Gear tooth-root bending strength — ISO 6336-1/-3

Maximum tangential force and drive torque for a spur/helical gear pair from permissible tooth-root bending stress, per ISO 6336-1/-3.

✓ validated against legacyoriginal: /calculators/e2_6b.htm

Gear tooth-root bending strength — ISO 6336-1/-3 — original diagram from /calculators/e2_6b.htm

Number of teeth, pinion, z₁ (≥12)Number of teeth, wheel, z₂ (≥12)Profile shift coefficient, pinion, x₁ (0…0.5)Profile shift coefficient, wheel, x₂ (0…0.5)Normal module, mₙmmPressure angle, αdegFace width, bmmNominal root fatigue strength, σ_F,limMPaRoot-stress factor, σ_FP/σ_F,lim (from ks.htm)Load factor, σ_F/σ_F0 = K_A·K_v·K_Fα·K_Fβ (from kf.htm)

Maximum tangential force, pinion, F_t,max,122.868696301784443 kN

Maximum tangential force, wheel, F_t,max,222.365968530079275 kN

Maximum drive torque, pinion, T_max,11224.4448750804156 Nm

Working pressure angle, α_w22.9 deg

Permissible root stress, σ_FP390 MPa

Contact-ratio factor, Y_ε0.7566905950647792

Transverse contact ratio, ε_α1.4801932526576977

Stress-correction factor, pinion, Y_Sa11.8619999999999999

Stress-correction factor, wheel, Y_Sa22.0654559999999997

Tooth-form factor, pinion, Y_Fa12.33

Tooth-form factor, wheel, Y_Fa22.147698666666667

Centre distance, a307 mm

Working pitch diameter, pinion, d_w1107.08479914396102 mm

Working pitch diameter, wheel, d_w2506.8680492814155 mm

Pitch diameter, pinion, d₁105 mm

Pitch diameter, wheel, d₂497 mm

Profile shift coefficient, pinion (as used), x₁0.5

Profile shift coefficient, wheel (as used), x₂0.418

Number of teeth, pinion (as used), z₁15

Number of teeth, wheel (as used), z₂71

If z₁ or z₂ is entered below 12, or x₁ or x₂ outside 0–0.5, the legacy source silently discards BOTH tooth-count (or both profile-shift) inputs and substitutes its own defaults (z₁=15, z₂=71, or x₁/x₂=0) rather than rejecting or clamping just the offending value — preserved exactly. The "(as used)" z₁/z₂/x₁/x₂ outputs always show the values the calculation actually ran with, so check those against what you entered if you supplied a value in the excluded range.

Method & references

ISO 6336-1/-3: Calculation of load capacity of spur and helical gears — tooth-root bending strength.

Gear normal module (m) preferred number series

The computation is a literal port of the original client-side JavaScript from /calculators/e2_6b.htm. Results are verified equal to the original by an automated golden-master test. No formula has been re-derived or “improved”.