Shaft Power Torque Torsion Calculator

The Shaft Power, Torque and Torsion Calculator solves whichever one of shaft power, torque or rotational speed you do not know from the two you do, and then rates a straight circular shaft in elastic torsion. It reports the polar second moment of area, the maximum torsional shear stress at the outside surface, the angle of twist over the length you enter, the torsional stiffness, and the maximum shear strain.

It handles a solid shaft or a concentric hollow shaft, and it plots shear stress across the shaft wall, which shows directly how little the material near the centre carries.

It works in SI units: metres and millimetres for geometry, gigapascals for shear modulus, kilowatts for power, newton metres for torque, revolutions per minute for speed, and megapascals for stress.

Use it as a strength-of-materials screen. It is not a shaft design. It does not rate allowable stress, and it does not touch fatigue, critical speed, keys, splines, couplings or bearings. It excludes stress concentrations entirely, which for a real shaft with a keyway or a shoulder is the single largest thing standing between this number and a safe one.

Purpose and model boundary

This model solves one member of the shaft power-torque-speed relationship and then evaluates elementary elastic torsion for a solid or concentric hollow circular shaft. It reports power, torque, speed, polar moment, stress, twist, stiffness and strain. It is an identity and elastic-response calculator, not a shaft rating or design acceptance.

The spreadsheet is the calculation authority. The page submits the named inputs to the calculation service and displays returned results, chart and status; no mechanical formula is duplicated in browser code.

Inputs and units

Power is in kW, torque in N·m, speed in r/min, diameters in mm, length in m and shear modulus in GPa. Geometry and material units are fixed in this model.

Governing relationships

The operating identity is P = Tω, where ω = 2πn/60. The selected solve mode rearranges this identity to derive power, torque or speed.

For the circular section, the workbook uses

• polar moment J = π(Do⁴ − Di⁴)/32, with Di = 0 for a solid shaft;
• maximum elastic shear stress τmax = T(Do/2)/J;
• angle of twist θ = TL/(JG);
• torsional stiffness kt = JG/L;
• maximum elastic shear strain γmax = τmax/G.

The chart samples τ(r) = Tr/J across seven radii. A hollow-shaft profile starts at the bore radius; a solid-shaft profile starts at the centreline.

Calculation sequence

1. Validate the solve mode and shaft type, the two active positive power/torque/speed inputs, positive outer diameter, length and modulus, and 0 < Di < Do for a hollow shaft.
2. Resolve the missing member of P = Tω and calculate angular speed.
3. Convert geometry and modulus to SI and calculate J.
4. Calculate maximum stress, twist, stiffness and strain using the resolved torque.
5. Verify that all required operating and torsional results are positive and finite.
6. Return the through-wall stress profile and workbook status.

Outputs and interpretation

Primary outputs are shaft power, torque, rotational speed, angle of twist and maximum torsional shear stress. Details provide angular speed, polar moment, torsional stiffness and maximum shear strain. The chart shows the ideal linear elastic shear-stress variation through the shaft material.

Maximum stress and twist are computed responses, not allowables. The model does not compare them with yield, fatigue, deflection or code criteria.

Validation and status logic

The workbook does not define a CHECK state for this calculator. Inactive power, torque or speed entries are not used by the selected solve branch.

Assumptions and limitations

• The shaft is straight, prismatic, circular, homogeneous and linearly elastic under steady Saint-Venant torsion.
• Power and torque are represented as positive steady magnitudes; shock, reversing and transient loads are excluded.
• Shear modulus is uniform and supplied by the user.
• No allowable stress, yielding, fatigue, buckling, critical speed, vibration, key, spline, coupling, bearing or stress concentration is evaluated.
• Noncircular sections, open thin-wall sections, warping restraint, plastic torsion and varying torque, geometry or material are outside scope.
• No motor, gearbox, material, service factor or design-code selection is performed.

Restrictions and non-computing states

The selected solve mode requires exactly the corresponding two active positive operating quantities. A hollow shaft requires a positive bore smaller than the outside diameter. All elastic formulas require positive length and modulus. A NOT VALID state supersedes any protected zero or formula residue.

Errors and warnings

A rejected entry means the values did not satisfy the published input rules. NOT VALID is the workbook's only non-success state; the model emits no CHECK warning. Calculation-service failures are availability errors, not evidence of zero load or acceptable shaft response.

No proprietary shaft table, material database or manufacturer catalogue is reproduced. There is no material property lookup in this calculator at all: the shear modulus is entered by the user. The shipped default geometry and modulus are synthetic demonstration values and represent no real shaft or material. The relations implemented are cited below.

• Saint-Venant, Adhemar Jean Claude Barre de. Memoire sur la torsion des prismes. 1855. (the origin of the torsion theory used here)
• Wikipedia. Torsion constant. https://en.wikipedia.org/wiki/Torsion_constant
• Wikipedia. Polar moment of inertia, for the solid and hollow circular section formulas. https://en.wikipedia.org/wiki/Polar_moment_of_inertia
• Wikipedia. Shear modulus, for typical values by material. https://en.wikipedia.org/wiki/Shear_modulus
• Wikipedia. Torque, for the power, torque and angular speed identity. https://en.wikipedia.org/wiki/Torque
• Wikipedia. Stress concentration, for what this calculator deliberately omits. https://en.wikipedia.org/wiki/Stress_concentration

Allowable stresses, fatigue limits, stress concentration factors and critical speeds are not supplied here. Take them from the governing design code and the material specification for your project.

Additional source notes migrated from Methodology

• NASA, Mechanical Drive System Description and Design Guide — public P = Tω identity.
• NASA, Wind Turbine Generator Drivetrain Analysis — public circular-shaft polar moment, twist and torsional-stiffness equations.
• NASA, Material Selection for Aerospace Systems — public elastic torsional shear-stress identity.
• NIST Guide to the SI, Chapter 8 — SI and rotational unit conventions used by the workbook.

Project loads, material allowables, the governing design code and qualified mechanical review control real shaft design.