Spring Rate Calculator — Compression Spring Rate, Load & Stress

Calculate spring rate (k), load, deflection, shear stress, spring index, Wahl factor, pitch and solid height — with live formulas. Works in metric (mm / N) or imperial (inch / lbf) units.

What is spring rate (spring constant)?

Spring rate, also called spring constant or stiffness, is the force a spring develops per unit of deflection. It is written k and expressed in newtons per millimetre (N/mm) in metric units or pounds-force per inch (lbf/in) in imperial units. A spring rated at 5 N/mm produces 5 N of force for every millimetre it is compressed; compress it 10 mm and it pushes back with 50 N. Rate is a property of the spring’s geometry and material alone — it does not change with how far the spring is compressed, as long as the coils stay within their elastic range and do not touch.

The spring rate formula, explained term by term

For a helical compression spring made from round wire, the rate is calculated with the classic formula:

Each symbol carries real design meaning. G is the shear modulus of the spring material — roughly 79.3 GPa for music wire and 69–72 GPa for stainless and chrome-silicon grades. d is the wire diameter, D is the mean coil diameter (outside diameter minus one wire diameter) and n is the number of active coils, that is the coils that actually deflect after the closed end coils are discounted. Because the formula is a pure geometry-and-material relationship, it applies equally to metric and imperial units — simply keep the unit set consistent.

Why wire diameter dominates: the d⁴ and D³ sensitivity

The exponents in the formula explain most spring design surprises. Wire diameter enters at the fourth power, so increasing d by 10% raises the rate by roughly 46%; doubling it multiplies the rate sixteen-fold. Mean coil diameter enters at the third power, so a 10% larger D lowers the rate by about 25%. Active coils act linearly: doubling n halves the rate. This is why a drawing that changes wire diameter by a fraction of a millimetre can shift the load curve far more than most engineers expect, and why wire diameter is the first variable to iterate when chasing a target rate.

Spring rate vs load vs stress — they are not the same thing

Rate (k) is stiffness; load (F) is the force at a given deflection, F = k · x; and stress (τ) is the internal material load that decides whether the spring survives. A spring can have a comfortable rate and still fail because the working stress is too high, or it can have a safe stress and an unusable rate. The inner-fibre shear stress is estimated with the Wahl-corrected torsion formula τ = K_w · 8 · F · D / (π · d³), where K_w accounts for curvature and direct shear. Tabs 2 and 3 of the calculator above compute load, stress, pitch and solid height so the three quantities can be checked together before a design is committed.

Which shear modulus (G) should I use?

Use the value for the actual wire grade. Music wire and oil-tempered spring steel are close to 79.3 GPa; stainless 302/304 and chrome-vanadium are around 69 GPa; chrome-silicon (60Si2Mn) is about 72–78.5 GPa; Inconel 718 is roughly 76 GPa; and non-ferrous wires such as phosphor bronze and brass are much lower. The reference table below lists the values used by this calculator. If your material is not listed, select custom and enter its shear modulus directly — G is a published material constant, not something to guess.

How to use this spring rate calculator

Enter wire diameter, mean coil diameter, active coils and the material, and the spring rate updates instantly. Switch to the load tab and enter a working deflection to see the force in newtons, kilograms-force and pounds-force and the resulting shear stress; switch to the geometry tab to check pitch and solid height. Use the metric/imperial buttons to work in inches and pounds if your drawing is imperial. The flags warn you when the spring index falls outside the practical 4–12 band or when the computed stress exceeds a typical static allowable value.

Common spring design mistakes

The most frequent errors are: mixing unit systems inside one calculation; counting total coils instead of active coils; forgetting that closed ends add two dead coils to the solid height; ignoring the spring index until after the drawing is frozen; and specifying a rate without specifying the load or stress limit that goes with it. A spring that meets a rate target but sits outside the index band is expensive to wind and prone to fatigue. Checking rate, index and stress together — exactly what this tool does — catches those problems before a quotation is placed.

Related spring resources

• Compression springs — the product range this calculator is built around.
• Torsion springs — rate here is a torque per degree, not a force per millimetre.
• Extension springs — add initial tension on top of the rate times deflection.
• How to get a custom spring quote — what to send us so we can confirm your design fast.

Shear modulus reference (G)

Frequently asked questions