Spring rate is the force needed per unit of travel. Find it from a helical spring’s geometry — wire size, coil diameter and turns — or straight from a measured force and deflection. Includes the spring index and a wire shear-stress check.
What Spring Rate Is
Spring rate (k), also called the spring constant or stiffness, is the force needed to deflect a spring by one unit of length — newtons per millimetre, or pounds per inch. A stiff spring has a high rate and barely moves; a soft one compresses easily. As long as the spring stays in its linear range, the rate is constant: double the load, double the travel.
Rate from Geometry
For a helical compression spring the rate comes from four things: the wire’s shear modulus G, the wire diameter d, the mean coil diameter D and the number of active coils N. Wire diameter is the strongest lever — it enters to the fourth power, so a 10% thicker wire is about 46% stiffer. More coils or a larger coil diameter make the spring softer. That is why a few extra turns noticeably soften a spring.
Spring Index and Stress
The spring index C is the coil-to-wire ratio D/d. Below about 4 the spring is hard to coil and highly stressed; above about 12 it is floppy and prone to buckling or tangling, so 4 to 12 is the practical window. Under load the wire sees a torsional shear stress, raised at the inner coil by curvature — the Wahl factor corrects for it. This tool reports both so you can sanity-check manufacturability and stress at once.
Frequently Asked Questions
How do you calculate spring rate?
From a test, divide force by deflection. From geometry, k = G d to the fourth, divided by 8 times D cubed times the active coils N.
What is a good spring index?
The coil-to-wire ratio D/d is usually kept between 4 and 12 – tight enough to coil cleanly, loose enough to avoid buckling.
Why does wire diameter matter so much?
It enters the rate to the fourth power, so small changes have a big effect: a 10 percent thicker wire is roughly 46 percent stiffer.
Does adding coils make a spring stiffer or softer?
Softer. Rate is inversely proportional to the number of active coils, so more turns lower the rate.
Related calculators
- Shear Stress Calculator — the stress mode a spring wire carries.
- Young’s Modulus Calculator — the tensile cousin of shear modulus G.
- Torque Calculator — spring wire is loaded in torsion.
- Factor of Safety Calculator — check the stress margin.
Worked example
A spring that compresses 0.5 inch under a 20 lb load has a rate of 20 ÷ 0.5 = 40 lb/in, so at 0.75 inch of compression the force is 30 lb. Two identical 40 lb/in springs side by side give 80 lb/in, and in series they give 20 lb/in.
Common mistakes
Spring rate is only valid inside the spring’s linear range, so it stops working near coil bind or past its elastic limit. Keep the units consistent, and remember that a preload adds force before any compression begins.
Related calculators
Try the Torque Calculator and the Beam Deflection Calculator.