Mechanical

Spring Compression Calculator

Calculate compression spring rate, load, deflection, stored energy, coil diameters, solid-height clearance, spring index, and corrected shear stress.

Formula k = G d^4 / (8 D^3 Na)Reviewed Sep 1, 2026

A compression spring is not defined by load and travel alone. Its stiffness comes from wire diameter, mean coil diameter, active coils, and material shear modulus: k = Gd^4 / (8D^3Na). This spring compression calculator turns that geometry into a first-pass design check, then adds the practical outputs users usually need next: force or compression, N/mm rate, stored energy, inner and outer diameters, solid height, coil-bind clearance, spring index, and a Wahl-corrected shear-stress screen.

Calculation Bench

Solve for

Coil Diameter Entered As

Material Presetcommon carbon spring steelEnd TypeUsed only to estimate total coils if you leave total coils blank.

01Wire Diameter

d · round wire diameter

02Mean Coil Diameter

D · choose how your catalog dimension is measured

03Active Coils

Na · coils that deflect under load

04Shear Modulus

G · material preset fills this value

05Spring Compression

x · travel from free length

06Free Length

Lf · optional, enables coil-bind and buckling checks

07Total Coils

Nt · optional, used for solid height

08Maximum Safe Deflection

xmax · optional design limit or catalog max travel

If you only know spring rate, use the Spring Force Calculator. Use this page when wire diameter, coil diameter, active coils, and material are known.

Solution

Enter spring geometry and either compression or load to calculate rate, stress, and clearance.

k = Gd^4/(8D^3Na); F = kx

Formula Sheet

k=\dfrac{Gd^4}{8D^3N_a}

F=kx

x=\dfrac{F}{k}

\tau=K_w\dfrac{8FD}{\pi d^3}

C=\dfrac{D}{d}

c=L_f-N_td-x

E=\dfrac{1}{2}kx^2

kSpring Rate
GShear Modulus
dWire Diameter
DMean Coil Diameter
NaActive Coils
FSpring Load
xCompression
CSpring Index
KwWahl Correction Factor
LfFree Length
NtTotal Coils
cSolid-Height Clearance

Common Shear Modulus Presets

Material	G value	Typical use
Music wire	79.3 GPa	General-purpose high-strength spring wire
302/304 stainless	69 GPa	Corrosion-resistant compression springs
Chrome silicon	79 GPa	Higher-stress and shock-service springs
Phosphor bronze	41 GPa	Electrical contact and nonmagnetic springs

Variables & Units

Symbol	Variable	Description	Common Units
k	Spring Rate	Load per unit compression.	N/mm, N/m, lbf/in
G	Shear Modulus	Material rigidity used for spring torsion.	GPa, MPa, ksi
d	Wire Diameter	Diameter of the round spring wire.	mm, in
D	Mean Coil Diameter	Diameter measured through the wire centerline.	mm, in
Na	Active Coils	Coils that deflect under load.
F	Spring Load	Axial compressive force.	N, lbf
x	Compression	Travel from free length.	mm, in
C	Spring Index	Mean coil diameter divided by wire diameter.
Kw	Wahl Correction Factor	Stress correction based on spring index.
Lf	Free Length	Unloaded spring length.	mm, in
Nt	Total Coils	All coils used to estimate solid height.
c	Solid-Height Clearance	Free length minus solid height and working compression.	mm, in

How to Use This Calculator

01Choose Load From Compression when you know how far the spring is compressed and need the force.
02Choose Compression From Load when you know the axial load and need the spring travel.
03Select whether your catalog dimension is mean, outside, or inside coil diameter; the calculator converts it to mean diameter internally.
04Pick a material preset for shear modulus, or choose Custom if your spring drawing gives a different G value.
05Add free length and total coils when you want the solid-height clearance and buckling warning to be meaningful.
06Treat high stress, low clearance, tight spring index, or buckling warnings as reasons to review the spring with a supplier or a full spring-design standard.

How the Formula Works

Round-wire helical compression springs twist the wire as the spring is loaded. That is why the spring-rate equation uses shear modulus G rather than Young's modulus E.

Mean coil diameter is the diameter through the centerline of the wire. If a catalog gives outside diameter, the mean diameter is OD - d; if it gives inside diameter, the mean diameter is ID + d.

Load and compression are then connected by Hooke's law, F = kx, while stored spring energy is E = 1/2 kx^2.

The direct torsional stress equation is multiplied by the Wahl correction factor to account for curvature and direct-shear effects in a close-wound spring.

Solid height is estimated as total coils multiplied by wire diameter. Free length minus solid height minus working compression gives the remaining travel before coil bind.

Worked Example 01

Music-wire spring compressed 32.69 mm

Known

Wire diameter: 2 mm
Mean coil diameter: 12 mm
Active coils: 30
Shear modulus: 79.3 GPa
Compression: 32.69 mm

Formula

k = G d^4 / (8 D^3 Na)

Substitution

k = 79.3 GPa x (2 mm)^4 / [8 x (12 mm)^3 x 30]; F = k x 32.69 mm

Result

k = 3.06 N/mm and F is about 100 N

The spring is relatively soft because the active-coil count is high. The calculator also reports stress, stored energy, and solid-height clearance when free length is entered.

Worked Example 02

Compression from a 100 N load

Known

Wire diameter: 2 mm
Outside coil diameter: 14 mm
Active coils: 30
Load: 100 N

Formula

x = F / k

Substitution

D = OD - d = 12 mm; x = 100 N / 3.06 N/mm

Result

x is about 32.7 mm

Outside diameter is converted to mean diameter before the spring-rate formula is used. This prevents the common mistake of using OD directly as D.

Applications

01Estimating load from a known compression spring geometry and travel
02Checking compression travel from a known machine load
03Comparing catalog springs when only dimensions and material family are available
04Screening coil bind clearance before ordering a spring
05Estimating spring energy and corrected shear stress for early mechanical design

Assumptions

01The spring is a close-coiled, round-wire helical compression spring operating in the linear elastic range.
02The load is axial and centered, with no side loading or guide friction included.
03Material behavior is represented by shear modulus only; the calculator does not apply a material allowable stress.
04If total coils are left blank, the calculator estimates total coils from active coils and end type for the solid-height check.
05The spring-rate equation uses mean coil diameter internally, even when outside or inside diameter is entered.

Where This Model Stops

01This is a first-pass screening calculator, not a final spring design or catalog substitute.
02Does not check fatigue life, set, relaxation, surge frequency, shot peening, temperature derating, corrosion, buckling guides in detail, or manufacturing tolerances.
03Does not calculate spring pitch, end grinding allowances, preload, installed height, load tolerance, or exact allowable stress by material grade.
04High corrected shear stress does not automatically mean failure, and low stress does not guarantee a safe design; compare against the actual spring material and application duty cycle.

References

[1]
Compression / Extension Spring Calculator
About Tribology
Reference for helical spring rate, Wahl factor, and stress relationships.
[2]
Compression Spring Calculator
MachineCalcs
Reference for compression spring geometry, spring index, and solid-height screening outputs.
[3]
Compression Spring Calculator
Lee Spring
Reference for catalog-style compression spring inputs such as diameter, length, material, and load.

Frequently Asked Questions

How is this different from the Spring Force Calculator?

The Spring Force Calculator assumes you already know spring constant k and only applies F = kx. This Spring Compression Calculator estimates k from the spring geometry, then adds stress, solid-height clearance, coil index, and buckling warnings.

Should I enter outside, inside, or mean coil diameter?

Enter whatever measurement you actually have and select the matching diameter basis. The formula needs mean coil diameter, so the calculator converts outside diameter to OD - wire diameter and inside diameter to ID + wire diameter.

What spring index is usually reasonable?

A spring index between roughly 4 and 12 is a common first-pass range. Lower values are harder to manufacture and create higher stress concentration; very large values can be less stable and more sensitive to tolerances.

Can this calculator choose a safe spring for fatigue loading?

No. It gives a useful screening result, but fatigue, set, temperature, surface finish, material grade, and supplier tolerances need a fuller spring design check.

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