12 categories · 100 engineering units · factors from the SI defining constants
All conversions pivot through SI base units · temperature pivots through °C · calorie and BTU are International Table (IT) · results shown to 6 significant figures
Unit Converter — 12 Engineering Categories, 100 Units (SI / Imperial)
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The MechanixCalc Unit Converter handles the full set of physical quantities that arise in mechanical engineering practice: length, area, volume, mass, force, pressure, torque, power, energy, linear velocity, angular velocity and temperature — 12 categories covering 100 units. Enter a value, choose your source and target units, and the result appears immediately. The all-equivalents broadcast panel simultaneously shows the entered quantity in every unit of the active category, so you can scan the entire range without extra clicks.
Conversion factors follow the SI definitions in the BIPM SI Brochure (9th edition) and the NIST SP 811 guide for US customary units. Each factor is computed in code from the exact defining constants — the international inch (0.0254 m), pound (0.45359237 kg) and standard gravity (9.80665 m/s²) — rather than stored as a rounded decimal, so a value such as 1 barrel = 42 US gallons comes out exact rather than as 41.9999. Temperature uses the exact affine scale relations (°C as pivot, exact offsets for K, °F and °R). The tool also includes the complete 24-prefix SI prefix reference (quetta 10³⁰ → quecto 10⁻³⁰, including the four prefixes added by the 27th CGPM in 2022) and a conversion-history log — making it a daily-use companion for engineers working across metric and imperial standards.
What this calculator does
- 12 engineering unit categories: length, area, volume, mass, force, pressure, torque, power, energy, linear velocity, angular velocity and temperature
- 100 engineering units with conversion factors computed from the exact SI and international yard-and-pound defining constants (BIPM / NIST SP 811)
- All-equivalents broadcast panel — shows the entered value in every unit of the active category simultaneously
- Common-conversions quick-reference card per category (e.g. MPa ↔ psi, kW ↔ hp, rpm ↔ rad/s)
- Temperature: correct affine (offset + scale) conversions for °C, K, °F and °R using the exact scale relations
- SI prefix reference table — all 24 prefixes quetta (10³⁰) to quecto (10⁻³⁰) with symbols and common examples, including the four adopted by the 27th CGPM in 2022
- Conversion history log with copy-to-clipboard for the last 15 conversions
Method & formulas
SI-pivot conversion method
Every non-temperature unit carries a single multiplier that converts it to the SI base unit for its quantity (e.g. metre for length, pascal for pressure, newton for force). To convert between any two units, the tool multiplies the input value by the source unit's toSI factor and divides by the target unit's toSI factor. Pivoting through SI means any pair of units in a category converts consistently from one set of constants, with no chained unit-to-unit table to accumulate error. Dividing by the target factor — rather than multiplying by a stored reciprocal — keeps the operation to a single rounding, and converting a unit to itself short-circuits to the input value exactly.
y = x · toSI_A / toSI_Bwhere x = input value in unit A; toSI_A = factor converting unit A to the SI base unit; toSI_B = factor converting unit B to the SI base unit; y = result in unit B
Temperature: affine (offset + scale) conversion
Temperature cannot be converted by a simple multiplier because its scales have different zero points. The tool uses Celsius (°C) as the intermediate pivot. Any input temperature is first converted to °C, then from °C to the target scale, using the exact scale relations: K = °C + 273.15 (the SI definition); °F = °C × 9/5 + 32; °R = (°C + 273.15) × 9/5 (both per NIST SP 811 §B.8). Converting a scale to itself short-circuits, and a residue smaller than 1e-9 is snapped to zero so that an input of exactly absolute zero reads 0 K rather than a floating-point remainder.
T_K = T_C + 273.15where T_C = temperature in Celsius; T_K = temperature in Kelvin (SI definition, exact)
T_F = T_C × (9/5) + 32where T_C = temperature in Celsius; T_F = temperature in Fahrenheit
Angular velocity conversion
Angular velocity is the quantity most frequently confused in rotating-machinery engineering. The SI unit is radian per second (rad/s), but speeds are reported in revolutions per minute (rpm) on motor nameplates and datasheets. The exact conversion is ω [rad/s] = n [rpm] × 2π / 60. The tool stores this factor directly (toSI = 2π/60 ≈ 0.104720 rad·s⁻¹·rpm⁻¹), so no intermediate rounding is introduced.
ω = n · 2π / 60where ω = angular velocity (rad/s); n = rotational speed (rpm); 2π = one full revolution in radians; 60 = seconds per minute
Worked example
Convert a motor speed of 1500 rpm to radians per second — a common step when computing centripetal acceleration or shaft power from torque in SI units.
Given
- Motor speed n1500 rpm
Result
- Angular velocity ω157.08 rad/s
- Identify the conversion factor: 1 rpm = 2π / 60 rad/s ≈ 0.104720 rad/s.
- Multiply: ω = 1500 × 0.104720 = 157.08 rad/s.
- Cross-check via the definition: 1500 rpm means 1500 / 60 = 25 revolutions per second. One revolution = 2π radians, so ω = 25 × 2π = 25 × 6.28318 = 157.08 rad/s. ✓
This is an illustrative single-step example. The converter handles all 12 categories identically — enter your value, select units, read the result.
Frequently asked questions
Which standard does the Unit Converter use?
Conversion factors follow the BIPM SI Brochure (9th edition, 2019) for SI-defined units and NIST SP 811 for US customary and other legacy units. Temperature conversions use the exact affine scale relations (°C as pivot; K = °C + 273.15 by the SI definition, °F and °R per NIST SP 811 §B.8). There is no single governing standard for a general-purpose converter — these are the authoritative international references for the values used.
Is the Unit Converter free?
Yes — the Unit Converter is permanently free with no sign-up required. You can also use it during a free 30-minute preview session that unlocks every calculator on the platform. A free 14-day account trial (no credit card) gives access to all tools; saved calculations and branded PDF reports are included in the free 14-day trial and in every paid plan.
How accurate are the conversion factors?
Every multiplicative factor is computed in code from the exact defining constants — the international inch (0.0254 m), yard (0.9144 m) and pound (0.45359237 kg), standard gravity (9.80665 m/s²), the US gallon (231 in³) and the International Table BTU and calorie — rather than typed in as a rounded decimal. Each factor therefore carries the full precision of an IEEE-754 double (15–16 significant figures), and quantities that are exact by definition come out exact: 1 barrel is 42 US gallons, 1 ounce-force inch is 0.0625 pound-force inch, 1 slug is 32.174 lb. Results are displayed to 6 significant figures, which is appropriate for engineering work. Temperature conversions use the exact offsets (273.15 K exactly, 32 °F exactly).
What engineering categories are covered?
The converter covers 12 categories: length (11 units including μm and nautical miles), area, volume (including Oil Barrel and UK/US gallons), mass (including slug and grain), force (including kgf, lbf and dyne), pressure (including bar, atm, psi, ksi and N/mm²), torque (including lbf·ft, lbf·in and kgf·m), power (metric and mechanical horsepower, BTU/h), energy (kWh, BTU, kcal), linear velocity (including m/s, km/h, mph and knot), angular velocity (rpm, rad/s, deg/s, rev/s) and temperature (°C, K, °F, °R). Where a unit name has more than one definition in engineering use, the variant is named on the unit itself — the two horsepowers are listed separately as hp (M) and hp (mech), and the calorie and BTU are the International Table values. New categories may be added in future updates.
Why does temperature conversion work differently from the other categories?
All other physical quantities have ratio scales — zero means 'none of the quantity' and a pure multiplication converts between units. Temperature scales (except Kelvin) are affine: they have different zero points, so conversion requires both a scale factor and an offset. The tool uses °C as an intermediate pivot, applying the exact scale relation for each target, so it correctly handles cases like 0 °C → 32 °F or 0 °C → 273.15 K.
Related calculators
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- Shaft Analysis CalculatorShaft stress and deflection are computed in SI; convert results to imperial with the Unit Converter.
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- Comparison ModeRun two calculator configurations side by side — useful for comparing designs in metric vs. imperial unit sets.
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