Spring Rate Calculator

Enter a helical coil spring's wire diameter, mean coil diameter, number of active coils, and material to calculate its spring rate: k = Gd⁴/(8D³Na).

Quick Facts

Spring rate formula
k = Gd⁴ / (8D³Na)
G = shear modulus, d = wire diameter, D = mean coil diameter, Na = active coils.
Spring index
C = D / d
Recommended range is 4-12 for practical manufacturability; below 4 is hard to coil, above 12 tends to buckle or tangle.
Typical shear modulus
≈ 79.3 GPa (11.5×10⁶ psi)
Typical value for music wire and hard-drawn spring steel; stainless steel and phosphor bronze are lower.
Units
N/mm or lbf/in
Spring rate is force per unit deflection; 1 N/mm = 1000 N/m.

Your Results

Calculated
Spring Rate
-
k = Gd⁴/(8D³Na)
Spring Rate (SI)
-
Always shown in N/m for reference
Spring Index (C = D/d)
-
Ratio of coil diameter to wire diameter
Manufacturability
-
Guidance based on spring index

Ready

Enter wire diameter, coil diameter, active coils, and material, then press Calculate.

Formula and Method for Spring Rate

The spring rate (also called the spring constant) of a helical coil spring is the force needed to compress or stretch it by one unit of length: k = F/x. If the spring already exists, you can measure that directly. But if you're designing a spring or checking a spec, you can predict its rate from geometry and material alone using the standard helical spring formula: k = Gd⁴ / (8D³Na), where G is the material's shear modulus, d is the wire diameter, D is the mean coil diameter, and Na is the number of active coils.

How the calculation works

Enter the wire diameter (d) and the mean coil diameter (D) — the mean diameter is the average of the spring's inside and outside diameter, or equivalently the outside diameter minus one wire diameter. Enter the number of active coils (Na), which excludes any inactive end coils that anchor the spring but don't flex under load. Choose a material (or enter a custom shear modulus), and the calculator raises the wire diameter to the fourth power and the coil diameter to the third power, then combines them with G and Na to solve for k. Because wire diameter enters as d⁴, small changes in wire size have an outsized effect: doubling the wire diameter increases the spring rate sixteen-fold if the coil diameter and coil count are unchanged.

Getting accurate results

  • Count only active coils, not total coils. Compression springs with closed-and-ground ends typically have about 2 fewer active coils than total coils; extension springs generally use close to the full body coil count, since the end hooks don't add stiffness.
  • Use the mean coil diameter, not the outside or inside diameter. If you only measured outside diameter (OD), subtract one wire diameter: D = OD − d.
  • Keep the spring index (C = D/d) between about 4 and 12. Outside that range the formula becomes less reliable and the spring is harder to manufacture consistently.
  • Shear modulus varies by alloy and temperature. Use the material's datasheet value when precision matters — generic textbook values can be off by 5-10% for less common alloys.

Frequently Asked Questions

What is the difference between spring rate and spring constant?
None — spring rate and spring constant both refer to k, the stiffness of a spring in force per unit deflection (F = kx). "Spring rate" is more common in mechanical and automotive engineering, while "spring constant" is the term usually used in physics.
What is spring index and why does it matter?
Spring index is C = D/d, the ratio of mean coil diameter to wire diameter. Most practical coil springs use an index between 4 and 12. Below 4 the wire is hard to coil and stress concentrates on the inside of each coil; above 12 the spring is prone to buckling and tangling and is harder to wind consistently.
How many active coils should I count?
Active coils (Na) are the coils that actually flex under load, excluding the inactive end coils used to seat or anchor the spring. For compression springs with closed and ground ends, subtract about 2 from the total coil count. For extension springs, the active coil count is typically close to the total number of body coils, since only the end hooks are excluded.
Does temperature affect spring rate?
Yes. Shear modulus decreases slightly as temperature rises, so a spring's rate drops a few percent at high temperatures and increases slightly in the cold. For most steel springs near room temperature the effect is small, but for high-temperature or cryogenic applications use the material's temperature-adjusted shear modulus rather than the room-temperature value.

Related calculators