Formula and method
k = G d⁴ / (8 D³ nₐ). Multiply G in GPa by 1000 to obtain N/mm². With d and D in mm, k is in N/mm; multiply by 1000 for N/m.
Worked example
With G=80 GPa, d=2 mm, D=20 mm and nₐ=8, the theoretical rate is 2.5 N/mm, or 2500 N/m. These are example parameters, not a manufacturer’s rating.
Assumptions and limits
- 80 GPa is an example input, not a value inferred from a material name. Replace it with the shear modulus for the actual material, condition and temperature.
- D is the mean coil diameter: if the outside diameter OD is known, D = OD − d. D must exceed d. Active coils differ from total coils; no end-coil deduction is assumed.
- Only the stated geometric model’s rate is estimated. Allowable load, travel, solid height, fatigue, buckling and resonance are not calculated; the result does not establish suitability or safety.
- Variable-diameter, variable-pitch, conical, extension, torsion and non-round-wire springs are outside scope. Nonlinear behaviour near initial contact or coil bind needs separate assessment.
Frequently asked questions
Can I enter outside diameter or total coils directly?
No. Supply mean coil diameter and active coils. End shape, contact and manufacturing details affect the active portion.
Does the rate tell me the maximum load?
No. Maximum load also depends on strength, stress, travel, coil bind, stability and operating conditions. Those checks are not performed here.
Why is there no steel or stainless-steel preset?
Shear modulus depends on material grade, condition and temperature. Entering G from the relevant data avoids treating an example as a guaranteed material property.