How to use this calculator
- Enter the wire and coil geometry. Enter the wire diameter d and the mean coil diameter D. The spring index C = D/d should be roughly 4–12.
- Enter the coils and free length. Enter the active coil count Nₐ and the free length L₀.
- Pick the material and end type. Select the spring material (this sets the shear modulus G and allowable stress) and the end type (closed & ground, closed, or open).
- Enter the working deflection. Enter the deflection x to get the force and Wahl-corrected stress at that point.
- Read the results. Read the spring rate, solid height, Wahl-corrected shear stress versus the allowable, the buckling verdict and the load–deflection curve.
How it works
The spring rate is k = G·d⁴ / (8·D³·Nₐ), where G is the
material shear modulus, d the wire diameter, D the mean
coil diameter and Nₐ the active coil count. A thicker wire or a
smaller coil makes the spring much stiffer — the wire diameter enters to the
fourth power and the coil diameter to the third.
Shear stress is corrected for coil curvature with the Wahl factor Kᵥᵥ = (4C−1)/(4C−4) + 0.615/C, where C = D/d is the
spring index. The corrected stress at a load F is
τ = Kᵥᵥ · 8·F·D / (π·d³)
and it is compared against the material’s maximum allowable static torsional
stress. That allowable is a fraction of the tensile strength, and tensile
strength is itself size-dependent — Sᵤₜ(d) = A / d^m — so the same
material allows a higher stress in thinner wire.
Solid height comes from the total coils and wire diameter (the end type sets how
many inactive coils there are), and a buckling check compares the
effective slenderness α·L₀/D against the critical value, assuming the
ends are seated between parallel flat surfaces. Formulas follow standard
spring-design practice (e.g. Shigley, Mechanical Engineering Design,
chapter 10). Use the spring buckling calculator
when you need critical deflection, critical load and no-buckling free length.
Approximate spring pitch is shown as a geometry screen: p ≈ d + (L₀ − Ls) / Nₐ It spreads the available open travel evenly across the active coils. Treat it as a first-pass body-pitch estimate, not as a replacement for a spring drawing with end transitions, grinding allowance and tolerances.
Compression spring design, solid height and coil bind checks
Use this as a compression spring design calculator when you need one worksheet for rate, working load, corrected stress, solid height and buckling. The same inputs cover common spring calculator compression searches: wire diameter, mean coil diameter, active coils, free length, material and working deflection. For the exact search paths, use the helical spring calculator and spring stress correction calculator pages.
As a spring rate calculator compression workflow, the rate comes from geometry and material rather than from two measured load points. As a coil bind calculator or solid height calculator, it compares working deflection against travel to solid so the load point is not accidentally beyond the available compression stroke.
If you only need stiffness, use the simpler spring rate calculator. If you measured two load points instead of the geometry, use the spring constant calculator. To work backward from a target load and travel, start with the spring design calculator or solve the wire directly with the spring wire size calculator. For a stability-only view, use the spring buckling calculator.
Worked example
Verified against the live calculator
Music wire, d = 1.0 mm, mean coil D = 10 mm (so the
spring index C = 10), Nₐ = 8 active coils, free length
L₀ = 40 mm, closed & ground ends. With G = 79.3 GPa
the rate is k ≈ 1.24 N/mm. At 10 mm of deflection the
force is F ≈ 12.4 N. The Wahl factor is Kᵥᵥ ≈ 1.14,
giving a corrected shear stress of τ ≈ 361 MPa — comfortably below
the ≈ 995 MPa allowable for 1 mm music wire. The solid height is
10 mm, leaving 30 mm of travel, and the slenderness L₀/D = 4
is within the no-buckling region for ground ends. Those are exactly the numbers the
calculator shows when you load this page.
Spring material data
Shear modulus G, Young’s modulus E and the maximum
allowable static stress for common spring materials. The calculator uses these
automatically when you pick a material; the table is here so you can audit the
source.
| Material | Standard | G — GPa (Mpsi) | E — GPa | Max static τ | Notes |
|---|---|---|---|---|---|
| Music wire | ASTM A228 | 79.3 (11.5) | 207 | 45% of Sᵤₜ | Highest tensile strength; best for small-diameter springs. |
| Oil-tempered | ASTM A229 | 77.2 (11.2) | 207 | 50% of Sᵤₜ | General-purpose; not for shock or fatigue service. |
| Hard-drawn | ASTM A227 | 77.2 (11.2) | 207 | 45% of Sᵤₜ | Lowest cost; general-purpose static service. |
| Chrome silicon | ASTM A401 | 77.2 (11.2) | 207 | 50% of Sᵤₜ | High stress; shock, fatigue and moderately elevated temperature. |
| Chrome vanadium | ASTM A232 | 77.2 (11.2) | 207 | 50% of Sᵤₜ | Shock loads and moderately elevated temperature. |
| Stainless 302/304 | ASTM A313 | 69 (10) | 193 | 35% of Sᵤₜ | Corrosion resistant; lower shear modulus and allowable stress. |
Source: Standard spring-design references (Shigley, Mechanical Engineering Design, Tables 10-4/10-5/10-6; ASTM wire standards). Verify against the governing standard and supplier data for production design.
Allowable stress is shown as a fraction of tensile strength because tensile
strength varies with wire diameter: Sᵤₜ(d) = A / d^m. The calculator
evaluates that at your wire size, so a 0.5 mm music wire is treated as stronger
than a 5 mm one.
Frequently asked questions
How do I calculate the spring rate of a compression spring?
Use k = G·d⁴/(8·D³·Nₐ), where G is the shear modulus, d the wire diameter, D the mean coil diameter and Nₐ the active coils. Enter those above and the calculator solves it. Spring rate formula explained →
What is the Wahl correction factor and do I need it?
It corrects the shear stress for the extra stress on the inner coil surface caused by curvature: Kᵥᵥ = (4C−1)/(4C−4) + 0.615/C, where C = D/d. Use it for any real spring — skipping it under-predicts the peak stress. The Wahl correction factor →
Will my spring buckle?
A compression spring buckles when it is too slender for its deflection. This page flags it from free length, mean coil diameter and end type using effective slenderness. For critical deflection, no-buckling free length and required mean diameter, use the spring buckling calculator.
Is this also a solid height calculator?
Yes. Solid height is calculated from wire diameter, active coils and end type. Closed & ground ends use Ls = d·(Nₐ + 2), closed/squared ends use Ls = d·(Nₐ + 3), and open/plain ends use Ls = d·(Nₐ + 1).
Can I use this as a spring pitch calculator?
Yes, as a screening worksheet. The calculator reports approximate body pitch as p ≈ d + (L₀ − Ls)/Nₐ, using the same solid-height model as the travel check. Exact pitch, closed-end transition turns and grinding details should come from the spring drawing or supplier.
What spring index should I use?
The spring index C = D/d is best kept between about 4 and 12. Below 4 the wire is hard to coil and over-stressed; above 12 the spring tangles and is fragile. The calculator warns outside that range.
How is the allowable stress determined?
It is the maximum allowable static torsional stress, taken as a fraction of the wire’s tensile strength — and tensile strength itself depends on wire diameter (Sut = A/d^m, so thinner wire is stronger). The calculator uses the selected material’s coefficients, not a single fixed number.
Does this work in metric and imperial?
Yes — toggle SI/Imperial in the header and every input and result converts. Copy a link to share your exact configuration.
Solid Height & Spring Pitch Worksheet
The live results expose the two geometry checks users usually need before a load point is trusted: solid height and approximate body pitch. Use this table to audit what each output means.
| Check | Formula | Use |
|---|---|---|
| Solid height | Ls = d x total coil stack | Minimum compressed length before coil bind; the end type controls inactive coils. |
| Travel to solid | L0 - Ls | Hard compression travel before any safety clearance, set allowance or manufacturing tolerance. |
| Approx. body pitch | p ≈ d + (L0 - Ls) / Na | Open-body coil spacing at free length for a first-pass pitch screen. |
| Working clearance | travel to solid - working deflection | Reserve against coil bind; production drawings usually keep extra margin. |
| End type | Solid-height model | Note |
|---|---|---|
| Closed & ground | d x (Na + 2) | Flat seating; standard conservative buckling end condition. |
| Closed / squared | d x (Na + 3) | Taller stack allowance because the closed ends are not ground flat. |
| Open / plain | d x (Na + 1) | Plain ends seat less cleanly and are more buckling-sensitive. |
Method & assumptions
- Static loading only — fatigue, set and stress relaxation are not modelled.
- The allowable stress is the static torsional limit before set removal; shot-peened or set-removed springs tolerate more.
- The buckling check assumes the ends are seated between parallel flat surfaces (end-fixity α = 0.5 for ground ends).
- For extension springs, use the extension spring calculator; hook and loop stresses are a different failure mode.
- Material constants are typical published values; for a safety-critical design, verify against the governing standard and your supplier’s certified data, and have a professional engineer review it.