Work out the rate of a helical compression spring from its wire diameter, coil diameter, number of active coils and material. Add the free length to get solid height, travel, force at solid and a load-deflection table.
Last updated:
Units
Spring geometry
Uncompressed length; enables solid-force and pitch results
Material
GPa in metric mode, Mpsi (10⁶ psi) in imperial mode
Compression distance for the load and stress results
Enter your values to see the result.
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How to use the Spring Rate Calculator
Pick metric or imperial units.
Enter the wire diameter, coil diameter and active coils, and say whether the diameter is OD, ID or mean.
Choose the end type and material (or enter a custom G).
Add the free length to see solid height, travel and force at solid.
Enter a deflection to get the load and stress at that point.
Example: music wire (G = 81.7 GPa), d = 2 mm, OD = 20 mm so D = 18 mm, 8 active coils. k = 81,700 × 2⁴ / (8 × 18³ × 8) ≈ 3.50 N/mm (about 20 lb/in). With closed and ground ends Nt = 10, so the solid height is 10 × 2 = 20 mm.
Shear modulus of spring materials
Material
G (GPa)
G (10⁶ psi)
Notes
Music wire, A228
81.7
11.85
Strong, common for small springs
Hard-drawn steel, A227
80.7
11.7
Low cost, static loads
Oil-tempered steel, A229
77.2
11.2
General purpose, larger sizes
Chrome vanadium, A232
77.2
11.2
Shock and fatigue loads
Chrome silicon, A401
77.2
11.2
High stress, higher temperature
Stainless steel 302, A313
69.0
10.0
Corrosion resistant
Phosphor bronze, B159
41.4
6.0
Electrical contacts
Beryllium copper, B197
44.8
6.5
Conductive, non-magnetic
Values are typical textbook figures (as in Shigley's Mechanical Engineering Design); suppliers may quote slightly different moduli.
End types and coil counts
End type
Total coils Nt
Solid height
Plain (open)
Na
(Nt + 1)·d
Plain and ground
Na + 1
Nt·d
Closed (squared), not ground
Na + 2
(Nt + 1)·d
Closed and ground
Na + 2
Nt·d
Tip: design so the working deflection stays below about 85% of the travel to solid, and keep the free length under about four times the mean diameter, or support the spring on a rod or in a bore to prevent buckling.
Frequently asked questions
What is the formula for spring rate?
For a helical compression spring k = G·d⁴ / (8·D³·Na), where G is the shear modulus of the wire, d the wire diameter, D the mean coil diameter and Na the number of active coils.
How do I count active coils?
Active coils are the ones free to deflect. For closed (squared) ends subtract 2 from the total coil count; for plain ends with ground tips subtract 1; for plain open ends all coils are active.
How is solid height calculated?
Solid height is the length when every coil touches. For ground ends it is total coils × wire diameter; for unground ends add one more wire diameter: (Nt + 1) × d.
Why does coil diameter matter so much?
Rate falls with the cube of the mean diameter and rises with the fourth power of wire diameter. Making the coil 10% larger cuts the rate by about 25%, while 10% thicker wire raises it by about 46%.
How do I convert N/mm to lb/in?
1 N/mm = 5.71 lb/in, and 1 lb/in = 0.1751 N/mm. A 10 N/mm spring is about 57.1 lb/in.
What is a good spring index?
The spring index C = D/d is ideally between about 4 and 12. Lower values are hard to coil and highly stressed on the inside of the coil; higher values tangle easily and can buckle.
Is this accurate enough for manufacturing?
It uses the standard textbook formulas, which usually agree with measured rates within a few percent. Wire tolerance, end coils and set-removal change the real rate, so verify critical springs with the manufacturer.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.