Mechanical & Civil Engineering
Torsion Spring Deflection & Stress Calculator
Calculate angular deflection and bending stress of a helical torsion spring under an applied moment.
Your inputs
Change any value to update the result instantly.
Angular deflection
149.208 deg
Bending stress
99,471.8 psi
Deflection (rad)
2.6042 rad
Applied moment
5 lb·in
What this calculator does
Torsion Spring Deflection & Stress Calculator: Applies the standard machine-element relationship used in design textbooks so the capacity, rating or geometry can be worked out step by step.
What your result means
The headline figure is the capacity, rating or geometric result for the element you described. Compare it with the manufacturer's rating and your required service factor.
Formula and working
θ = 64MDN/(Ed^4); σ = 32M/(πd^3)
- 1
Collect the inputs
Applied moment = 5 lb·in; Mean coil diameter = 1 in; Number of coils = 10; Wire diameter = 0.08 in; Modulus of elasticity = 30,000,000 psi
- 2
Apply the formula
θ = 64MDN/(Ed^4); σ = 32M/(πd^3)
- 3
Result
Angular deflection = 149.208 deg
Frequently asked questions
Symbols and assumptions
- M
- Applied moment (lb·in)
- D
- Mean coil diameter (in)
- N
- Number of coils
- d
- Wire diameter (in)
- E
- Modulus of elasticity (psi)
- • Standard textbook geometry and steady operating conditions are assumed; shock, misalignment and wear factors are not applied automatically.
- • Material and surface-finish allowances must be chosen by the user for their actual component.
Sources and review
Reviewed 2026-09-22 · Next review 2027-09-22
- • This is an educational estimate for learning and checking, not a design deliverable.
- • Real design must follow the governing code or standard for your jurisdiction and be reviewed and signed off by a qualified engineer.
- • Safety factors, load combinations and material certification are the responsibility of the designer, not of this page.
Important limitation
This is an educational estimate based only on the values and formula shown. Verify current rates, rules, units, and professional standards before relying on the result. It is not personalized financial or investment advice.
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