Extension Spring Load & Rate Formula (with worked example)
Quick answer: Extension spring load is F = F0 + k·x, where F0 is initial tension, k the spring rate (same formula as a compression spring) and x the extension beyond free length.
By Gurudatta Trading Co., Mumbai · Updated 2026-09-28
The formulas
k = G · d⁴ / (8 · D³ · Na) and F = F0 + k · x
- F0 — initial tension: the force needed to start separating the coils
- k — spring rate (N/mm), where Na is the number of body coils
- x — extension beyond free length (mm)
Worked example
Steel spring, d = 1.5 mm, outer diameter 15 mm (D = 13.5 mm), 20 body coils, G = 79300 MPa: k ≈ 1.02 N/mm. With an initial tension of 5 N, the load at 20 mm extension is 5 + 1.02 × 20 ≈ 25.40 N.
Initial tension depends on how the spring is coiled and cannot be reduced below what the wire and diameter allow; hooks are usually the highest-stress area. Use the free Spring Rate Calculator for a design check, and see the compression spring formula for background.
Need springs made to your specification?
Gurudatta Trading Co. (Mumbai, since 2000, ISO 9001:2015) manufactures compression, extension and torsion springs to drawing or sample. Use the free Spring Rate Calculator or message us on WhatsApp.
FAQs
What is initial tension in an extension spring?
It is the force that holds the coils together; the spring does not begin to extend until the applied load exceeds it.
How do I calculate the load of an extension spring?
Load equals initial tension plus spring rate times extension: F = F0 + k·x.
Is the extension spring rate formula the same as for compression springs?
Yes, the rate formula is the same, using the number of body coils.