How to use this calculator
- Measure the first load point. Apply a known load F₁ and record the length or deflection x₁.
- Measure the second load point. Apply a second known load F₂ and record the length or deflection x₂.
- Enter both points. Enter F₁, x₁, F₂ and x₂ above.
- Read the spring constant. Read k = ΔF / Δx in N/mm or lbf/in, with the force and deflection changes.
How it works
The spring constant (spring rate) k is the slope of the
force-versus-deflection line. Measure any two load points and it is:
k = (F₂ − F₁) / (x₂ − x₁) = ΔF / Δx
where x can be the measured length or the deflection — the slope is the
same either way. A genuinely linear (constant-rate) spring gives the same
k anywhere on the curve, so the two points need not start from the free
length. To get the rate from the spring's geometry instead, use the
spring rate calculator; for stress, solid height
and a buckling check, use the
compression spring calculator.
Worked example
Verified against the live calculator
A spring reads 10 N at 5 mm and 50 N at
25 mm. The force changes by ΔF = 40 N over a deflection
change of Δx = 20 mm, so:
k = 40 N / 20 mm = 2 N/mm
That is about 11.4 lbf/in. The calculator returns exactly this for these inputs.
Frequently asked questions
What is a spring constant?
The spring constant (or spring rate) is the force a spring takes per unit of deflection — N/mm in SI or lbf/in in imperial. A higher constant means a stiffer spring.
How do I calculate the spring constant from two measurements?
Take two load points and use the slope: k = ΔF / Δx = (F₂ − F₁) / |x₂ − x₁|, the change in force divided by the change in length or deflection. Enter both points above and the calculator solves it.
Is the spring constant the same as the spring rate?
Yes — "spring constant" and "spring rate" are two names for the same quantity: force per unit deflection. Stiffness, k, is the symbol for both.
How do I calculate the spring constant from the spring geometry instead?
For a helical compression spring the rate from geometry is k = G·d⁴ / (8·D³·Nₐ), where G is the shear modulus, d the wire diameter, D the mean coil diameter and Nₐ the active coils. Use the spring rate calculator for that.
What are the units, and how do I convert them?
The constant is N/mm in SI or lbf/in in imperial; they convert as 1 N/mm ≈ 5.71 lbf/in. Toggle SI/imperial in the header and the inputs and result convert.
Does this work in metric and imperial?
Yes — enter the two loads in N or lbf and the two lengths in mm or inches; the spring constant is shown in N/mm or lbf/in.
Method & assumptions
- Linear (constant-rate) spring; the constant is the same at any deflection up to solid.
- Measure two well-separated points for accuracy — points close together magnify measurement error in the slope.
- For a geometry-based rate (wire size, coil diameter, material), use the spring rate calculator.