Spring Rate Explained: How to Calculate the Rate Your Car Needs

Spring rate is the force it takes to compress a spring by one unit of travel, written as lb/in, kg/mm or N/mm. A 400 lb/in spring needs 400 pounds to compress one inch and 800 pounds to compress two, and 1 kg/mm equals about 56 lb/in.

To pick a rate, work backward from the stiffness you want at the tire, then correct for where the spring is mounted. Our free spring rate calculator does the math for you, and this guide shows the formulas behind it so you can check the result.

Most complete coilover kits on our store cost $799 to $1,195 and come with springs already chosen for the car. Single coilover springs from Aldan American, Eibach and QA1 start at about $102, and Aldan American alone lists rates from 100 to 750 lb/in.

Spring rate units and conversions

US brands such as Aldan American list rates in lb/in. Most import coilover brands, including Megan Racing and SF Racing, list kg/mm. Use these conversions:

• 1 kg/mm = 55.997 lb/in = 9.807 N/mm
• 1 lb/in = 0.0179 kg/mm = 0.175 N/mm

How to calculate the rate of a coil spring

If you have a spring with no markings, the simplest test is to load it with a known weight and measure how far it compresses: rate = force ÷ deflection. A spring that compresses 0.5 in under 200 lb is a 400 lb/in spring.

You can also calculate it from the spring's dimensions:

k = G × d⁴ ÷ (8 × D³ × n)

• G is the shear modulus of the wire. Spring makers list 11.5 million psi for chrome silicon, chrome vanadium and music wire.
• d is the wire diameter.
• D is the mean coil diameter: outside diameter minus wire diameter.
• n is the number of active coils. Closed or ground end coils don't flex, so they are not counted.

Example: 0.5 in wire, 2.5 in ID (so 3.5 in OD and a 3.0 in mean diameter) and 8 active coils gives 11,500,000 × 0.0625 ÷ (8 × 27 × 8) = about 416 lb/in. Take one active coil away and it rises to about 475 lb/in. That is why cutting a spring makes it stiffer as well as shorter. Treat the formula as a check; the manufacturer's listed rate is the number to trust.

Spring rate vs wheel rate

The spring is rarely mounted right at the wheel. On most suspensions it sits partway along a control arm, so the spring moves less than the wheel does. The ratio of spring travel to wheel travel is the motion ratio (MR), and the rate the tire actually feels is the wheel rate:

Wheel rate = spring rate × MR²

The ratio is squared because it counts twice: the spring moves less, and it has less leverage over the wheel. A 500 lb/in spring at a 0.7 motion ratio gives 500 × 0.49 = 245 lb/in at the wheel. The same spring on a strut at 0.95 gives about 451 lb/in. A spring mounted at a lean loses a little more rate again, so a heavily angled coilover is softer at the wheel than this formula shows.

To measure your own motion ratio, take the spring off, raise the wheel 1 inch and measure how far the spring seat moves. Note that some engineers define motion ratio the other way up (wheel travel over spring travel), so check which one a source uses before you plug numbers in.

Picking a rate with ride frequency

Ride frequency is how fast the car bounces on its springs, in hertz (Hz), so light and heavy cars compare on the same scale:

f = (1 ÷ 2π) × √(wheel rate ÷ sprung corner mass)

In US units, with the wheel rate in lb/in and the corner weight in lb, that becomes: wheel rate = corner weight × (2π × f)² ÷ 386.1. The 386.1 is gravity in inches per second squared, which turns pounds of weight into mass.

Published starting points from HP Academy are about 0.5 to 1 Hz for ordinary road cars, 1 to 1.5 Hz for high-performance road cars, 1.5 to 2.5 Hz for low-downforce circuit cars, 2 to 3.5 Hz for medium-downforce race cars, and 1 to 2 Hz for rally cars. Our calculator uses 1.2 Hz for a comfortable daily, 1.6 Hz for a sporty street car, 2.0 Hz for street and track days, 2.4 Hz for drift or track cars without aero, and 2.9 Hz for race cars with real downforce.

Worked example

Take a 3,300 lb car with 55% of its weight on the front, about 90 lb of unsprung weight per corner (wheel, tire, brake, hub and half the arms) and MacPherson struts at a 0.95 motion ratio.

1. Sprung front corner weight: 3,300 × 0.55 ÷ 2 − 90 = 817.5 lb.
2. Wheel rate at 1.6 Hz: 817.5 × (2π × 1.6)² ÷ 386.1 = about 214 lb/in.
3. Spring rate: 214 ÷ 0.95² = about 237 lb/in, or 4.2 kg/mm.

The rear of the same car carries 3,300 × 0.45 ÷ 2 − 90 = 652.5 lb per corner. With the coilover on a lower arm at 0.7, it needs a much stiffer spring for the same frequency.

Notice that the rate goes up with the square of the frequency. Going from 1.6 to 2.0 Hz sounds small, but it needs a spring about 56% stiffer. Run your own numbers in the spring rate calculator.

Real spring rates in kits we sell

Here is what brands ship on some popular coilover kits, straight from the listings.

A higher spring rate on one end does not always mean that end is stiffer at the wheel. The Camaro's 12 kg/mm rear spring, for example, works through its own rear motion ratio, so compare wheel rates, not spring rates.

Linear, progressive, helper and tender springs

• Linear springs have the same rate through their travel. Most coilover main springs are linear, which makes the car predictable.
• Progressive springs get stiffer as they compress. Many lowering springs are progressive, for a softer ride over small bumps and more support in corners.
• Tender springs sit on top of the main spring and give a softer initial rate until they close up, then the main spring takes over. Two springs stacked act in series: combined rate = 1 ÷ (1/k1 + 1/k2). An 8 kg/mm main with a 2 kg/mm tender starts at 1.6 kg/mm.
• Helper springs are very light springs that only keep the main spring seated at full droop. Eibach says its helpers have so little rate that they do not affect handling.

Choosing coilover springs

1. Inside diameter. It must match the spring seat. 2.5 in is the most common ID for US-style coilovers, and many import kits use 62 mm, such as Godspeed's custom springs.
2. Free length. Long enough to stay seated at full droop, short enough to leave thread for height adjustment.
3. Rate. Start from the frequency you want, then compare with the rates on kits for your car.
4. Damper match. A damper is valved for a range of spring rates. Going far stiffer than that makes the car skip over bumps.
5. Balance. Change front and rear together, or the car's balance shifts.

Common mistakes

• Comparing spring rates between cars without accounting for motion ratio.
• Mixing up kg/mm and lb/in. An "8" spring is 8 kg/mm, or 448 lb/in.
• Using total curb weight instead of sprung corner weight.
• Going very stiff on a street car. A lowered car needs a bit more rate, but too much makes it skip over bumps.

Our picks

• Aldan American 350 lb/in, 2.5 in ID, 9 in spring, $101.99 each. A street rate for 2.5 in ID coilovers.
• Aldan American 450 lb/in, 2.5 in ID, 8 in spring, $131.99 each. For heavier cars or a firmer street and track setup.
• Godspeed custom coilover springs, 180 mm, 62 mm ID, pair, $100. Lets you pick 6 to 16 kg/mm for import-style coilovers.
• Megan Racing EZ II coilovers for Miata 1990-2005, $799. A complete kit with 8 and 6 kg/mm springs already matched.
• Megan Racing EZ coilovers for Civic 2016+ hatchback, $849. A street-friendly 6 and 5 kg/mm setup.

FAQ

How do I convert kg/mm to lb/in?

Multiply by 55.997, or about 56. A 10 kg/mm spring is about 560 lb/in.

How do I calculate the spring rate I need?

Find the sprung weight on one corner, pick a ride frequency, and work out the wheel rate with wheel rate = corner weight × (2π × f)² ÷ 386.1. Then divide by the motion ratio squared to get the spring rate.

What is a good spring rate for a street car?

It depends on the car's weight and motion ratio, so aim for a ride frequency instead. High-performance road cars usually sit around 1 to 1.5 Hz, and sporty street coilovers a bit higher.

Should the front and rear rates be the same?

Not usually. Front and rear corner weights and motion ratios differ, and the balance between them changes how the car handles.

Sources

• Penske Racing Shocks: spring rate, wheel rate and motion ratio
• HP Academy: suspension frequency
• Eibach motorsport catalog: main, tender and helper springs
• Acxess Spring: spring rate formula
• Acxess Spring: properties of spring wire materials