Spring Rate Calculator

Stiff springs make a race car feel every pothole. Soft ones let a sedan glide over the same road. Spring rate is what separates them, and Hooke's Law ties it to two related quantities: force and displacement. Give any two of the three and the calculator returns the missing one.

What is spring rate?

Spring rate (written as $k$ , sometimes called spring constant or stiffness) is the force a spring resists per unit of compression or extension. A rate of 100 N/mm means it takes 100 newtons to push the spring in by one millimeter. Twice the rate, twice the force for the same compression.

Linear springs hold the same rate the whole way through their travel. Progressive springs, common in performance suspensions and mountain bike forks, get stiffer the further they compress. Soft for small bumps, firm under load.

How to use this calculator

Fill in any two of the three input fields and read the third. N/mm and lb/in are the usual stiffness units; displacement is normally in millimeters or inches. Mix metric and imperial as you go, units are converted to a common base before the math runs.

Understanding the formula

Hooke's Law says the force a spring exerts is directly proportional to how far it has been displaced from its rest position:

k = \frac{F}{\Delta x}

where $k$ is spring rate, $F$ is force, and $\Delta x$ is displacement. Rearrange and you get the other two forms: $F = k \cdot \Delta x$ and $\Delta x = F / k$ .

Worked example: a coil rated at $k = 80 \text{ N/mm}$ is pushed in by $\Delta x = 30 \text{ mm}$ . The force it pushes back with is $F = 80 \times 30 = 2{,}400 \text{ N}$ , around 245 kgf. Enough to hold up a corner of a small hatchback.

When you are designing the spring itself rather than picking one off a shelf, $k$ comes out of the geometry:

k = \frac{G \cdot d^4}{8 \cdot D^3 \cdot n}

Here $G$ is the material's shear modulus, $d$ is the wire diameter, $D$ is the mean coil diameter, and $n$ is the number of active coils. Wire diameter has the heaviest pull (it's raised to the fourth power), so a small change in wire thickness shifts the rate dramatically. Wider coils and more turns soften the spring.

Applications

Suspension tuning is the most familiar use. Road cars typically run springs in the 25 to 150 N/mm range, soft for comfort and stiff for cornering grip. Mountain bike forks and rear shocks land between 30 and 90 lb/in, picked to match the rider's weight. The same number sets behavior for things you don't usually think about as springs: garage doors, industrial valves, retractable pens, trampoline mats. At the small end, watch escapements and surgical instruments use springs with rates of just a few mN/mm.

Tips

If you swap car springs, look at damping at the same time. A stiffer spring needs more damping force to control its rebound, so a stock shock can feel uncontrolled on aftermarket rates. For progressive springs the manufacturer gives a curve or a rate range rather than a single number, pick the value at the part of the travel you actually use. When measuring rate on the bench, start from the spring's free (unloaded) length; the installed length already has compression baked in and will throw the numbers off.

Frequently asked questions

What units is spring rate measured in?

Metric uses N/mm or N/m. Imperial uses lb/in, sometimes written pound-force per inch. kgf/mm and kN/m also show up, especially in suspension and industrial specs.

Does Hooke's Law work for any spring?

Only inside the spring's elastic range. Push it past the yield point and it deforms permanently; once that happens the linear F = kΔx relationship stops holding. Progressive springs also don't have a single constant k by design, the rate changes with displacement.

How do I measure spring rate experimentally?

Measure the free length first. Then apply a known force (or hang a known weight) and measure how far the spring compresses or stretches. Divide the force by the change in length. Repeat with several different loads, if the rate stays the same across them, the spring is linear in that range.

What happens with springs in series or parallel?

Springs in parallel act stiffer: the rates add, so $k_{\text{total}} = k_1 + k_2$ . Springs in series act softer: the compliances add, so $\frac{1}{k_{\text{total}}} = \frac{1}{k_1} + \frac{1}{k_2}$ Stacking springs this way is a common trick for tuning the effective rate of a suspension without buying new springs.