Shaft Torque, Power & Stress
Torque from power and rpm (or power from torque), shear stress in a solid or hollow shaft, twist with your shear modulus, and diameter for an allowable stress.
Torque, power and angular speed, the polar moment, nominal shear stress and twist for your shaft, or the diameter for an allowable stress — no stress concentration or safety factor built in.
Example: 15 kW at 1,450 rpm is 98.8 N·m; on a Ø40 solid shaft that is 7.86 MPa shear and 0.28° of twist per metre at G 80 GPa; for 40 MPa allowable the solid shaft needs Ø23.3 mm.
Power, torque,
and what the shaft feels.
The power–torque relation, the torsion formulas, and what is left to you.
Power and torque
P = T × ω with ω = 2π × rpm ÷ 60: 15 kW at 1,450 rpm is 98.8 N·m. In imperial units the same relation reduces to hp = lbf·ft × rpm ÷ 5,252. Enter either quantity and the page gives the other.
Torsion
A round shaft in torsion carries a shear stress τ = T·r ÷ J at the surface, with J = π(D⁴ − d⁴)/32 the polar moment (d = 0 for solid). The angle of twist over a length L is θ = TL ÷ (GJ) with the shear modulus you enter. For a chosen allowable stress the solid diameter is d = ∛(16T ÷ (π·τ)).
What you add
These are nominal figures: keyways, shoulders and holes concentrate stress, belt and gear loads add bending, and fatigue with a safety factor decides the real size. Material values (G, allowable stress) are yours; round the diameter up to a stock size and check deflection and critical speed separately. Nothing leaves the browser; the same four anonymous usage counts as the rest of the site apply.
SOURCES
- P = T·ω (ω = 2π·rpm/60); τ = T·r/J with J = π(D⁴ − d⁴)/32; θ = TL/(GJ); d = ∛(16T/(π·τ_allow)) — mechanics of materials; material values and safety factors are the user’s
Last reviewed 21 September 2026. How results are checked: How we verify.