Spring Rate Calculator
Enter your coil spring dimensions and material to calculate the spring rate (stiffness) using the standard torsion-bar formula. Switch between metric and imperial units. The calculator also outputs wheel rate for automotive suspension, spring force at a given deflection, and the natural frequency of a sprung mass, with a full show-your-work panel.
What is spring rate and why does it matter?
Spring rate (also called spring constant or stiffness) is the force a spring exerts per unit of compression or extension. A spring with a rate of 50 N/mm produces 50 newtons of resistance for every millimetre it is compressed, or equivalently 100 N when compressed 2 mm. In Hooke's Law notation this is F = k * x, where F is force, k is the spring rate, and x is deflection. Spring rate governs ride quality, handling, load capacity and fatigue life in virtually every mechanical system that uses springs, from automotive suspensions and bicycle shocks to industrial machinery and electronic switches.
The spring rate formula for helical coil springs
The rate of a helical round-wire compression spring is derived from the theory of torsion in a curved rod: k = G * d^4 / (8 * D^3 * n) where G is the shear modulus of the wire material, d is the wire diameter, D is the mean coil diameter (outer diameter minus wire diameter), and n is the number of active coils. Stiffness grows with the 4th power of wire diameter and shrinks with the cube of coil diameter, so small changes in wire size or coil diameter have a large effect. Doubling the wire diameter makes a spring roughly 16 times stiffer; doubling the coil diameter makes it about 8 times softer.
Active coils and end types
Not every coil in a spring contributes to deflection. End coils that are ground flat and pressed against adjacent coils become inactive, behaving like rigid blocks rather than flexible wire. The most common end style - closed and ground - leaves 2 inactive coils (one at each end), so a spring with 10 total coils has 8 active coils. Open-ended springs have no inactive coils. Double-closed springs lose 4 coils. Specifying the correct end type is essential for accurate spring rate calculations, because the same spring with open versus closed-ground ends will compute to a different rate if the total coil count is held constant.
Wheel rate and motion ratio for automotive suspensions
In a suspension system the spring is rarely mounted directly above the wheel. Instead it sits on a control arm at some distance from the pivot. The motion ratio (MR) is the ratio of spring travel to wheel travel. When the spring is mounted at a point 60% of the way along a control arm, MR is approximately 0.6. Wheel rate is the effective spring stiffness felt at the tyre contact patch: k_w = k * MR^2. Because MR is squared, a spring with a rate of 100 N/mm and a motion ratio of 0.7 delivers only 49 N/mm at the wheel. Ride quality and handling targets are typically specified in wheel rate terms, so you need to work backwards from the desired wheel rate and motion ratio to choose the correct spring. For springs that are not perfectly vertical, the cosine of the angle from vertical also reduces the effective MR.
Shear modulus by material
G is the material property that determines how much a wire twists under shear stress. Standard high-carbon spring steel has G around 80,000 MPa (11.6 million psi). Stainless steel (grade 302) is somewhat more flexible at 69,000 MPa, making stainless springs about 14% softer than the same steel spring. Chrome-silicon alloys (SAE 9254) are slightly stiffer at 82,700 MPa and are common in high-performance and motorsport applications for their superior fatigue resistance at elevated temperatures. Titanium (Ti-6Al-4V) has a shear modulus around 41,370 MPa, roughly half that of steel, so a titanium spring with identical geometry produces about half the rate. This is why titanium springs need a larger wire diameter or fewer active coils to match the rate of a steel equivalent, though they weigh about 40-45% less.
Typical spring rate ranges by application
| Application | Spring rate (N/mm) | Spring rate (lbf/in) | Notes |
|---|---|---|---|
| Mountain bike rear shock | 30 - 70 | 170 - 400 | Depends on rider weight and geometry |
| Economy car - front | 15 - 25 | 85 - 143 | Soft for comfort on poor roads |
| Saloon / sedan - front | 20 - 35 | 114 - 200 | Balance of ride and handling |
| Sports car - front | 35 - 70 | 200 - 400 | Reduced body roll |
| Performance coilover | 50 - 150 | 285 - 857 | Adjustable damping required |
| Track / race car | 100 - 400 | 571 - 2,285 | Very stiff for aerodynamic downforce |
| Industrial machinery | 1 - 1000+ | 6 - 5,700+ | Huge range by application load |
Approximate spring rate ranges for helical compression springs in common applications.
Frequently asked questions
What is the difference between spring rate and spring constant?
They are the same thing. Spring rate is the engineering term used in spring design and automotive suspension; spring constant (often written k) is the physics and dynamics term from Hooke's Law. Both express stiffness in units of force per unit deflection - N/mm, N/m, or lbf/in.
How do I measure spring rate if I do not know the material?
The easiest approach is to compress the spring a known distance and measure the force with a scale or load cell, then divide: k = F / x. For example, if a spring produces 250 lbf when compressed 0.5 in, its rate is 500 lbf/in. You can also estimate G by comparing the measured rate to the calculated rate for two different coil counts, but direct force measurement is simpler and more accurate.
What does wheel rate mean and why is it different from spring rate?
Wheel rate is the effective spring stiffness at the contact patch of the tyre, accounting for the leverage effect of the suspension geometry. Because the spring sits on a control arm at some fraction of the arm length, it moves less than the wheel does - this ratio is the motion ratio (MR). Wheel rate = spring rate * MR^2. A car with a spring rate of 100 N/mm and a motion ratio of 0.7 has a wheel rate of just 49 N/mm. Handling and ride comfort targets are expressed in wheel rate terms.
Does cutting a coil spring increase its rate?
Yes. Cutting coils reduces the number of active coils (n in the formula), which increases the spring rate inversely. Removing 2 coils from a 10-active-coil spring to leave 8 active coils increases the rate by 10/8 = 25%. However, cutting also reduces free length and can alter the end geometry, so it changes ride height and may affect coil bind. It is generally a low-cost tuning method but cannot replicate a properly engineered spring.
What is natural frequency and why does it matter for suspensions?
Natural frequency is the rate at which an unforced sprung mass bounces on its spring, in cycles per second (Hz). For a passenger car body the target is roughly 1.0-1.5 Hz for luxury ride quality, 1.5-2.0 Hz for a sporty feel, and above 2 Hz for race use. The front and rear natural frequencies should be within about 0.2-0.3 Hz of each other to avoid the "pitch-bounce" coupling that causes nausea at motorway speeds. Formula: f = (1 / 2pi) * sqrt(k_wheel / m_corner), where k_wheel is the wheel rate in N/m and m_corner is the quarter-car sprung mass in kilograms.
What is spring index and why does it matter?
Spring index C = D/d (mean coil diameter divided by wire diameter). Springs with a very low index (below 4) are hard to manufacture and develop high stress concentrations in the wire at the inner surface of the coil. Springs with a very high index (above 12-15) tend to buckle sideways under load, especially if the free length is several times the coil diameter. The preferred design range is a spring index of 4-12, which balances manufacturability, fatigue life and stability.
How does material choice affect spring rate?
Material affects spring rate through the shear modulus G. Steel alloys cover a range from about 69,000 MPa (stainless) to 82,700 MPa (chrome-silicon), a difference of about 20%. Titanium sits around 41,370 MPa, roughly half of steel, so a titanium spring of identical geometry produces half the rate of a steel one. To match a steel spring rate in titanium you need a larger wire diameter or fewer coils, which is why titanium springs are lighter but larger in some dimension than their steel equivalents.
What is the difference between free length, solid height and working deflection?
Free length is the unloaded length of the spring. Solid height is the length when every coil is in contact: solid height = total coils * wire diameter for closed-ground springs. Working deflection is the range of compression between the loaded (installed) height and the maximum compressed height before reaching solid height. A well-designed spring should have at least 10-15% of its total deflection as additional "clash clearance" above solid height to prevent coil clash under bump loads, which would cause a hard stop and rapid fatigue.