This Gear Tooth Design spreadsheet from 3D-LABS follows ISO standards and gives instant, checkable results for practising engineers — no manual derivation required.
This spreadsheet calculates gear tooth stress, geometry, and dynamic factors for spur and helical gears per AGMA 2001-D04 (Fundamental Rating Factors for Involute Spur and Helical Gear Teeth) and ISO 6336:2019 Parts 1–6. It determines the required face width, module, and number of teeth for a given power/speed input and target safety factor against bending fatigue and contact (pitting) fatigue — the two primary gear failure modes.
What standard does this calculation follow?
AGMA 2001-D04 (Fundamental Rating Factors for Involute Spur and Helical Gear Teeth), ISO 6336-2:2019 (Calculation of load capacity — Surface durability / pitting), ISO 6336-3:2019 (Calculation of tooth root bending strength), DIN 3990:1987 (German equivalent), and AGMA 908-B89 (Geometry factors for determining the pitting resistance and bending strength of spur, helical, and herringbone gear teeth).
What formula is used?
AGMA bending stress: σF = Wt/(FmtY) × Ko × Kv × Ks × KH × KB / Ym ≤ σFP = St × YN/(SF × KT × KR), where Wt = tangential load (N), F = face width (mm), mt = transverse metric module, Y = Lewis form factor, Ko = overload factor, Kv = dynamic factor. AGMA contact stress: σH = ZE √(Wt × Ko × Kv × Ks / (d1 F ZR) × KH) ≤ σHP = Sc × ZN ZW/(SH² KT KR).
Frequently Asked Questions
What is the AGMA gear bending stress formula (AGMA 2001)?
AGMA 2001-D04 bending stress: σF = Wt/(FmtY) × Ko × Kv × Ks × KH/Ym (MPa), where Wt = tangential tooth load (N), F = face width (mm), mt = transverse metric module (mm), Y = geometry factor for bending (from AGMA 908-B89 charts). Allowable: σFP = St × YN/(SF × KT × KR), where St = AGMA bending strength (MPa), YN = stress cycle factor, SF = safety factor ≥ 1.20.
What is the difference between AGMA 2001 and ISO 6336 gear design?
Both assess bending and pitting fatigue but use different factor structures. AGMA uses empirical stress cycle factors (YN, ZN) from S-N curves; ISO 6336 uses explicit fatigue life equations from Part 6. AGMA factors Ko, Kv, Ks, KH roughly correspond to ISO’s KA (application), Kv (dynamic), KB (helix angle), KHβ (load distribution). For export projects, ISO 6336 is required; AGMA is standard in North America.
What are typical AGMA gear material allowable stresses for through-hardened steel?
AGMA 2001 Table 3: Grade 1 through-hardened steel (180–400 HB): bending St = 0.533 × HB + 88.3 MPa (max 310 MPa), contact Sc = 2.22 × HB + 200 MPa (max 1,380 MPa). For HB = 300: St = 248 MPa, Sc = 866 MPa. Carburised and case-hardened steel (Grade 3, 55–64 HRC): St = 380 MPa, Sc = 1,550 MPa.
What’s Included
An instant Excel download with the complete formula set, a worked numerical example, and reference to the governing standard — ready to adapt to your own project inputs.
