Calculating the correct rear end spring rate is crucial for optimizing your vehicle's suspension balance, ride quality, and handling characteristics. Whether you are setting up a solid axle muscle car, a dedicated track car, or tuning a coilover setup, understanding the relationship between the sprung weight, motion ratio, and desired frequency is key.
The weight resting on one rear wheel (excluding unsprung weight like wheels/brakes).
Coilovers on axle = 1.0. Inboard springs often 0.5 – 0.9.
0 degrees is perfectly vertical. Larger angles reduce effective rate.
Calculated Wheel Rate:
Motion Ratio Effect:
Angle Correction Factor:
Required Spring Rate:
function calculateRearSpringRate() {
// Get input values
var weightInput = document.getElementById('sprungWeight').value;
var freqInput = document.getElementById('targetFreq').value;
var mrInput = document.getElementById('motionRatio').value;
var angleInput = document.getElementById('springAngle').value;
var errorDiv = document.getElementById('error-msg');
var resultContainer = document.getElementById('result-container');
// Reset display
errorDiv.style.display = 'none';
resultContainer.style.display = 'none';
// Validate inputs
if (weightInput === "" || freqInput === "" || mrInput === "") {
errorDiv.innerHTML = "Please fill in all required fields (Weight, Frequency, and Motion Ratio).";
errorDiv.style.display = "block";
return;
}
var weight = parseFloat(weightInput);
var freq = parseFloat(freqInput);
var mr = parseFloat(mrInput);
var angle = parseFloat(angleInput);
if (weight <= 0 || freq <= 0 || mr = 80) {
errorDiv.innerHTML = "Spring angle is too extreme (>80 degrees). Physics breakdown likely.";
errorDiv.style.display = "block";
return;
}
// 1. Calculate Cycles Per Minute (CPM)
var cpm = freq * 60;
// 2. Calculate Required Wheel Rate (WR)
// Formula derived from: Frequency (CPM) = 187.8 * sqrt(WR / SprungWeight)
// Rearranged: WR = SprungWeight * (CPM / 187.8)^2
var wheelRate = weight * Math.pow((cpm / 187.8), 2);
// 3. Calculate Angle Correction Factor
// Convert degrees to radians
var radians = angle * (Math.PI / 180);
var cosine = Math.cos(radians);
// Effective rate is reduced by cosine^2
var angleFactor = Math.pow(cosine, 2);
// 4. Calculate Required Spring Rate (SR)
// WR = SR * (MotionRatio)^2 * (AngleFactor)
// SR = WR / ( (MotionRatio)^2 * AngleFactor )
var mrSquared = Math.pow(mr, 2);
var denominator = mrSquared * angleFactor;
if (denominator === 0) {
errorDiv.innerHTML = "Calculation error: Effective motion ratio is zero.";
errorDiv.style.display = "block";
return;
}
var springRate = wheelRate / denominator;
// Display Results
document.getElementById('displayWheelRate').innerHTML = wheelRate.toFixed(1) + " lbs/in";
document.getElementById('displayMREffect').innerHTML = "x" + mrSquared.toFixed(3) + " (Leverage)";
document.getElementById('displayAngleFactor').innerHTML = (angleFactor * 100).toFixed(1) + "% Efficiency";
document.getElementById('displaySpringRate').innerHTML = Math.round(springRate) + " lbs/in";
resultContainer.style.display = 'block';
}
Understanding Rear End Spring Rate Math
Calculating the correct spring rate for your rear suspension involves more than just guessing a stiffness. You must account for geometry (Motion Ratio), installation angle, and the actual weight supported by the suspension (Sprung Weight).
1. Sprung Weight vs. Unsprung Weight
The "Sprung Weight" is the portion of the car's weight that is supported by the springs. This includes the chassis, body, engine, and driver. It does not include "Unsprung Weight," which consists of components that move with the road, such as wheels, tires, brakes, and roughly half of the control arms/axle weight.
Tip: To get an accurate Corner Sprung Weight, weigh the corner of the car and subtract the estimated unsprung weight (usually 80-120 lbs for a solid axle rear end).
2. The Motion Ratio (MR)
Springs are rarely mounted directly in line with the wheel. The Motion Ratio describes the leverage the wheel has on the spring.
MR = Spring Travel / Wheel Travel
If the wheel moves 1 inch and the spring compresses 0.8 inches, the MR is 0.8.
On many coilover solid-axle setups, the shock is mounted near the wheel, making the MR close to 1.0.
On inboard setups or control arms where the spring is halfway between the pivot and the wheel, the MR might be 0.5.
Because the spring rate effectiveness is squared relative to the motion ratio, accurate measurement here is critical.
3. Choosing a Suspension Frequency
Suspension frequency (measured in Hertz) represents how fast the suspension oscillates. It normalizes stiffness regardless of vehicle weight.
Application
Target Frequency Range
Luxury / Comfort Street
0.8 Hz – 1.2 Hz
Performance Street / Canyon
1.2 Hz – 1.5 Hz
Track Day / Autocross
1.8 Hz – 2.2 Hz
Dedicated Race Car (Aero)
2.5 Hz +
4. The Formula
The calculator uses the standard natural frequency formula for suspension design:
Frequency (CPM) = 187.8 × √(Wheel Rate / Sprung Weight)
We rearrange this to solve for the required Wheel Rate, and then apply the Motion Ratio and Angle Correction to find the physical spring rate you need to purchase.
Frequently Asked Questions
Why is my calculated spring rate so high?
If your Motion Ratio is low (e.g., 0.5), your spring needs to be significantly stiffer than the wheel rate. A 0.5 motion ratio means the spring has a mechanical disadvantage of 4:1 (since 0.5 squared is 0.25). A 500 lbs/in spring would only provide 125 lbs/in of force at the wheel in this scenario.
Does the angle of the shock matter?
Yes. If your rear shocks/springs are angled inward (common in drag racing or truck setups), they lose efficiency. A spring angled at 20 degrees is less effective than one standing straight up (0 degrees). Our calculator applies a cosine-squared correction to account for this efficiency loss.
What if I have a sway bar?
This calculator determines the primary spring rate required to support the vehicle's weight and handle vertical frequencies (heave). Sway bars add roll stiffness but do not support the vehicle's static weight. You should calculate your primary spring rate first, then tune roll stiffness with sway bars.