Shaft Torsion Calculator
The maximum shear stress in a solid shaft is 16T/πd³: 1 kN·m on a 50 mm shaft gives τmax = 40.7437 MPa.
For transmitted power; 0 to skip.
40.7436654315252 MPa
Full answer, then cut to fewer decimals (not rounded):
- 40.7436654315252 MPa
- 40.743665431525 MPa
- 40.74366543152 MPa
- 40.7436654315 MPa
- 40.743665431 MPa
- 40.74366543 MPa
- 40.7436654 MPa
- 40.743665 MPa
- 40.74366 MPa
- 40.7436 MPa
- 40.743 MPa
- 40.74 MPa
- 40.7 MPa
- Polar moment of inertia J
- 613592 mm⁴
- Angle of twist θ
- 0.0203718 rad
- Angle of twist θ
- 1.16722 °
- Torsional stiffness GJ/L
- 49087.4 N·m/rad
Step-by-step solution
- T/J = τ/r = Gθ/L
- J = π(D⁴ − d⁴)/32 = 613592 mm⁴
- τ = T r / J = 1000000 N·mm × 25 mm ÷ 613592 mm⁴ = 40.7437 MPa
- θ = TL/GJ = 0.0203718 rad = 1.16722°
Shaft Torsion Formula
T/J = τ/r = Gθ/L
J = π(D⁴ − d⁴)/32, r = D/2, G modulus of rigidity
Worked Example
A 50 mm solid steel shaft (G = 80 GPa), 1 m long, carrying 1 kN·m:
- T/J = τ/r = Gθ/L
- J = π(D⁴ − d⁴)/32 = 613592 mm⁴
- τ = T r / J = 1000000 N·mm × 25 mm ÷ 613592 mm⁴ = 40.7437 MPa
- θ = TL/GJ = 0.0203718 rad = 1.16722°
Angle of twist θ: 0.0203718 rad · Angle of twist θ: 1.16722 ° · Torsional stiffness GJ/L: 49087.4 N·m/rad
More Mechanics of Materials Calculators
-
Mohr’s Circle Calculator
σ₁,₂ = (σx + σy)/2 ± √[((σx − σy)/2)² + τxy²]
centre C = (σx + σy)/2, radius R = τmax
Example: σx = 80 MPa, σy = −40 MPa and τxy = 45 MPa: Major principal stress σ₁ = 95 MPa.
-
Beam Deflection Calculator
δ = PL³/3EI, wL⁴/8EI, PL³/48EI, 5wL⁴/384EI
P point load, w load per length, L span, E Young’s modulus, I second moment of area
Example: A 2 m steel cantilever (E = 200 GPa, I = 8 × 10⁶ mm⁴) with 10 kN at the free end: Maximum deflection δ (free end) = 16.6667 mm.
-
Bending Stress Calculator
σ = M y / I = M / Z
M bending moment, y distance from the neutral axis, I second moment of area, Z = I/y
Example: A 100 × 200 mm rectangular beam carrying a 20 kN·m bending moment: Maximum bending stress σ = 30 MPa.
-
Euler Buckling Calculator
Pcr = π²EI / Le²
Le effective length: L pinned, 2L fixed–free, L/2 fixed–fixed, L/√2 fixed–pinned
Example: A 3 m pinned steel column with I = 8 × 10⁶ mm⁴ and A = 5000 mm²: Critical buckling load Pcr = 1754.6 kN.
Frequently asked questions
Why are hollow shafts used?
Material near the centre carries little shear stress, so a hollow shaft transmits nearly the same torque with much less weight.
How do I find shaft power from torque?
P = 2πNT/60 with N in rpm and T in N·m gives watts. Enter the speed to get it.
Sources
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Shaft Torsion Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/shaft-torsion-calculator/
IEEE
Scientific Converters, "Shaft Torsion Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/shaft-torsion-calculator/