Compression, extension and torsion springs: sizes, rate formula, printed envelopes — dimension sheet
Source: Xem Studio, https://xemstudio.com/objects/springs/  (CC BY 4.0)
Basis: Music-wire (ASTM A228) spring design: k = G·d⁴ / (8·D³·n) with G = 79.3 GPa, D = mean diameter, n = active coils; envelopes in common hobby sizes
Catalog version: 2026-10-20

Sizes: see table below
- Rate k (N/mm) = G d⁴ / (8 D³ n): wire 1.0 mm, OD 10 (D = 9), 10 active coils → 79300 × 1 / (8 × 729 × 10) = 1.36 N/mm. Halve the coils, double the rate. Spring index D/d between 4 and 12 is makeable; 6–9 is comfortable.
- Compression: free length L, solid height ≈ (n + 2) × d, max deflection about 0.8 × (L − solid). Extension: same k, plus initial tension; hooks need D/2 of extra length each end. Torsion: rate in N·mm/deg = E d⁴ / (3667 D n) with E = 207 GPa.
- Printed TPU springs work for small forces (ratchet pawls, detents); PLA/PETG helices break. The files here are envelopes for fit and to check pocket clearance (pocket ID = OD + 0.5; guide rod = ID − 0.5).
- Where they go on the LES rigs: pawl return (torsion 0.8 × 8), diaphragm return and displacer-rod bias (compression 0.5 × 6 × 20), belt tensioner (extension 1.0 × 10 × 50).

type  wire_mm  od_mm  length_mm  coils  rate_n_per_mm  index_d_over_d
compression  0.5  6  20  8  0.47  11.0
compression  0.8  8  25  10  1.09  9.0
compression  1.0  10  30  10  1.36  9.0
compression  1.2  12  40  12  1.36  9.0
compression  1.6  16  50  10  2.18  9.0
extension  0.6  6  30  20  0.41  9.0
extension  1.0  10  50  25  0.54  9.0
torsion  0.8  8  10  6  —  9.0

Files elsewhere (not hosted by Xem Studio; license as stated by the publisher):
- Wikipedia: Spring (device) — web — CC BY-SA 4.0 (text) — https://en.wikipedia.org/wiki/Spring_(device)
- McMaster-Carr: Compression springs (free STEP per part, for your own design use; no redistribution) — STEP, PDF — McMaster-Carr site terms [verify license at link] — https://www.mcmaster.com/products/compression-springs/
- Lee Spring: Spring design formulas — web — Lee Spring site [verify license at link] — https://www.leespring.com/learn-about-springs
- Long Earth Society: Engine and rig builds — web, video — LES site — https://longearthsociety.com/engineering/

Free files (CC BY 4.0, Xem Studio; STEP + STL, 8 parts): https://xemstudio.com/files/hardware/springs/index.json
API: https://xemstudio.com/api/geometry?object=springs