Shaft Torque Calculator

Compute maximum shear stress (τ_max) using the torsion formula, determine power transmission capacity at given RPM, and evaluate safety factor against material yield strength in shear.

Typical: 0.577 × tensile yield
⚙️ Motor shaft: d=25mm, T=250Nm, 3000 RPM, τ_y=180MPa
? Driveshaft: d=45mm, T=1200Nm, 800 RPM, τ_y=220MPa
? Light load: d=20mm, T=80Nm, 1000 RPM, τ_y=150MPa
⚡ High speed: d=18mm, T=45Nm, 10000 RPM, τ_y=200MPa
All calculations performed locally in your browser. No data transmitted. This tool is intended for educational, preliminary design, and concept validation purposes. For final critical engineering designs, verification with professional finite element analysis (FEA) software and consultation with a licensed professional engineer is recommended.

Torsion of Circular Shafts: Theory & Application

For solid circular shafts, the elastic torsion formula relates applied torque to shear stress: τ = T·r / J, where τ is the shear stress at radius r, T is torque, and J is the polar moment of inertia. Maximum shear stress occurs at the outer surface (r = d/2). This calculator uses J = π·d⁴ / 32 for solid shafts, then computes τmax = 16·T / (π·d³) (in consistent units).

τmax = 16·T / (π·d³)   (N/mm² → MPa, T in N·mm, d in mm)

Power P (kW) = 2π·N·T / 60,000   (T in N·m, N in RPM)

Safety Factor SF = τyield / (τmax × Design Factor)

Angle of twist per meter: θ = (T·L) / (J·G), with G = 80 GPa (steel)

Assumptions and Limitations: This calculator applies to solid, prismatic, straight circular shafts under static torque and within the linear elastic material region. It assumes a homogeneous, isotropic material and neglects stress concentrations from keyways, grooves, or abrupt cross-section changes. For shafts under combined loading (bending, axial, torsion) or dynamic conditions, additional analysis is required.

Unit Consistency: The formula τmax = 16T/(πd³) yields stress in megapascals (MPa) when torque T is in newton-millimeters (N·mm) and diameter d is in millimeters (mm). This tool internally converts torque from N·m to N·mm for your convenience. Always verify unit consistency when applying these formulas manually.

This tool follows fundamental mechanical engineering principles (Shigley, Budynas) and is validated against standard shaft design procedures. It helps engineers quickly size shafts for motors, gearboxes, and rotating machinery.

Why Use This Shaft Torque Calculator?

  • Time-saving: Instant torsional stress without manual formulas.
  • Comprehensive: Includes power conversion (kW/HP), safety factor, and twist angle.
  • Material-aware: User-defined shear yield strength (typical τ_y ≈ 0.577·Sy for ductile metals).
  • Educational: Visual representation of torque direction and stress distribution.

Step-by-Step Calculation Method

  1. Compute polar moment J = π·d⁴/32 (mm⁴).
  2. Convert torque to N·mm if needed: T(N·m) × 1000.
  3. Max shear stress τ_max = T·r / J = 16·T / (π·d³) (MPa).
  4. Power: P(kW) = 2π·N·T(N·m)/60,000; HP = kW / 0.7457.
  5. Safety factor = τ_yield / (τ_max × design_factor).
  6. Angle of twist per meter: θ = (T·1000) / (J·G) radians → degrees.

Reference Table: Material Shear Yield Strength

Material Tensile Yield S_y (MPa) Shear Yield τ_y (MPa)* Typical Use
Low-carbon steel (A36) 250 144 General shafts
Medium carbon steel (1045) 450 260 Driveshafts
Alloy steel (4140 QT) 655 378 High strength
Stainless 304 215 124 Corrosive environments
Aluminum 6061-T6 240 138 Lightweight shafts

*τ_y ≈ 0.577 × S_y (von Mises criterion). For conservative design, use 0.5×S_y.

Data Sources and Theory: The above values are typical and derived from common engineering references such as the ASM Handbook (Vol. 1 & 2) and Mark's Standard Handbook for Mechanical Engineers. The shear yield strength (τ_y) is estimated as 0.577 times the tensile yield strength (S_y) based on the von Mises yield criterion. For a more conservative design, the Tresca criterion (τ_y = 0.5 S_y) may be used. Always refer to the material's official datasheet for critical applications.

Case Study: Electric Motor Shaft Design

A 15 kW electric motor runs at 1450 RPM, delivering 98.8 N·m torque. The designer selects a 35 mm diameter solid steel shaft (τ_y = 180 MPa). Calculation yields τ_max = 16·98.8e3 / (π·35³) = 11.7 MPa, safety factor = 180/11.7 = 15.4, which is extremely safe. By increasing speed or reducing diameter, weight can be optimized. This calculator allows instant trade-off analysis.

Common Mistakes & Engineering Notes

  • Incorrect units: Always ensure torque in N·mm when using mm diameter in formula (τ_max = 16·T/(π·d³) gives MPa if T in N·mm). Our tool handles unit conversion internally.
  • Shear yield vs tensile yield: For ductile materials, failure under pure shear occurs at τ_y ≈ 0.577·S_y. Using tensile yield directly would be overly conservative.
  • Dynamic effects: For cyclic or shock loads, apply a higher design factor (2–4) and consider fatigue.
  • Hollow shafts: This tool currently supports solid shafts. For hollow sections, a separate tool is recommended.
  • Stress concentrations: Keyways, holes, and shoulder fillets create stress concentrations that can significantly reduce fatigue life. Use a theoretical stress concentration factor (Kt) to adjust the nominal shear stress and account for it in the safety factor.
  • Dynamic loads and fatigue: Shafts subjected to fluctuating or reversing torque (e.g., in automotive driveshafts) are prone to fatigue failure. A static safety factor is insufficient; fatigue analysis using S-N curves and cumulative damage models (e.g., Miner's rule) is essential for such applications.

Based on authoritative sources: Formulas from Shigley's Mechanical Engineering Design (10th ed.), ISO 6336 for gears, and ASME Shaft Design Code. Reviewed by getzenquery Tech team. Updated April 2026.

Frequently Asked Questions

J is a geometric property of the cross-section that resists torsion. For a solid circle, J = πd⁴/32. It directly influences shear stress and twist angle.

Use τ_y = 0.577 × S_y (tensile yield) for conservative estimate. For exact values, refer to material datasheets (e.g., ASTM standards).

Static: SF ≥ 1.5; dynamic/fatigue: SF = 2–4. For automotive driveshafts, SF ~ 2.5 is common.

This version is for solid shafts only. For hollow, use J = π(do⁴ - di⁴)/32 and adjust stress formula. We plan a dedicated hollow shaft tool soon.

Assumes uniform torque, linear elastic material, and G=80 GPa for steel. For other materials, adjust G accordingly. Provides good approximation for preliminary design.

The calculation uses G = 80 GPa, typical for steel. For other materials, use appropriate values: aluminum alloys ~26 GPa, titanium alloys ~44 GPa, and copper alloys ~48 GPa. Consult material specifications for precise data.

This calculator provides nominal shear stress. Keyways, grooves, and sudden diameter changes create stress concentrations. Multiply the nominal stress by a theoretical stress concentration factor (Kt ≥ 1.5-3 typical for keyways) for critical design. For fatigue applications, the fatigue stress concentration factor (Kf) must be used. This tool's results are for smooth, uniform shafts.
References: Shigley's Mechanical Engineering Design, ASME B106.1M-1985, Roark's Formulas for Stress and Strain, ASM Handbook Vol. 1 & 2.