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
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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. ⚠️ SCOPE: the MechanixCalc cylindrical gear calculator does NOT compute an AGMA rating — it does not evaluate the contact stress number sc or the bending stress number st shown below, and reports no AGMA safety factor. It rates gears to ISO 6336 (σH, σF, SH, SF) and borrows exactly one factor from the AGMA method: the face-load distribution factor Km (KHβ in ISO notation), via the Shigley §14-11 closed form for a commercial enclosed unit. That single factor is why this hub lists the tool at all. The equations below are AGMA 2101's own, given so you can see what the standard specifies and how its notation maps to the ISO chain the tool actually runs — not as a description of what the calculator outputs.
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 stress-cycle life factors for fatigue rating under variable load. NOTE: of everything in this scope list, the MechanixCalc gear calculator implements only the load-distribution factor Km — the rest is what AGMA 2101 itself specifies
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. ⚠️ Reference only — the MechanixCalc gear calculator does not evaluate sc or SH; it computes the ISO 6336-2 contact stress σH and safety factor SH instead.
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. ⚠️ Reference only — the MechanixCalc gear calculator does not evaluate st or SF here; it computes the ISO 6336-3 root stress σF and safety factor SF instead.
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). This is the single AGMA quantity the MechanixCalc gear engine computes, as its K_Hβ; the Cma polynomial it uses is the commercial-enclosed-unit fit in US customary units (face width in inches), which is numerically the same factor either edition states. Supply your own ISO 6336-1 Method B/C value to override it.
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 runs the ISO 6336 analysis and borrows only the AGMA Km factor — it does not produce a second, AGMA-rated answer to compare against.
How much of AGMA 2101 does MechanixCalc implement?
One factor, not the rating. The cylindrical gear calculator implements the AGMA load-distribution factor Km using the Shigley §14-11 (10th edition) closed forms for Cpf, Cpm, Cma and Ce, applied as its K_Hβ. It does NOT compute the AGMA contact stress number sc, the bending stress number st, or any AGMA safety factor — the rating it performs and reports is ISO 6336 (σH, σF, SH, SF), and that is what appears in the PDF engineering report. If you need a full AGMA 2101 rating for a North American submittal, this tool will not produce one.
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