Quotation
Spring calculators

Spring force calculator

Calculate the force (load) a compression spring exerts and the maximum safe load before the material yields.

Units
in
in
in
Result
Spring rate37.793 lbf/in [6.62 N/mm]
Max safe load37.104 lbf [165.04 N]
Max safe deflection0.982 in [24.94 mm]
Solid height0.689 in [17.50 mm]
Spring index9.00
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Formula

k = G·d⁴ / (8·D³·Na)
F = k·x

Symbols

kspring rate (N/mm or lbf/in)
Gshear modulus of the material (psi or MPa)
dwire diameter (in or mm)
Dmean coil diameter: OD − d (in or mm)
Nanumber of active coils
Fforce at deflection x (lbf or N)
xdeflection from free length (in or mm)

Worked example

Inputs
Wire diameter0.098 in [2.50 mm]
Outer diameter0.984 in [25.00 mm]
Free length2.362 in [60.00 mm]
Total coils7
MaterialOil tempered MB (OT)
Result
Spring rate37.793 lbf/in [6.62 N/mm]
Max safe load37.104 lbf [165.04 N]
Max safe deflection0.982 in [24.94 mm]

Computed by the same engine as the calculator above, using the form's starting values.

Force is rate times deflection (F = k·x). Use the designer to simulate specific operating points and see the stress margin.

The calculator also reports solid height and maximum safe deflection, with the Wahl correction applied to the shear stress.

If you know the required force and travel instead, use the required rate calculator to find out which spring to look for.

Quick tuning: more or less force

More force
  • Thicker wire
  • Smaller outer diameter
  • Fewer active coils
Less force
  • Thinner wire
  • Larger outer diameter
  • More active coils

How to measure your spring

  1. Measure the wire diameter (d) with calipers or a micrometer, away from the ends.
  2. Measure the outer diameter (OD) across the coils. The mean diameter is OD minus d.
  3. Measure the free length (FL) with no load, end to end.
  4. Count the total number of coils. Closed and ground ends reduce the active coil count.
  5. Identify the end type: closed and ground, closed, double closed or open.

Material moduli and density

MaterialShear modulus GElastic modulus EDensity
Carbon steel (MW)11.5 × 10⁶ psi (79.3 GPa)29.5 × 10⁶ psi (203.4 GPa)7.85 g/cm³
Stainless 302 (SS302)10.0 × 10⁶ psi (69.0 GPa)28.0 × 10⁶ psi (193.0 GPa)7.90 g/cm³
Stainless 17-7 (SS177)11.0 × 10⁶ psi (75.8 GPa)29.4 × 10⁶ psi (203.0 GPa)7.81 g/cm³
Stainless 316 (SS316)10.0 × 10⁶ psi (69.0 GPa)28.0 × 10⁶ psi (193.0 GPa)7.98 g/cm³
Oil tempered MB (OT)11.2 × 10⁶ psi (77.2 GPa)29.5 × 10⁶ psi (203.4 GPa)7.85 g/cm³
Chrome silicon (CS)11.2 × 10⁶ psi (77.2 GPa)29.5 × 10⁶ psi (203.4 GPa)7.85 g/cm³
Hard drawn (HD)11.5 × 10⁶ psi (79.3 GPa)29.5 × 10⁶ psi (203.4 GPa)7.85 g/cm³
Phosphor bronze (PB)6.0 × 10⁶ psi (41.4 GPa)14.9 × 10⁶ psi (103.0 GPa)8.86 g/cm³
Beryllium copper (BC)7.0 × 10⁶ psi (48.3 GPa)18.6 × 10⁶ psi (128.0 GPa)8.25 g/cm³
Chrome vanadium (CV)11.2 × 10⁶ psi (77.2 GPa)29.5 × 10⁶ psi (203.4 GPa)7.85 g/cm³

Frequently asked questions

What is the formula for spring force?

F = k·x (Hooke's law): force equals the spring rate times the deflection. A 45 lbf/in spring compressed 0.5 in exerts 22.5 lbf.

What limits the maximum load of a spring?

The shear stress in the wire, corrected by the Wahl factor, compared with the material's allowable stress. Exceeding it causes permanent set (the spring loses free length).

Does force stop growing at solid height?

No: at solid height the spring becomes a rigid tube and force rises abruptly. Running into solid damages the spring and the mechanism, so keep design clearance.

Design the spring and get an instant quote

Open the 3D designer, tune the dimensions and see quantity pricing with a technical drawing and stress analysis.

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