CALCULATORS / SHAFTS, COUPLINGS AND ROTATING ASSEMBLIES

Shaft torsional stress and twist calculator

Uniform solid circular shaft elastic twist.

shafts-torsion.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

This source describes an analytical model. Its quantities and checks are the view.

Scenario	polarmm^4	stressMPa	twistrad
	4970.1	15.0902	0.00764063
	4970.1	12.0722	0.0061125

All calculated quantities are listed with the inputs. Switch to Source to inspect the equations.

SCENARIOS / CALCULATED VALUESSAME SOURCE

Change an input to see the consequences.

twist budget0.44 deg✓ passes

BASELINE INPUTS

torque10 N*mdiameter15 mmlength300 mmshearModulus79 GPa

CALCULATED

polar4970.1 mm^4

stress15.09 MPa

twist0.0076406 rad

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Shaft torsional stress and twist
# Scope: Uniform solid circular shaft elastic twist.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

torque = 10 N*m
diameter = 15 mm
length = 300 mm
shearModulus = 79 GPa

polar := pi*diameter^4/32 [mm^4]
stress := torque*diameter/(2*polar) [MPa]
twist := torque*length/(shearModulus*polar) [rad]

check twist budget: twist <= 1 deg

scenario alternative: torque = 8 N*m

Calculated from your source · not saved

Baseline · Baseline

twist budget0.44 deg ✓ passes

alternative · alternative

twist budget0.35 deg ✓ passes

Illustrative first-order example. Checks are editable requirements, not design standards. The broader topic may require additional equations, data, and validation.

Formula and units

This example uses the following equations. Input names and units match the editable source above.

polar: polar = pi*diameter^4/32 [mm^4]
stress: stress = torque*diameter/(2*polar) [MPa]
twist: twist = torque*length/(shearModulus*polar) [rad]

Original worked example

These are the baseline values in the downloadable source. Edits above let you test your own values.

Given

torque: 10 N*m
diameter: 15 mm
length: 300 mm
shear modulus: 79 GPa

Calculated

polar: 4970.1 mm^4
stress: 15.0902 MPa
twist: 0.00764063 rad

Assumptions and limits

Uniform solid circular shaft elastic twist.

The requirement checks use the limits written in this example. Passing a check does not establish that the model covers every load, material behavior, or operating condition in a real design.

Download this .napkin example ↓

Take it further with your agent

Napkin keeps the inputs, equations, checks and assumptions together in one study. Your agent sets it up; you change the numbers.

Try with Claude ↗

codex 'Use Napkin (https://napkin.engineering/mcp, or the local Napkin plugin) to build a study: Shaft torsional stress and twist. Inputs: torque; diameter; length; shear modulus. Outputs: shear stress; twist angle. Model scope: Elastic shaft models and specified supports. Read napkin_capabilities and the current snapshot. Ask me for the values that matter, label assumptions with units, author .napkin source, validate it and apply it with napkin_source using the current revision, then open the study. Add checks for the limits I supply. Keep unsupported analyses explicit.'

Claude needs the Napkin connector; Codex needs the Napkin plugin. Set up your agent ↗

The broader study

The topic brief below describes the broader scope. The worked example above states the particular calculation it implements.

Inputs: torque, diameter, length, shear modulus
Outputs: shear stress, twist angle
Modes: calculate, compare, sweep
Drawing: Shaft load diagram

EXECUTABLE WORKED EXAMPLE · FIRST-ORDER MODEL · CHECK THE SCOPE & ASSUMPTIONS