Introduction
A spring rate tells you how stiff a spring is. It is the amount of force needed to move a spring one inch or one millimeter. A high spring rate means a stiff spring. A low spring rate means a soft, easy-to-move spring.
This Spring Rate Calculator works out that number. Pick your spring type (compression, extension, torsion, or conical), then enter the wire size, coil diameter, and number of coils. The tool uses the shear modulus of your chosen material, like music wire or stainless steel, to find the rate. You can also use Hooke's Law instead: enter a force and how far the spring moved, and the tool divides one by the other.
Results show in lbs/in, N/mm, and kg/mm at the same time, so you do not need to convert by hand. You can switch between imperial and metric units at any point, and your numbers convert with you.
The calculator also shows extra details that matter in real design work. You get the spring index, solid height, maximum safe load, buckling risk, and natural frequency. A step-by-step solution lists every formula and number used, so you can check the math or use it for school and shop work.
The second part of the tool handles springs stacked in series. Enter two or three spring rates, and it finds the combined rate. Springs in series are always softer than the softest spring in the stack, and a chart shows how each one compares.
How to use our Spring Rate Calculator
Enter your spring type, units, and a few simple measurements, and the calculator gives you the spring rate in lbs/in, N/mm, and kg/mm, plus a step-by-step solution, a load chart, and extra results like spring index and max load.
Section 1: Single Spring Rate
Spring Type: Pick compression, extension, torsion, or conical. The input fields change to match your choice.
Unit System (Section 1): Choose Imperial (inches and pounds) or Metric (mm and newtons). Your typed numbers convert for you.
Calculation Method: Pick Engineering Formula to use spring size and material. Pick Hooke's Law if you already measured force and travel. Hooke's Law works only for compression and extension springs.
Spring Material: Choose your wire material. This fills in the shear modulus for you.
Shear Modulus, G: This shows how stiff the wire material is. Leave the auto value, or type your own if you know it.
Diameter Entry: Tell the tool if you are typing the outside diameter or the inside diameter. The other one is worked out for you.
Outside or Inside Diameter: Measure across the coil and enter that size.
Wire Diameter (d): Measure the thickness of the wire itself.
Free Length: Enter the length of the spring when nothing is pushing on it.
Total Coils: Count all the coils on the spring, ends included.
End Type: Pick open, closed, or ground ends. This sets how many coils are active.
Length Inside Hooks (extension springs): Measure from the inside of one hook to the inside of the other.
Initial Tension (extension springs): Enter the force needed before the coils start to pull apart. Leave blank for zero.
Body Length (torsion springs): Enter the length of the coiled body only, not the legs.
Leg Length (torsion springs): Enter the length of one leg. Both legs are treated as equal.
Free Position (torsion springs): Enter the leg angle in degrees when the spring is at rest.
Wind Direction (torsion springs): Pick right hand or left hand to match how the coil is wound.
Small and Large Outside Diameter (conical springs): Enter the width of the small end and the wide end.
Applied Force, F (Hooke's Law): Enter the force you put on the spring during your test.
Measured Deflection, x (Hooke's Law): Enter how far the spring moved under that force.
Calculate: Press this to see your spring rate, the math steps, and the chart.
Section 2: Series Spring Rate
Unit System (Section 2): Choose lbs/in or N/mm for the rates you type. This setting is separate from Section 1.
Spring Rate 1 (K₁): Enter the rate of the first spring in the stack.
Spring Rate 2 (K₂): Enter the rate of the second spring.
Spring Rate 3 (K₃): Enter a third rate if you have one. Leave it blank to use just two springs.
Result Unit: Pick lbs/in, N/mm, or kg/mm for your answer.
Calculate Series Rate: Press this to get the combined rate, the math steps, and a bar chart.
What Is Spring Rate?
Spring rate is how stiff a spring is. It tells you how much force it takes to move a spring one unit of distance. A rate of 200 lbs/in means you need 200 pounds of force to squeeze or stretch that spring one inch. A higher number means a stiffer spring. A lower number means a softer spring.
Spring rate is also called spring constant, and engineers write it as k. It is measured in lbs/in, N/mm, or kg/mm. For torsion springs, the rate is torque per degree of turn, like lbf·in/deg or N·mm/deg.
Hooke's Law
Most springs follow Hooke's Law: k = F ÷ x. Force (F) divided by the distance the spring moved (x) gives the rate. If you already have a spring and a scale, this is the fastest way to find its rate. The rate stays the same no matter how far you push, as long as you do not squash the spring flat or stretch it past its limit.
The Engineering Formula
If you do not have the spring in hand, you can find the rate from its shape and material. For a normal round-wire coil spring:
k = (G × d⁴) ÷ (8 × D³ × n)
- G, shear modulus of the wire material (how stiff the metal is)
- d, wire diameter
- D, mean coil diameter (outside diameter minus wire diameter)
- n, number of active coils
Notice that wire size is raised to the fourth power. A small change in wire thickness makes a huge change in stiffness. Doubling the wire diameter makes the spring about 16 times stiffer. Adding more coils or making the coil wider makes the spring softer.
Types of Springs
- Compression springs push back when you squeeze them. Think of pens, valves, and car suspension.
- Extension springs pull back when you stretch them. They often have hooks on each end and some built-in initial tension, which is the force needed before the coils even start to separate.
- Torsion springs twist instead of push or pull. They work in bending, so they use Young's modulus (E) instead of shear modulus (G). Clothespins and garage doors use them.
- Conical springs are cone shaped. The big coils bend first and the small coils bend last, so the rate can climb as the spring closes.
Spring Index
Spring index is C = D ÷ d. It compares coil size to wire size. Most good springs land between 4 and 12. Below 4, the wire is hard to bend and stress builds up in the inside of the coil. Above 12, springs get floppy and tangle with each other in a bin.
Active Coils and End Types
Not every coil helps the spring flex. The coils at each end that sit flat against a surface are dead weight. Closed ends and closed-and-ground ends remove about 2 coils. Open-and-ground ends remove about 1. Open plain ends remove none. Using total coils instead of active coils is a common mistake that makes the answer too soft.
Springs in Series
When you stack springs end to end, each one carries the same load, but the movements add up. So the stack is always softer than the softest single spring. The math uses reciprocals:
1/k = 1/K₁ + 1/K₂ + 1/K₃
Two 200 lbs/in springs in series give 100 lbs/in. This is the opposite of springs side by side (in parallel), where the rates simply add up.
Why Spring Rate Matters
Picking the right rate keeps parts working the way you want. Too stiff, and a suspension rides rough or a latch will not click. Too soft, and a valve leaks or a spring bottoms out solid. Engineers also watch for buckling in tall compression springs, and for natural frequency, which is the speed at which a spring starts to shake on its own. Keep working speeds well below that frequency to avoid coil surge.