How to use this calculator
- Enter the spring geometry. Enter wire diameter, mean coil diameter and active coil count. These set the spring rate.
- Enter free length and deflection. Use free length for the solid-height and buckling checks, then enter the working compression deflection.
- Choose material and end type. The material sets shear modulus and allowable stress; the end type sets solid height and buckling end fixity.
- Read force and checks. Read the force at deflection, rate, corrected stress, solid height, travel to solid and buckling verdict.
How it works
Spring force is Hooke's law once the spring rate is known:
F = k · x
where x is compression from the free length. For a helical compression
spring, the rate comes from geometry and material:
k = G · d⁴ / (8 · D³ · Nₐ)
Here G is shear modulus, d is wire diameter,
D is mean coil diameter and Nₐ is active coils.
The calculator also checks the practical spring design around that force. It reports
the spring index C = D/d, solid height, remaining travel to solid, and
Wahl-corrected shear stress:
tau = Kw · 8 · F · D / (pi · d³)
Use the stress and buckling warnings before treating the force as a usable design load.
Worked example
Verified against the live calculator
Music wire with d = 1.0 mm, D = 10 mm and
Nₐ = 8 has rate k ≈ 1.24 N/mm. At
x = 10 mm deflection, spring force is
F = 1.24 × 10 ≈ 12.4 N. The same calculation also shows
the corrected shear stress and remaining travel to solid for that operating point.
Frequently asked questions
How do you calculate spring force?
For a linear compression spring, force is F = k·x, where k is the spring rate and x is the deflection from free length. This page calculates k from the spring geometry first, using k = G·d⁴/(8·D³·Nₐ), then multiplies by your entered deflection.
What is the difference between spring force and spring rate?
Spring rate k is stiffness, usually N/mm or lb/in. Spring force F is the actual load at a specific deflection. A 10 N/mm spring deflected 20 mm carries 200 N before preload, seating effects or nonlinearity.
Does this include stress in the spring wire?
Yes. The calculator uses the Wahl factor to correct shear stress for coil curvature and compares the corrected stress with the selected spring material allowance.
Can I use this for extension springs?
This page is for compression springs. Extension springs include initial tension, so use the extension spring calculator when the coils are pulled apart.
Why does wire diameter change force so much?
Spring rate scales with wire diameter to the fourth power. Doubling wire diameter makes the same spring geometry about 16 times stiffer, before practical limits such as spring index and stress are considered.
Method & assumptions
- Linear helical compression spring, static loading only.
- Force is calculated from deflection from free length; preload or assembly compression must be included in the entered deflection.
- Fatigue life, set, relaxation and manufacturing tolerances are not modelled.