How do I calculate spring rate?

k = G·d⁴/(8·D³·N), where G is the shear modulus, d the wire diameter, D the mean coil diameter and N the number of active coils. For steel, G is about 11,500,000 psi.

What is the spring index and why does it matter?

It is the ratio of mean coil diameter to wire diameter, D/d. Practical springs fall between 4 and 12. Below 4 the spring is hard to wind and stresses concentrate; above 12 it is floppy and may buckle. Six to ten is the comfortable range.

Why does wire diameter matter so much?

Because it appears to the fourth power in the numerator, while coil diameter appears cubed in the denominator. Increasing the wire diameter by 10% raises the rate by about 46%, while increasing the coil diameter by 10% lowers it by about 25%.

How many coils are active?

Active coils are the coils free to deflect. For a spring with closed and ground ends, the two end coils are inactive, so a spring with 10 total coils has 8 active. Using total coils instead of active coils overestimates the spring's stiffness.

What is solid height and why does it matter?

The height of the spring when all coils touch, approximately wire diameter times (active coils + 2). A spring cannot be compressed past solid height, so the available travel is the free length minus solid height — a limit that catches people out when specifying a spring for a short stroke.

Spring Rate Calculator

Sources and scope for this page: Formulas as shown on this page (standard engineering relationships, no single governing revision), covering every value this calculator produces. No independent source check is recorded for this page: the content rests on the sources listed and on the working shown on the page. Full sources, values and limits on this page.

Page last changed 2026-11-08 · based on n/a — standard engineering relationships, no single governing revision

Quick Answer

Spring rate is k = G·d⁴ ÷ (8·D³·N) — wire diameter to the fourth power over coil diameter cubed. That asymmetry is why small changes in wire diameter change the rate dramatically while changes in coil diameter have a much gentler effect.

Compression Spring Rate

Wire diameter, d (in)

Mean coil diameter, D (in)

Active coils, N

Shear modulus, G (psi)

Deflection to check (in)

The Formulas Used

Spring rate: k = G·d⁴ ÷ (8·D³·N)
Spring index: C = D ÷ d Wahl factor: Kw = (4C − 1)/(4C − 4) + 0.615/C
Stress: τ = 8·F·D ÷ (π·d³) × Kw

The Spring Index Is the Design Constraint

The spring index C = D/d is the ratio of coil diameter to wire diameter, and it governs whether a spring is practically manufacturable. Below about 4 the coils are so tight that the spring is difficult to wind and the stress concentration is severe. Above about 12 the spring is floppy and prone to buckling. The practical range is 4 to 12, with 6 to 10 being the comfortable middle.

The Wahl factor in the outputs corrects for two effects the simple stress formula ignores: the direct shear across the wire, and the stress concentration on the inside of the coil, where the radius of curvature is smallest. It is the inside of the coil that fails, and the Wahl factor can raise the computed stress by 15% or more at low spring indices.

Frequently Asked Questions

How do I calculate spring rate?: k = G·d⁴/(8·D³·N), where G is the shear modulus, d the wire diameter, D the mean coil diameter and N the number of active coils. For steel, G is about 11,500,000 psi.
What is the spring index and why does it matter?: It is the ratio of mean coil diameter to wire diameter, D/d. Practical springs fall between 4 and 12. Below 4 the spring is hard to wind and stresses concentrate; above 12 it is floppy and may buckle. Six to ten is the comfortable range.
Why does wire diameter matter so much?: Because it appears to the fourth power in the numerator, while coil diameter appears cubed in the denominator. Increasing the wire diameter by 10% raises the rate by about 46%, while increasing the coil diameter by 10% lowers it by about 25%.
How many coils are active?: Active coils are the coils free to deflect. For a spring with closed and ground ends, the two end coils are inactive, so a spring with 10 total coils has 8 active. Using total coils instead of active coils overestimates the spring's stiffness.
What is solid height and why does it matter?: The height of the spring when all coils touch, approximately wire diameter times (active coils + 2). A spring cannot be compressed past solid height, so the available travel is the free length minus solid height — a limit that catches people out when specifying a spring for a short stroke.

Value Sources

References and calculation methods used for this page are listed below. Numbered markers connect table columns where present. A reference listing does not itself establish that every value has been independently checked.

#	Source	Type	Revision / method
[1]	Values computed in your browser	derived	Evaluated locally from the formulas shown on the page. No data leaves the device.

Data Sources

Standard	Revision	What it covers on this page
Formulas as shown on this page	n/a — standard engineering relationships, no single governing revision	every value this calculator produces

Verification scope

No page-specific independent source review is recorded here. The listed references and formulas explain the basis of the compilation; automated consistency checks do not verify the original sources or establish product conformity.

Derived values — the following values on this page are calculated, not taken directly from the standard:

Value	How it is derived
All outputs	Computed in the browser from the formulas above. No data leaves the device.

Outputs are computed from the formulas shown. Verify against the governing standard for design or acceptance work.

Accuracy and use. Use the source notes and recorded verification scope above to assess each value. Calculated values follow the stated derivations; compilation values may lack a confirmed original document or product condition. No warranty, express or implied, is made as to the accuracy or completeness of this information, and no liability is accepted for any loss or damage arising from its use. Engineering reference data is provided for guidance in preliminary work — before a value is used for design, fabrication or acceptance testing, verify it against the current revision of the governing standard and against your own inspection. The user assumes all risk and responsibility in connection with the use of this information.

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Plain text

Engineering Reference. "Spring Rate Calculator." https://refmanual.com/calculators/spring-rate/ (accessed 2026-11-09). Data from Formulas as shown on this page, n/a — standard engineering relationships, no single governing revision.

BibTeX

@misc{spring-rate,
  title        = {Spring Rate Calculator},
  author       = {{Engineering Reference}},
  howpublished = {\url{https://refmanual.com/calculators/spring-rate/}},
  note         = {Accessed: 2026-11-09},
  source       = {Formulas as shown on this page, n/a — standard engineering relationships, no single governing revision}
}

RIS (EndNote, Zotero, Mendeley)

TY  - ELEC
TI  - Spring Rate Calculator
AU  - Engineering Reference
PB  - Engineering Reference
UR  - https://refmanual.com/calculators/spring-rate/
PY  - 2026
DA  - 2026-11-09
N1  - Source: Formulas as shown on this page, n/a — standard engineering relationships, no single governing revision
ER  -