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Engineering Mechanics

Spring Force Calculator

Calculate spring force, spring constant, or displacement with Hooke's Law, F = kx, including elastic potential energy.

Formula F = kxReviewed Aug 27, 2026

This Spring Force Calculator uses Hooke's Law for an ideal linear spring. Enter any two of spring force, spring constant, and displacement to solve the third. The calculator treats force as a positive magnitude for practical spring-rate work, while also showing the restoring-force sign convention: a spring pulls or pushes opposite the displacement. It also reports the elastic potential energy stored in the spring, U = 1/2 kx².

Calculation Bench
Solve for
01

k · Spring stiffness or spring rate: force per unit displacement.

02

x · Stretch or compression measured from the spring's natural unloaded length.

This uses magnitudes: stretch and compression are entered as positive displacement from the natural length. The signed restoring force is opposite the displacement.

Solution

Enter the required values to calculate spring force.

F = k x

Formula Sheet

F=kxF = kx
k=Fxk = \dfrac{F}{x}
x=Fkx = \dfrac{F}{k}
Frestoring=−kxF_{\text{restoring}} = -kx
U=12kx2U = \dfrac{1}{2}kx^2
  • FSpring Force
  • kSpring Constant
  • xDisplacement
  • UElastic Potential Energy

Variables & Units

SymbolVariableDescriptionCommon Units
FSpring ForceForce magnitude required to stretch or compress the spring by displacement x.N, kN, lbf
kSpring ConstantSpring stiffness or spring rate: force per unit displacement.N/m, kN/m, lbf/in, lbf/ft
xDisplacementStretch or compression measured from the spring's natural unloaded length.mm, cm, m, in, ft
UElastic Potential EnergyEnergy stored in the spring when it is stretched or compressed by x.J, kJ, ft·lbf

How to Use This Calculator

  • 01Choose what you want to solve for: spring force, spring constant / spring rate, or displacement.
  • 02Enter the two known values. You can use N, kN, or lbf for force; N/m, kN/m, lbf/ft, or lbf/in for spring constant; and metric or US length units for displacement.
  • 03Use displacement as the change from the spring's natural, unloaded length. Stretch and compression both use positive magnitudes here.
  • 04Read the primary result, then check the secondary conversions and stored spring energy for context.
  • 05Use the restoring-force sign note only if you are working with a signed coordinate axis. For sizing and spring-rate checks, the magnitude is usually what you need.

How the Formula Works

Hooke's Law says the force needed to stretch or compress an ideal linear spring is proportional to displacement: F = kx. The spring constant k is the slope of the force-displacement line, so a larger k means a stiffer spring.

In vector or signed-coordinate form, the restoring force is written F = -kx. The minus sign means the spring force acts opposite the displacement from equilibrium. This calculator reports the practical force magnitude, and also shows the signed restoring force for a positive displacement.

The energy stored in a linear spring is U = 1/2 kx². This comes from the fact that spring force rises linearly from zero to kx as the spring is stretched or compressed.

Worked Example 01

Force from spring rate and compression

Known

  • Spring constant (k): 800 N/m
  • Compression (x): 50 mm

Formula

F = k x

Substitution

F = 800 × 0.05

Result

F = 40 N

A spring with stiffness 800 N/m compressed by 50 mm produces a 40 N force magnitude.

Worked Example 02

Spring constant from a force-deflection test

Known

  • Force (F): 120 N
  • Displacement (x): 80 mm

Formula

k = F / x

Substitution

k = 120 / 0.08

Result

k = 1500 N/m

If a 120 N load deflects the spring by 80 mm, the spring rate is 1500 N/m, assuming the test stays in the linear range.

Worked Example 03

Displacement from force and spring rate

Known

  • Force (F): 25 N
  • Spring constant (k): 500 N/m

Formula

x = F / k

Substitution

x = 25 / 500

Result

x = 0.05 m = 50 mm

A 500 N/m spring moves 50 mm under a 25 N load.

Applications

  • 01Estimating spring force from a known spring rate and compression
  • 02Finding spring rate from a force-deflection test
  • 03Checking elastic potential energy stored in a compressed or stretched spring
  • 04Converting between N/m, kN/m, lbf/in, and lbf/ft spring-rate units

Assumptions

  • 01The spring behaves linearly, so force is proportional to displacement.
  • 02Displacement is measured from the spring's natural unloaded length.
  • 03Force, spring constant, and displacement are treated as scalar magnitudes; the restoring-force direction is shown separately.

Where This Model Stops

  • 01Not for nonlinear springs, progressive springs, plastic deformation, coil bind, buckling, damping, or dynamic vibration response.
  • 02Real springs have manufacturing tolerances, preload, friction, temperature effects, and fatigue limits that this simple model does not include.
  • 03Do not use this as the only basis for safety-critical spring, suspension, or stored-energy hardware design.

References

  1. [1]
    16.1 Hooke's Law: Stress and Strain Revisited

    OpenStax College Physics 2e

    Defines Hooke's Law as F = -kx, explains the restoring-force sign, and identifies k as the force constant in N/m.

  2. [2]
    7.4 Conservative Forces and Potential Energy

    OpenStax College Physics 2e

    Derives the spring potential energy relation U = 1/2 kx² for a linear spring.

Frequently Asked Questions

Is spring force F = kx or F = -kx?

Both are used, but for different purposes. F = kx is the force magnitude. F = -kx is the signed restoring force, where the minus sign means the spring acts opposite the displacement from equilibrium.

Is spring constant the same as spring rate?

Yes. Spring constant and spring rate both mean k, the force required per unit displacement. Common units include N/m, kN/m, lbf/in, and lbf/ft.

Can this calculator handle compression springs and extension springs?

Yes for simple linear force-deflection calculations. Use the displacement from the spring's natural length as a positive magnitude. Real extension springs may have initial tension, and real compression springs can reach coil bind, so check manufacturer data for design work.

Why does the calculator show spring energy?

Spring energy, U = 1/2 kx², helps show how much stored energy is present at the calculated displacement. That is useful for lab checks and for understanding stored-energy hazards.

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