Shaft Torsion & Angle of Twist Calculator

Shaft Torsion & Angle of Twist Calculator

Shaft Torsion & Angle of Twist

CE Style

Inputs

Steel ≈ 79–82 GPa (11.5–12 Mpsi), Al ≈ 26 GPa
Use > 1 if keyways, shoulders, etc.
MPa (SI) or psi (Imp)
deg over length L
deg/m (SI) or deg/ft (Imp)

Section Properties

Results

Formulas: τ = Kt · T·c / J, θ = T·L / (J·G). Solid: J = π·d⁴/32, Hollow: J = π(Dₒ⁴ − Dᵢ⁴)/32.

Sizing (Solid Shaft)

If τallow or θlim is provided and d is blank, the calculator reports the minimum solid diameter required by strength and stiffness; the governing value is highlighted.

How to Use the Shaft Torsion & Angle of Twist Calculator

Enter torque, length, material shear modulus, and shaft geometry (solid or hollow). The tool returns maximum shear stress and total twist, plus per-length twist and quick sizing checks.

1) Pick Units & Shaft Type

  • Units: SI (mm, N·m, GPa) or Imperial (in, lbf·in, Mpsi).
  • Type: Solid round or Hollow round (Do, t).

2) Enter Geometry

  • Solid: diameter d.
  • Hollow: outer Do and thickness t (Di = Do − 2t).
  • The calculator derives J (polar moment) and c (outer radius).
Formulas: solid J = π·d⁴/32, hollow J = π(Dₒ⁴ − Dᵢ⁴)/32.

3) Material & Length

  • G (shear modulus): steel ≈ 79–82 GPa (11.5–12 Mpsi), Al ≈ 26 GPa.
  • L: free span under torque.

4) Torque & Kt

  • T: applied torque (pick matching unit).
  • Kt (optional): > 1 for keyways, shoulders, sharp fillets.
Core relations: τ = Kₜ · T·c / J, θ = T·L / (J·G).

5) Read the Results

  • τmax (with Kt) in MPa or psi.
  • θ (total twist over L) in degrees and radians.
  • Twist per length (deg/m or deg/ft) for quick service-limit checks.

6) Sizing & Limits (Optional)

  • Enter τallow to check shear stress or get dmin (solid shaft).
  • Enter θlim to limit total twist; tool gives stiffness-based dmin.
  • Enter twist per length limit to compare against computed value.
The tool highlights the governing minimum diameter when both strength and stiffness limits are set (solid shaft sizing).

Quick Checklist

  • Correct units and shaft type selected
  • Geometry fields filled properly (Dₒ and t for hollow)
  • Material G matches alloy/temper
  • Torque T reflects the worst expected load
  • Kt > 1 if keyways/shoulders exist
  • τmax ≤ τallow with safety factor
  • θ and twist/length within service limits
  • Consider fatigue and notch sensitivity for cyclic loads
FAQ & Tips

What Kt should I use?
For a plain shaft, Kt ≈ 1. Keyways, steps, or sharp fillets raise Kt. Use handbook charts or FEA if critical.

G vs E?
This calculator uses G (shear modulus), not E. For steels, a rough link is G ≈ 0.38–0.40·E.

Why is my twist high?
Twist scales with L and inversely with J. Shorten the span or increase diameter (J ∝ d⁴) to reduce θ.

Fatigue considerations?
For cyclic torque, check alternating shear stress with mean load, apply fatigue strength reduction (notch effects), and verify life targets.

Copy-Paste Mini Workflow

1) Pick units and shaft type
2) Enter geometry (d or Dₒ & t)
3) Enter G and shaft length L
4) Enter torque T and (optional) Kₜ
5) Read τ_max, θ, and twist/length
6) (Optional) Set τ_allow / θ_lim to size d_min (solid shafts)