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
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.
Related calculators
- Compression Spring Calculator — Rate, Wahl-corrected stress, solid height and buckling, with built-in material data.
- Spring Rate Calculator — Spring rate (spring constant) from wire size, coil diameter and material.
- Extension Spring Calculator — Rate, spring index and force at extension including initial tension.