Free online extension spring calculator — get the spring rate, estimated initial tension, safe load, maximum extension and hook-stress check in seconds, with a live 3D preview.
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Free Online Tool
Extension Spring Calculator — What It Works Out
This extension spring calculator (also called a tension spring calculator) turns a few dimensions into a specification report: spring rate, estimated initial tension, safe load, maximum extension and the stress that governs, with a live 3D preview. Enter the wire diameter, outside diameter and number of body coils, choose the material and press Calculate. It works in inches or millimetres.
Spring rate and initial tension
Force per unit of extension from the wire, mean diameter, body coils and shear modulus, plus an estimate of the initial tension that holds the coils together.
Safe load and max extension
The lowest of the body shear, hook bending and hook torsion limits, and how far the spring can stretch before reaching it.
Lengths
Body length (close-wound), length inside the hooks and maximum length of the stretched spring.
The formulas the calculator uses
Mean diameter D = OD − d Spring index C = D ÷ d Spring rate k = G · d⁴ ÷ (8 · D³ · Na) (Na = body coils) Load F = Fi + k · x Body length Lb = n · d (close-wound) Max extension xmax = (Fsafe − Fi) ÷ k Stress checks body shear · hook bending (point A) · hook torsion (point B)
d = wire diameter, OD = outside diameter, n = number of body coils, G = shear modulus of the wire, Fi = initial tension. More in our extension spring load and rate guide.
Worked example
Entering these values in the calculator above (metric, mild steel) gives:
Input
Value
Wire diameter
1.5 mm
Outside diameter
15 mm
Body coils
20
Material
Mild steel IS 4454 (G = 80,000 N/mm²)
Result
Value
Mean diameter / spring index
13.5 mm / 9
Spring rate
1.029 N/mm
Initial tension (estimated)
7.5 N
Body length / length inside hooks
30 mm / 43.5 mm
Safe load
30.7 N (3.13 kg)
Maximum extension
22.62 mm
Maximum length
66.12 mm
Governing stress
Hook bending (point A), 700 N/mm²
Check by hand: k = 80,000 × 1.5⁴ ÷ (8 × 13.5³ × 20) = 1.03 N/mm. The load at 10 mm of extension is then about 7.5 + 1.03 × 10 ≈ 17.8 N.
Why hook stress matters
In an extension spring the hooks are usually the most highly stressed part, not the body. Where the hook bends away from the coil the wire is loaded in bending (point A), and further round the hook it is loaded in torsion (point B). That is why the safe load shown above is the lowest of three limits. The calculator assumes the hook bend radius equals the mean radius of the coil; a tighter bend raises the stress and lowers the real limit, so send us your drawing for a hook check.
How to use the extension spring calculator
Choose units. Select English (inch) or Metric (mm). Extension is already selected as the spring type.
Enter the dimensions. Enter the wire diameter, outside diameter and number of body coils. The length inside the hooks is optional; if left blank the calculator estimates it.
Select the material. Choose the wire material (music wire, hard drawn, stainless steel, mild steel and more) and the direction of wind.
Calculate. Enter your name and 10-digit mobile number, then press Calculate.
Review and request a quote. Check the rate, initial tension, safe load, maximum extension and the stress that governs, then send the specification to us on WhatsApp for a quote.
Frequently asked questions
How do I calculate the load of an extension spring?
Load F = Fi + k·x, where Fi is the initial tension, k the spring rate and x the extension beyond the free length inside the hooks. The calculator gives k and Fi; multiply k by your extension and add Fi.
What is initial tension and how is it estimated here?
Initial tension is the force that holds the coils together at rest; the spring does not begin to stretch until the load exceeds it. The calculator estimates a typical value for the spring index. Your manufactured spring can be made with a different initial tension, so tell us if you need a specific value.
Why is the safe load often limited by the hooks?
The hooks usually carry the highest stress. The calculator checks the body in shear, the hook in bending (point A) and the hook in torsion (point B), and reports the lowest as the safe load and the governing stress.
What is the length inside the hooks?
It is the free length of the extension spring measured between the inside of the two hooks. If you leave it blank, the calculator estimates it from the body length and the mean diameter.
How do I find the maximum extension?
Maximum extension = (safe load − initial tension) ÷ spring rate. The calculator shows it together with the maximum length of the spring.
Can I use inches as well as millimetres?
Yes. Switch between English (inch) and Metric (mm) at the top of the calculator; results follow the unit you choose.
Can you manufacture the extension spring I design here?
Yes. Send the specification to Gurudatta Trading Co. on WhatsApp from the results page and we will quote and make it to your drawing or sample, with the hook type you need.