AGMA 2101 Gear Rating — Metric Spur & Helical Gear Calculator
AGMA 2101 — Fundamental Rating Factors and Calculation Methods for Involute Spur and Helical Gear Teeth — Metric Edition
AGMA 2101 is the metric edition of the American Gear Manufacturers Association's fundamental gear-rating standard for involute spur and helical gears. It defines how to calculate the two governing failure modes — surface durability (pitting) from the contact stress number sc and tooth-root bending strength from the bending stress number st — and the safety factors SH and SF against each. The standard draws on the same physical principles as ISO 6336 but uses AGMA factor notation and allows SI units throughout, making it the preferred reference in North American projects that demand metric outputs.
AGMA 2101-D04 is the most widely adopted revision and is the edition implemented in the MechanixCalc cylindrical gear calculator. The tool applies the AGMA face-load distribution factor Km (corresponding to KHβ in ISO 6336 notation) using the Shigley §14-11 formulae derived directly from AGMA 2101-D04, and reports the results alongside the governing ISO 6336 contact and bending stresses so engineers can cross-check both methods in a single pass.
Calculators that implement AGMA 2101
What AGMA 2101 covers
- Surface durability (pitting) — contact stress number sc and allowable contact stress number sac with safety factor SH (Part 2 method)
- Tooth-root bending strength — bending stress number st and allowable bending stress number sat with safety factor SF
- Overload factor Ko, dynamic factor Kv, size factor Ks, load-distribution factor Km and rim thickness factor KB
- Geometry factors for bending strength (J) and pitting resistance (I) for spur and helical involute gears
- Material grade classification and allowable stress numbers for through-hardened, carburized and nitrided steels
- Reliability factor KR and life factor KL / ZN for fatigue rating under variable load
Governing formulas
sc = Cp · √( Ft · Ko · Kv · Ks · Km / (d_w1 · b · I) ) ; SH = sac · ZN · CH / (sc · KT · KR)where Cp = elastic coefficient (√MPa); Ft = tangential load (N); Ko = overload factor; Kv = dynamic factor; Ks = size factor; Km = load-distribution factor (= 1 + Cmc·(Cpf·Cpm + Cma·Ce)); d_w1 = operating pitch diameter of pinion (mm); b = face width (mm); I = geometry factor for pitting resistance; sac = allowable contact stress number (MPa); ZN = stress-cycle life factor; CH = hardness ratio factor; KT = temperature factor; KR = reliability factor; SH = safety factor for pitting
st = Ft · Ko · Kv · Ks · Km · KB / (b · mt · J) ; SF = sat · YN / (st · KT · KR)where mt = transverse metric module (mm); J = geometry factor for bending strength; KB = rim thickness factor; sat = allowable bending stress number (MPa); YN = stress-cycle life factor for bending; SF = safety factor for tooth-root bending; other factors as above
Km = 1 + Cmc · (Cpf · Cpm + Cma · Ce)where Cmc = lead correction factor (1.0 uncrowned, 0.8 crowned); Cpf = pinion proportion factor from face-width-to-diameter ratio F/d; Cpm = pinion proportion modifier (1.0 for symmetric mounting); Cma = mesh alignment factor from commercial enclosed unit curve; Ce = mesh alignment correction factor (1.0 unadjusted at assembly)
Frequently asked questions
What is AGMA 2101 used for?
AGMA 2101 is used to rate the load capacity of involute spur and helical gears in metric units. It calculates the contact stress number sc (for pitting / surface durability) and the bending stress number st (for tooth-root fatigue), then derives safety factors SH and SF against the material's allowable stress numbers. It is the standard gear-rating reference for North American projects that use SI units, and the one most commercial gear software in the US implements alongside or instead of ISO 6336.
How does AGMA 2101 differ from AGMA 2001?
AGMA 2001 uses US customary units (inch, pound, rpm) throughout. AGMA 2101 is the metric companion — the same fundamental rating method and factor structure, but with module (mm) instead of diametral pitch, face width in mm, and stress in MPa. The two are otherwise methodologically identical: the load-distribution factor Km, the geometry factors I and J, and the material allowable stress numbers are defined the same way in both editions.
How does AGMA 2101 relate to ISO 6336?
Both standards address the same two failure modes — pitting (surface durability) and tooth-root bending fatigue — using Hertz contact mechanics and stress-life fatigue. They give broadly comparable safety factors for the same gear pair, but use different factor names and definitions. ISO 6336 is the international reference, while AGMA 2101 is the North American metric standard. Many projects run both methods and use the more conservative result; MechanixCalc reports the AGMA Km factor alongside the full ISO 6336 analysis so engineers can compare directly.
Which version of AGMA 2101 does MechanixCalc implement?
The cylindrical gear calculator implements the AGMA 2101-D04 load-distribution factor Km using the Shigley §14-11 (10th edition) formulae for Cpf, Cpm, Cma and Ce — the industry-standard textbook derivation from the AGMA 2101-D04 closed-form equations. The full ISO 6336 contact and bending stress chain is also computed in parallel. The governing standard and all intermediate factors are reported in the generated PDF engineering report.
Is the AGMA 2101 gear calculator free?
You can use it during a free 30-minute preview with no sign-up, and a free 14-day account trial unlocks every calculator with no credit card required. The branded PDF engineering report with the full calculation trail and saved calculations are part of a paid plan.
Related standards
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