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

Rate and force for a compression spring from its dimensions and material, using the standard spring rate formula.

Data verified 2026-09-29 · 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

Each data column on this page is tied to the source it came from. The numbers in square brackets correspond to the table headers above.

#	Source	Type	Revision / method
[1]	ASME B1.1 — Unified Inch Screw Threads	standard	ASME B1.1-2019 — source
[2]	ASTM A615 — Deformed steel bars for concrete reinforcement	standard	ASTM A615/A615M-20 — source
[3]	ASTM E140 — Hardness Conversion Tables	standard	ASTM E140-12b — source
[4]	Values computed in your browser	derived	Evaluated locally from the formulas shown on the page. No data leaves the device.
[5]	ISO 4287 — Surface texture: Profile method	standard	ISO 4287:1997 — source
[6]	ISO 68-1 — Basic profile	standard	ISO 68-1:2023 — source
[7]	NFPA 70 NEC Table 310.16	standard	NEC 2023 (NFPA 70-2023) — source

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

Cross-checked against:

Formulas verified against the corresponding reference chart on this site, so the calculator and the published tables agree

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. The values on this page are compiled from the published standards and cross-checked sources listed above. Where values are derived, the derivation is stated. 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.

Cite This Page

Every value on this page is traceable to the sources listed above. If you use the data in a document, paper or report, cite it as:

Plain text

Engineering Reference. "Spring Rate Calculator." https://refmanual.com/calculators/spring-rate/ (accessed 2026-09-29). 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: 2026-09-29},
  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  - 2026-09-29
N1  - Source: Formulas as shown on this page, n/a — standard engineering relationships, no single governing revision
ER  -

Each row in the tables above also has a permanent link — hover a row and use the # link to cite a single value rather than the whole page.