# Compression springs, wire Ø0.5–1.6, OD 6–16

> How do I calculate the rate of a compression spring?

- Category: Hardware › Motion
- Kind: Hardware
- Basis: Helical compression spring with closed ends; rate k = G d⁴ / (8 D³ n), D = OD − d
- Page: https://xemstudio.com/objects/compression-springs/ · JSON: https://xemstudio.com/api/geometry?object=compression-springs · Plain text: https://xemstudio.com/objects/compression-springs/sheet.txt
- License: dimension sheet CC BY 4.0 (Xem Studio); linked files under their publishers' licenses

**Exact dimensions.** Every file is drawn at true size with no printing tolerance. The holes and pins that meet another part are listed below under Mating features, with the fit each joint needs; open those by your printer's or process's clearance before making the part.

## Notes

- Envelopes at exact wire Ø, OD, ID (OD − 2 × wire) and free length, with closed (flat-ring) ends.
- Rate k = G d⁴ / (8 D³ n): G the shear modulus of the wire, d the wire Ø, D the mean coil Ø (OD − d), n the active coils. Halving the coils doubles the rate.
- Spring index D/d between 4 and 12 is makeable, 6–9 comfortable; these are 9 except the 0.5 × 6 at 11.
- Solid height is about (n + 2) × d; usable deflection about 0.8 × (free length − solid height). A pocket for one is drawn at the OD and a guide rod at the ID (see Mating features).

## Mating features (exact size; open press / slide / run / socket by your process clearance, leave designed and clamp as drawn)

| feature | exact | mates with | fit | files |
|---|---|---|---|---|
| spring OD | OD (6–16) | pocket of the same Ø | socket | all |
| spring ID | OD − 2 × wire | guide rod or arbor of the same Ø | socket | all |

## Sizes

| file | wire Ø | OD | ID | free length | coils | index D/d |
|---|---|---|---|---|---|---|
| compression-d0.5-od6-l20 | 0.5 | 6 | 5.0 | 20 | 8 | 11.0 |
| compression-d0.8-od8-l25 | 0.8 | 8 | 6.4 | 25 | 10 | 9.0 |
| compression-d1-od10-l30 | 1.0 | 10 | 8.0 | 30 | 10 | 9.0 |
| compression-d1.2-od12-l40 | 1.2 | 12 | 9.6 | 40 | 12 | 9.0 |
| compression-d1.6-od16-l50 | 1.6 | 16 | 12.8 | 50 | 10 | 9.0 |

## Where the files are

- Wikipedia: [Spring (device)](https://en.wikipedia.org/wiki/Spring_(device)) — web — CC BY-SA 4.0 (text)
- McMaster-Carr: [Compression springs (free STEP per part, for your own design use; no redistribution)](https://www.mcmaster.com/products/compression-springs/) — STEP, PDF — McMaster-Carr site terms (verify at link)
- Lee Spring: [Spring design formulas](https://www.leespring.com/learn-about-springs) — web — Lee Spring site (verify at link)
- Long Earth Society: [Engine and rig builds](https://longearthsociety.com/engineering/) — web, video — LES site

## Free STEP/STL (5 parts, CC BY 4.0, Xem Studio)

Index: https://xemstudio.com/files/hardware/compression-springs/index.json

- compression-d0.5-od6-l20: [STEP](https://xemstudio.com/files/hardware/springs/compression-d0.5-od6-l20.step) · [STL](https://xemstudio.com/files/hardware/springs/compression-d0.5-od6-l20.stl) — compression spring envelope: wire Ø0.5, OD 6, ID 5, 20 mm free length, closed ends, 8 coils
- compression-d0.8-od8-l25: [STEP](https://xemstudio.com/files/hardware/springs/compression-d0.8-od8-l25.step) · [STL](https://xemstudio.com/files/hardware/springs/compression-d0.8-od8-l25.stl) — compression spring envelope: wire Ø0.8, OD 8, ID 6.4, 25 mm free length, closed ends, 10 coils
- compression-d1-od10-l30: [STEP](https://xemstudio.com/files/hardware/springs/compression-d1-od10-l30.step) · [STL](https://xemstudio.com/files/hardware/springs/compression-d1-od10-l30.stl) — compression spring envelope: wire Ø1.0, OD 10, ID 8, 30 mm free length, closed ends, 10 coils
- compression-d1.2-od12-l40: [STEP](https://xemstudio.com/files/hardware/springs/compression-d1.2-od12-l40.step) · [STL](https://xemstudio.com/files/hardware/springs/compression-d1.2-od12-l40.stl) — compression spring envelope: wire Ø1.2, OD 12, ID 9.6, 40 mm free length, closed ends, 12 coils
- compression-d1.6-od16-l50: [STEP](https://xemstudio.com/files/hardware/springs/compression-d1.6-od16-l50.step) · [STL](https://xemstudio.com/files/hardware/springs/compression-d1.6-od16-l50.stl) — compression spring envelope: wire Ø1.6, OD 16, ID 12.8, 50 mm free length, closed ends, 10 coils

## How it fits

### Goes in or on
- [Metric shafts Ø3 to Ø10 with D-flats and clip grooves](https://xemstudio.com/objects/metric-shafts/): guide rod at the spring ID

### Alternatives
- [Extension springs, wire Ø0.6 and Ø1.0](https://xemstudio.com/objects/extension-springs/): pulls instead of pushes

## Questions

**How do I calculate a compression spring rate?**

k = G·d⁴ / (8·D³·n), with d wire Ø, D = OD − d, n active coils, G the wire's shear modulus.

**What is the solid height?**

About (coils + 2) × wire Ø: the 10-coil, 1.0 wire, 30 long spring is about 12 mm solid.

## Fits with

- [Extension springs, wire Ø0.6 and Ø1.0](https://xemstudio.com/objects/extension-springs/)
- [Torsion spring wire Ø0.8, OD 8, 6 coils](https://xemstudio.com/objects/torsion-spring/)
- [Pawl 24 mm with a Ø3 pivot for the Ø40 ratchet wheels](https://xemstudio.com/objects/ratchet-pawl/)