, LMTD).SI K (°C difference) · Imperial °F differenceMotor Sizing & VFD Bolted Joints Pressure Vessels Clutches & Brakes Ball Screws Press Fits Journal Bearings Bevel & Worm Gears Compressor Analysis Thermal Analysis Pipe Stress Heat Exchanger	K (°C difference)	°F difference
Q	Heat flow / dutyHeat transferred per unit time.SI W / kW · Imperial BTU/hHeat Exchanger Roller Chain Drive O-Ring & Seals Thermal Analysis Journal Bearings Clutches & Brakes	W / kW	BTU/h
q	Heat fluxHeat flow per unit area.SI W/m² · Imperial BTU/(h·ft²)Clutches & Brakes	W/m²	BTU/(h·ft²)
U	Overall heat-transfer coefficientHeat flow per area per kelvin through the whole wall, fouling included.SI W/(m²·K) · Imperial BTU/(h·ft²·°F)Heat Exchanger	W/(m²·K)	BTU/(h·ft²·°F)
h	Film heat-transfer coefficientConvective coefficient on one side of a wall.SI W/(m²·K) · Imperial BTU/(h·ft²·°F)Heat Exchanger	W/(m²·K)	BTU/(h·ft²·°F)
ε	Heat-exchanger effectivenessActual over maximum possible heat duty (ε-NTU method).SI — · Imperial —Heat Exchanger	—	—
c_p	Specific heatHeat per mass per kelvin at constant pressure.SI J/(kg·K) · Imperial BTU/(lb·°F)Heat Exchanger Compressor Analysis Thermal Analysis Clutches & Brakes	J/(kg·K)	BTU/(lb·°F)

Electrical

Symbol	Name, meaning and tools	SI	Imperial
I	Electric currentMotor line current (I_r rated, I_start) or welding current.SI A · Imperial AMotor Sizing & VFD Weld Design	A	A
U (V)	VoltageLine or arc voltage.SI V · Imperial VWeld Design Motor Sizing & VFD	V	V
cos φ	Power factorActive over apparent power of an AC motor.SI — · Imperial —Motor Sizing & VFD	—	—
C	CapacitanceCapacitance of an isolated conductor (electrostatic ignition check).SI pF · Imperial pFDust Collection	pF	pF
Q_ch	Charge generation rateElectrostatic charge generated per second.SI nC/s · Imperial nC/sDust Collection	nC/s	nC/s

Symbols follow the standard each tool implements (ISO 6336, VDI 2230, ISO 281, Eurocode 3, ASME …). See also the standards reference and the unit converter.