How to use the torsion calculator
Prepare the values for this calculation
Calculate angle of twist for a uniform circular shaft using entered polar moment. Use the formula below to check that it answers your question. Read the input units before transferring figures from a statement, measurement or dataset.
Enter and check each input
- Torque T (N·m): enter a finite number. Use the unit named in the label or selected above. Do not leave this required field blank.
- Shaft length L (m): enter a value at least 0. Use the unit named in the label or selected above. Do not leave this required field blank.
- Polar moment J (m⁴): enter a value at least 1e-20. Use the unit named in the label or selected above. Do not leave this required field blank.
- Shear modulus G (Pa): enter a value at least 1e-12. Use the unit named in the label or selected above. Do not leave this required field blank.
The input table gives a complete example. Keep units and time periods consistent across related fields.
Calculate and resolve any input error
Choose Calculate after entering the values. Changes also update the answer after a short pause. If an error appears, follow its message, correct the field and calculate again. Reset restores the example values.
Interpret the answer
Check Angle of twist first. With the unchanged example inputs, it is 0.0025 rad. Interpret it using the formula and assumptions on this page.
Compare and keep a useful result
For a controlled comparison, keep every other example input unchanged and change Torque T (N·m) from 1000 to 1100. The resulting Angle of twist is 0.00275 rad. This illustrates the equation’s response to that input, rather than a forecast of real events.
Read the chart’s axis labels and data table. A scenario curve changes one stated input while holding the others fixed; it does not add external observations. Use Download graph to save an available chart as a PNG.
Use Copy result or Download CSV to keep the answer. Share tool shares the page address without placing your input values in the URL. Recheck inputs and assumptions before using the result for a decision.
Torsion Calculator formula
θ=TL/(JG).
Inputs and units
| Input | Format / range | Example |
|---|---|---|
| Torque T (N·m) | Number | 1000 |
| Shaft length L (m) | minimum 0 | 2 |
| Polar moment J (m⁴) | minimum 1e-20 | 1e-05 |
| Shear modulus G (Pa) | minimum 1e-12 | 80000000000 |
Worked example
Using the example inputs above, the angle of twist is 0.0025 rad.
- Angle of twist
- 0.0025 rad
Results and assumptions
Uniform elastic torsion using the entered polar moment and shear modulus.
Fix an input or unexpected result
Torque T (N·m) is required. Enter torque t (n·m) using the format and bounds in the input table. Zero and an empty field are different: use zero only if it is allowed and represents your data.
If your answer differs from the example, choose Reset and compare every field, including selected units and options. Check percentage versus decimal entry and whether values describe the same period. Round only the final displayed answer when reproducing the formula.
If a discrepancy remains, report the calculator issue with the page address, non-sensitive example inputs, actual result, expected result and a reference for your calculation.