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ISO 10300 Bevel Gear Rating — Contact & Bending Stress Calculator

ISO 10300 — Calculation of load capacity of bevel gears

ISO 10300 is the international standard for the load-carrying capacity of bevel gears — straight, spiral and hypoid. It rates the two critical failure modes: surface durability (pitting) via the Hertzian contact stress σH on the virtual cylindrical gear at the mean section, and tooth-root bending strength via the bending stress σF. The method is built on the Tregold back-cone construction, which maps the three-dimensional bevel tooth onto an equivalent spur gear (the virtual gear) so that the well-validated ISO 6336-2/3 cylindrical-gear stress formulae can be applied directly. The empirical bevel factor ZK = 0.85 (Part 2, Method B) reconciles the virtual-gear model with bevel test evidence.

ISO 10300 is cited in gear-box data books, PE sign-off checklists and the purchase specifications of industrial OEMs wherever bevel drives are specified. MechanixCalc runs the ISO 10300-2:2014 Method B contact stress check and the ISO 6336-3 root-bending check on the virtual cylindrical gear, with AGMA 2003-B97 load factors, in your browser — showing every factor and producing a shareable PDF engineering report you can attach to a design package.

Calculators that implement ISO 10300

What ISO 10300 covers

  • Surface durability (pitting) — contact stress σH on the virtual cylindrical gear and permissible stress σHP (ISO 10300-2, Method B)
  • Tooth-root bending strength — bending stress σF at the virtual tooth number and permissible stress σFP (ISO 10300-3 / ISO 6336-3)
  • Load factors: application KA, dynamic Kv, load-distribution Km (AGMA 2003-B97, applied alongside ISO 10300-2 nominal stress)
  • Virtual gear geometry via the Tregold back-cone construction: virtual diameters d_v = d_m / cos δ, virtual tooth numbers z_v = z / cos δ
  • Bevel-specific influence factors: zone ZH (straight-bevel form), elasticity ZE, bevel factor ZK = 0.85
  • Tooth forces at the mean pitch circle: tangential Ft, radial Fr and axial Fa components for shaft and bearing sizing

Parts of the standard

  • ISO 10300-1Introduction and general influence factors (virtual gear, load factors, material data)
  • ISO 10300-2Calculation of surface durability (pitting) — Method B nominal contact stress on the virtual cylindrical gear
  • ISO 10300-3Calculation of tooth root bending strength on the virtual cylindrical gear

Governing formulas

ISO 10300-2 nominal contact stress (Method B, virtual cylindrical gear)
σ_H = Z_H · Z_E · Z_K · √( F_t · K_A · K_v · K_m · (u_v + 1) / (b_eff · d_v1 · u_v) ) ; S_H = σ_HP / σ_H

where Z_H = zone factor = √(2 / (cos²α_n · tan α_n)) — 2.4946 at α_n = 20° for a straight bevel; Z_E = 189.8 √MPa — elasticity factor for a steel/steel pair (ISO 6336-2); Z_K = 0.85 — ISO 10300-2:2014 bevel factor (empirical); F_t = tangential force at mean pitch circle (N); K_A = overload factor; K_v = dynamic factor; K_m = load-distribution factor (AGMA 2003-B97); b_eff = effective face width ≤ R/3 (mm); d_v1 = virtual pinion pitch diameter = d_m1 / cos δ_1 (mm); u_v = virtual gear ratio = z_v2 / z_v1; σ_HP = permissible contact stress (MPa); S_H = pitting safety factor

Tooth-root bending stress on virtual gear (ISO 10300-3 / ISO 6336-3)
σ_F = (F_t · K_A · K_v · K_m · Y_Fa · Y_Sa) / (b_eff · m_n) ; S_F = σ_FP / σ_F

where Y_Fa = tooth-form factor at virtual pinion tooth number z_v1 = z_1 / cos δ_1 (ISO 6336-3, x = 0 basic rack, α_n = 20°); Y_Sa = stress-correction factor at z_v1 (ISO 6336-3); m_n = normal module at mean section (mm); σ_FP = permissible root bending stress (MPa); S_F = bending safety factor; remaining symbols as above

Virtual gear geometry (Tregold back-cone construction)
d_v = d_m / cos δ ; z_v = z / cos δ ; u_v = z_v2 / z_v1

where d_m = mean pitch diameter (mm); δ = pitch cone angle of pinion (δ_1) or gear (δ_2) — for shaft angle Σ: tan δ_1 = sin Σ / (u + cos Σ), δ_2 = Σ − δ_1; z = actual tooth number; d_v, z_v = virtual cylindrical gear diameter and tooth number at the mean section; u_v = virtual gear ratio (differs from actual ratio u = z_2 / z_1 when δ_1 ≠ 45°)

Frequently asked questions

What is ISO 10300 used for?

ISO 10300 calculates the load capacity of bevel gears — specifically the safety factor against surface fatigue (pitting, σH) and against tooth-root breakage (bending, σF). It applies to straight, spiral and hypoid bevel gears and is the international reference method cited in gear-box specifications, PE sign-off packages and transmission standards worldwide.

What is the Tregold construction and why does ISO 10300 use it?

The Tregold (back-cone) construction replaces the three-dimensional bevel tooth with an equivalent spur gear — the virtual cylindrical gear — at the mean section: the virtual diameter d_v = d_m / cos δ and virtual tooth number z_v = z / cos δ, where δ is the pitch cone angle. This lets ISO 10300-2 apply the proven ISO 6336-2 Hertzian line-contact formula to bevel gears with only one empirical correction: the bevel factor ZK = 0.85 that aligns the model with bevel test data.

Does MechanixCalc implement the full ISO 10300 method?

The bevel calculator implements the ISO 10300-2:2014 Method B nominal contact stress on the virtual cylindrical gear — including the zone factor ZH, elasticity factor ZE, bevel factor ZK, and AGMA 2003-B97 load factors KA, Kv, Km — and ISO 6336-3 root stress at the virtual tooth number. Mid-zone load-sharing factors (ZLS, ZM-B) are conservatively set to 1.0 because no closed-form expression exists for them; the result is slightly conservative at the top end. Every factor and the governing standard reference are shown in the generated PDF report.

How does ISO 10300 relate to ISO 6336?

ISO 10300 is the bevel-gear counterpart to ISO 6336 (spur and helical gears). They share the same stress framework — ISO 6336-2 contact stress and ISO 6336-3 root stress — applied to the virtual (back-cone) cylindrical gear. The key bevel-specific addition in ISO 10300-2 is the empirical bevel factor ZK = 0.85 and the virtual-gear geometry transformation. If you already use ISO 6336 for cylindrical gears, ISO 10300 follows naturally.

Is the ISO 10300 bevel gear calculator free?

You can run calculations during a free 30-minute preview with no sign-up required, and a free 14-day account trial unlocks every calculator with no credit card needed. The branded PDF engineering report and saved calculation history are part of a paid plan.

Related standards

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