Spring Rate Calculator — Geometry & Measured Loads
Estimate a compression spring rate from round-wire geometry, or measure rate between two force and loaded-length readings. Compare the model and its provenance.
Estimate a compression spring’s rate from its dimensions, or find the rate between two measured loads. Keep the model and measurements distinct.
Wire 2 mm, mean diameter 16 mm, 8 active coils, shear modulus 79.3 GPa.
Chart and diagram show the entered model; they do not establish an allowable operating range.
For round-wire, close-coiled cylindrical compression springs in their linear elastic region. Rate does not establish strength, fatigue life, buckling resistance or suitability. Measured rate describes only the interval between your readings; it is not instrument accuracy.
Calculation record
Illustrative example: k = Gd⁴/(8D³n) = 4.840087890625 N/mm.
Formula, definitions and sources
Geometry: k = Gd⁴ / (8D³n). D is mean diameter; n is active coils. Ideal load F = k(L₀ − L); stored energy E = ½F(L₀ − L), with length in metres for joules. The geometry model assumes zero load at the entered free length. A supplied solid length is an additional geometric limit, not a safe compression limit.
Measurements: k = (F₂ − F₁)/(L₁ − L₂); interpolate F(L) = F₁ + k(L₁ − L). Reversing both pairs does not change the result. No extrapolation or assumed zero-load length. Coils should not contact during either reading. Progressive springs and changing active-coil counts need a different model.
Shown digits describe arithmetic, not measurement precision. Inches = 25.4 mm; 1 lbf = 4.4482216152605 N. Shear modulus is supplied explicitly; the example 79.3 GPa is illustrative.
