Spring Calculator: Compression and Extension Springs

For engineers who already know the math—but still lose projects. For the last few years, I’ve been sharing technical guides here on Mechanical Design Handbook —how to size a motor, how to calculate fits, and (as you recently read) how to choose between timing belts and ball screws. But after 25 years in industrial automation, I realized something uncomfortable: Projects rarely fail because the math was wrong. They fail because: The client changed the scope three times in one week. A critical vendor lied about a shipping date (and no one verified it). The installation technician couldn’t fit a wrench into the gap we designed. University taught us the physics. It didn’t teach us the reality. That gap is why I wrote my new book, The Sheet Mechanic . This is not a textbook. It is a field manual for the messy, political, and chaotic space between the CAD model and the factory floor. It captures the systems I’ve used to survive industrial projec...

Spring Calculator: Compression and Extension Springs

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Tool · Springs · Shigley Ch. 10

Design helical compression and extension springs in your browser. Get spring rate, solid length, forces at free, installed and working length, shear stress with the Wahl factor, safety factors, buckling and surge checks, and hook stresses. Compare every common spring wire side by side, then print the result to PDF.

Length-

Deflection-

Force-

Stress use-

Inputs

Material and wire

Material

Curvature factor

Wire dia. d

Coil dia. given as

Coil dia.

Custom material data

Shear mod. G

Young's mod. E

Tensile Sut

Density

Allowable stress class

Compression spring

Active coils Na

End type

Free length L0

Installed L1

Working L2

End support (for buckling)

Extension spring

Body coils Nb

Initial tension Fi

Installed L1

Working L2

Hook radius r1

Bend radius r2

Lengths are inside the hooks, with standard full-loop machine hooks. Hook radii are to the wire center; leave them blank to use r1 = D/2 and r2 = 2d.

Results update as you type. Copy link saves this exact design in the URL, so you can bookmark it or send it to a colleague.

Forces, deflection and stress

Design checks

Charts

Force vs deflection and length

Stress utilization vs deflection

Geometry and properties

Material comparison

Same wire size, coil diameter, coils and lengths for every material. Click a row to select it. Rows marked * are outside that wire's Table 10-4 size range. Relative cost is from Shigley Table 10-4 (hard-drawn = 1.0).

Equations, assumptions and limits

All equations and material data follow Shigley's Mechanical Engineering Design, Chapter 10 (Budynas and Nisbett). Table and equation numbers refer to that chapter and can shift slightly between editions.

Spring rate and stress

C = D/d k = d⁴G / (8D³N_a) τ = K · 8FD / (πd³)

K_W = (4C − 1)/(4C − 4) + 0.615/C K_B = (4C + 2)/(4C − 3)

D is the mean coil diameter, d the wire diameter, N_a the number of active coils and G the shear modulus. The Wahl factor K_W and the Bergsträsser factor K_B both correct for direct shear and coil curvature. For C between 4 and 12 they differ by less than 1.5 %.

Compression springs

End coils, total coils, solid length and pitch: Table 10-1. Plain: N_e = 0, L_s = d(N_t + 1). Plain and ground: N_e = 1, L_s = dN_t. Squared: N_e = 2, L_s = d(N_t + 1). Squared and ground: N_e = 2, L_s = dN_t.
Allowable shear stress: Table 10-6, static loading, set not removed. 45 % of S_ut for music wire and cold-drawn steel, 50 % for hardened and tempered steels, 35 % for austenitic stainless and nonferrous wire.
Buckling (absolute stability): L₀ < 2.63 D/α for steels (Eq. 10-13), with α from Table 10-2. Phosphor bronze and custom materials use the general form, Eq. 10-12.
Surge (first natural frequency) with both ends on flat plates: f = ½√(k/m), where m is the mass of the active coils (Eqs. 10-25, 10-27). Keep f at 15 to 20 times the operating frequency.
Recommended ranges: 4 ≤ C ≤ 12, 3 ≤ N_a ≤ 15, fractional overrun to solid ξ ≥ 0.15, and safety factor at solid length n_s ≥ 1.2.

Extension springs

F = F_i + kx. Free length inside hooks L₀ = 2(D − d) + (N_b + 1)d (Eq. 10-39), and N_a = N_b + G/E (Eq. 10-40).
Preferred initial tension stress (Eq. 10-41): τ_i = 231/e^0.105C ± 6.9(4 − (C − 3)/6.5) MPa.
Hook bending at point A (Eqs. 10-34, 10-35): σ_A = F[(K)_A16D/(πd³) + 4/(πd²)], with (K)_A = (4C₁² − C₁ − 1)/(4C₁(C₁ − 1)) and C₁ = 2r₁/d.
Hook torsion at point B (Eqs. 10-36, 10-37): τ_B = (K)_B8FD/(πd³), with (K)_B = (4C₂ − 1)/(4C₂ − 4) and C₂ = 2r₂/d.
Allowable stresses: Table 10-7, static loading. For steels: body torsion 45 % of S_ut (cold-drawn) or 50 % (hardened and tempered), end torsion 40 %, end bending 75 %. For stainless and nonferrous wire: 35 %, 30 % and 55 %. The lowest of the three force limits governs.

Material data

Minimum tensile strength S_ut = A/d^m, with A and m from Table 10-4, read in the unit system you select. E and G come from Table 10-5, by wire size for music wire and hard-drawn wire.
Density is a typical handbook value used only for mass and surge frequency. Use your wire supplier's data where it matters.

Validity

Results are for static or infrequent loading at room temperature, with set not removed. They do not cover fatigue, shot peening, preset, corrosion, elevated temperature, or coil clash at high speed. Treat them as design estimates and confirm the final spring with your supplier.

Checked in code against Shigley Chapter 10 worked problems 10-3, 10-6 and 10-7 (compression) and 10-41 (extension). In 10-41 the published solution checks hook torsion against 50 % of S_ut. This tool uses the Table 10-7 end-torsion value of 40 %, so it reports a lower allowable force for that spring.

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