Spring Rate Calculator
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.