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MachineCalcs

Spring Constant Calculator

The spring constant (spring rate) from two measured load points — k = ΔF / Δx, the slope of Hooke's law. Use it when you can load a spring and measure two lengths. Metric and imperial.

Inputs

N
mm
N
mm

Results

Spring constant(k)
2 N/mm

Force per unit deflection — the same anywhere on a linear spring.

Slope of the load–deflection line.

Force change(ΔF)
40 N

Deflection change(Δx)
20 mm

  • Spring constant k = (F₂ − F₁) / |x₂ − x₁| — the slope of the force–deflection line (Hooke's law).
  • Assumes a linear (constant-rate) spring; pick two well-separated points for accuracy.
  • To get the rate from spring geometry instead, use the spring rate calculator.

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.

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