Shaft Torque and Power Calculator

Results

The key results from this calculation are summarised below. The final math regions above display each value inline. The interpretation is as follows:

• Torque T — the steady-state torsional load the shaft must carry. Use this to size keys, splines, couplings, and interference fits.
• Maximum shear stress τ_max — occurs at the outer surface. Compare against the allowable shear stress for the chosen material and heat treatment.
• Factor of safety FS — a value ≥ 2 is recommended for general power transmission shafts; ≥ 1.5 may be acceptable where loads are well-defined and the geometry is smooth. If FS < 1.5, increase the shaft diameter or select a higher-strength material.
• Angle of twist φ — if φ_deg exceeds 0.5°/m, consider increasing the shaft diameter to improve torsional stiffness, even if the stress check already passes.

Assumptions & Limitations

• The shaft is assumed to be a solid, homogeneous, isotropic cylinder with a circular cross-section. Hollow shafts require a different J formula.
• Only steady-state (mean) torque is considered. Dynamic effects (shock, vibration, start-up surges) require a service factor applied to T before checking stresses.
• Stress concentrations at keyways, shoulders, grooves, and press fits are not included. Apply a stress concentration factor Kt to τ_max in detailed design.
• The torsion formula τ = Tr/J is valid for circular sections only. Non-circular shafts (square, splined) require different approaches.
• Lateral bending loads are not considered. In most real shafts, combined torsion and bending must be checked using the von Mises or ASME–DE fatigue criteria.
• The von Mises criterion (τ_y = σ_y/√3) applies to ductile materials. For brittle materials, the maximum normal stress criterion should be used instead.
• Angle of twist assumes uniform torque along the shaft length. For multi-load-point shafts, analyse each segment separately.

Shaft Torque and Power Calculator

This worksheet calculates the torque transmitted by a rotating shaft and the corresponding mechanical power output. It is fundamental to the design of drive shafts, gearboxes, motors, pumps, and any rotating machinery.

The governing relationship between torque, rotational speed, and power is derived from the definition of mechanical work. As a shaft rotates, the power transmitted is the product of the torque and the angular velocity: P = T · ω, where angular velocity ω = 2π·n/60 for speed n given in RPM.

This worksheet also calculates the shear stress induced in a solid circular shaft cross-section, using the torsion formula from Saint-Venant's torsion theory: τ = T·r / J, where J is the polar second moment of area and r is the outer radius. A factor of safety against the material's shear yield strength is then evaluated.

Together these checks ensure the shaft is both capable of transmitting the required power and structurally safe under the applied torsional loading.

Inputs

Enter the shaft operating conditions, geometry, and material properties below. Typical engineering steels have a yield strength in the range 250–700 MPa, and shear yield strength is approximately 0.577 × σ_y (von Mises criterion). Shaft diameters for power transmission commonly range from 20 mm to 200 mm.

Calculations

Step 1 — Angular Velocity

The angular velocity ω (in radians per second) is obtained from the rotational speed n (in RPM) using the conversion:

ω = 2π · n / 60

This converts revolutions per minute into radians per second, which is the SI unit required in the power equation. At 1450 RPM, ω is approximately 152 rad/s, which is typical of a 4-pole induction motor running at near-synchronous speed on a 50 Hz supply.

Step 2 — Transmitted Power After Efficiency Losses

Not all of the rated input power reaches the driven load. Accounting for the transmission efficiency η, the actual power delivered at the shaft is:

P_out = P_rated · η

An efficiency of 98% is typical for a well-aligned flexible coupling or a single-stage gear drive. The remaining 2% is dissipated as heat in bearings, seals, and meshing surfaces.

Step 3 — Transmitted Torque

Rearranging the power equation P = T · ω for torque gives:

T = P / ω

Here P is the transmitted output power (W) and ω is the angular velocity (rad/s). The result is the steady-state torque the shaft must carry. This is the primary design load for sizing the shaft cross-section.

Step 4 — Shaft Cross-Section Properties

For a solid circular shaft of diameter d, the key geometric properties are the outer radius r and the polar second moment of area J:

• r = d / 2 — the distance from the shaft axis to the outer fibre, where shear stress is maximum.
• J = π · d⁴ / 32 — the polar second moment of area, which resists torsional deformation. It depends strongly on diameter (to the fourth power), so small increases in d give large improvements in torsional rigidity.

Step 5 — Maximum Shear Stress

From Saint-Venant's torsion theory, the shear stress τ at the outer surface of a circular shaft carrying torque T is given by the torsion formula:

τ = T · r / J

where:

• T is the applied torque (N·m)
• r is the outer radius (m) — the location of maximum stress
• J is the polar second moment of area (m⁴)

This formula assumes linear elastic behaviour, a prismatic circular cross-section, and that plane cross-sections remain plane after twisting. The shear stress is zero at the shaft axis and peaks at the outer surface.

Step 6 — Shear Yield Strength and Factor of Safety

The allowable shear stress is governed by the material's shear yield strength τ_y. According to the von Mises yield criterion (the most widely used for ductile metals), shear yielding occurs when:

τ_y = σ_y / √3 ≈ 0.577 · σ_y

The factor of safety FS is then the ratio of the shear yield strength to the maximum operating shear stress:

FS = τ_y / τ_max

A factor of safety greater than 1.5–2.0 is generally required in power transmission shafts to account for dynamic loads, stress concentrations at keyways and shoulders, and manufacturing tolerances. Values below 1.0 indicate yielding — the shaft must be redesigned (larger diameter or stronger material).

Step 7 — Angle of Twist

The angle of twist φ over a shaft length L is a measure of torsional flexibility. From the torsion formula:

φ = T · L / (G · J)

where G is the shear modulus of the shaft material. For steel, G ≈ 80 GPa. Excessive twist causes vibration, misalignment of driven components, and fatigue. A common design limit is φ ≤ 0.5° per metre of shaft length.