Helical Compression Spring Calculator — Spring Force, Spring Rate & Shear Stress Validator
Calculate spring force, spring rate and maximum shear stress using deflection, coil geometry and material stiffness.
Enter the known values and review the calculated result
Input parameters
Use consistent values and select the intended engineering units.
Calculation mode
Spring geometry
Load & stiffness
Spring parameters
Load input (one required)
Allowable stress (optional)
Results
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Method, application and limitations
Review the calculation method, intended application and engineering assumptions before using the result in a design decision.
Formula and calculation method
Spring force formula:
Force mode:
F = k · Δx
Design mode:
k = (G · d⁴) / (8 · D³ · n)
If force is provided:
F = F
If deflection is provided:
F = k · Δx
Maximum shear stress formula:
τmax = (8 · F · D · Kw) / (π · d³)
Wahl correction used in the stress formula:
C = D / d
Kw = ((4 · C − 1) / (4 · C − 4)) + (0.615 / C)
where:
- F — spring force [N]
- k — spring rate [N/m]
- Δx — deflection [m]
- d — wire diameter [m]
- D — mean coil diameter [m]
- n — active coils [—]
- G — shear modulus [Pa]
- C — spring index [—]
- Kw — Wahl correction factor [—]
- τmax — maximum shear stress [Pa]
When to use this calculator
When to use this calculator:
- Calculate spring force from a known spring rate and compression deflection.
- Calculate spring rate from wire diameter, mean coil diameter, active coils and shear modulus.
- Check maximum shear stress in a helical compression spring using the Wahl correction factor.
- Evaluate whether calculated shear stress exceeds the allowable shear stress limit.
- Check coil bind risk from free length, solid height and calculated deflection when free length is provided.
- Check spring slenderness from free length and mean coil diameter when free length is provided.
How to interpret the result
Spring force is defined as the load generated from spring rate and deflection. Spring rate is defined as the stiffness calculated from shear modulus, wire diameter, mean coil diameter and active coils in design mode. Maximum shear stress is defined as the Wahl-corrected shear stress caused by spring force in the wire.
Spring force increases when deflection increases. In design mode, spring rate increases when shear modulus or wire diameter increases, and decreases when mean coil diameter or active coils increase. Maximum shear stress increases when spring force or mean coil diameter increases, and decreases when wire diameter increases.
- Safe — allowable shear stress is provided and calculated stress utilization is ≤ 0.75; slenderness is ≤ 4 when free length is provided; deflection is ≤ 90% of available travel before solid height when free length is provided.
- Warning — calculated stress utilization is > 0.75 and ≤ 0.90; active coils are < 3 and ≥ 2; slenderness is > 4 and ≤ 6; or deflection is > 90% of available travel before solid height.
- Limit — calculated stress utilization is > 0.90 and ≤ 1.00 when allowable shear stress is provided.
- Unsafe — calculated stress utilization is > 1.00; active coils are < 2; slenderness is > 6; available travel before solid height is ≤ 0; or deflection exceeds available travel before solid height.
- Info — allowable shear stress or free length is not provided, so the related stress or geometry check cannot be classified.
- Invalid — required inputs are missing, non-finite, not greater than zero where required, mean coil diameter is not greater than wire diameter, spring index is outside 3–20, design mode has active coils ≤ 0.5, or design mode has neither force nor deflection.
The result is used to evaluate spring load, stiffness and stress utilization for the selected calculation mode.
Calculation example
Example:
A user wants to check a helical compression spring in force-from-deflection mode before using it under a compressed position.
- Mode: Force from deflection
- k — Spring rate: 10000 N/m
- Δx — Deflection: 0.02 m
- d — Wire diameter: 0.005 m
- D — Mean coil diameter: 0.04 m
F = 10000 · 0.02 = 200 N
C = 0.04 / 0.005 = 8
Kw = ((4 · 8 − 1) / (4 · 8 − 4)) + (0.615 / 8) = 1.184
τmax = (8 · 200 · 0.04 · 1.184) / (π · 0.005³) = 193000000 Pa
Assumptions and limitations
- The spring is evaluated as a helical compression spring using mean coil diameter, wire diameter and the Wahl correction factor.
- The spring index is restricted to 3 ≤ D/d ≤ 20.
- Force-from-deflection mode assumes a provided linear spring rate.
- Spring design mode calculates spring rate from shear modulus, wire diameter, mean coil diameter and active coils.
- Stress classification is only calculated when allowable shear stress is provided.
- Slenderness and coil bind checks are only calculated when free length is provided.