Hooke's Law states that the force exerted by a spring is proportional to the distance it is stretched or compressed from its natural (equilibrium) length. The formula is F = kx, where F is the restoring force in newtons (N), k is the spring constant in newtons per metre (N/m), and x is the displacement from the natural length in metres (m). The law applies as long as the spring is not stretched beyond its elastic limit.

How do I find the spring constant (k)?

Rearranging Hooke's Law gives k = F / x. To measure a spring's constant experimentally, hang a known mass on the spring (so F = mg, where m is mass in kg and g = 9.81 m/s^2) and measure the extension x in metres. For example, a 1 kg mass creates a force of 9.81 N. If the spring extends 0.05 m (5 cm), the spring constant is k = 9.81 / 0.05 = 196.2 N/m. Stiffer springs have higher k values.

What is elastic potential energy and how is it calculated?

When a spring is stretched or compressed, it stores energy called elastic potential energy. The formula is E = 0.5 x k x x^2, where E is in joules (J), k is the spring constant (N/m), and x is the displacement (m). For example, a spring with k = 200 N/m compressed by 0.05 m stores E = 0.5 x 200 x 0.05^2 = 0.25 J. This energy is released when the spring returns to its natural length.

Hooke's Law Spring Calculator

Calculate spring force, spring constant, or displacement using Hooke's Law: F = kx. Enter any two known values and select what you want to solve for. The calculator also computes the elastic potential energy stored in the spring.

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Standard Physics Hooke's Law (1678). Valid within the elastic limit of the spring.

F = k × x

1. What to Solve For

Solve for

Enter spring constant (k) and displacement (x) to calculate force.

Spring Force (F) newtons

Spring Constant (k) N/m

N/m

Displacement (x) metres

Please enter valid positive numbers for both known values.

2. Common Spring Constants

Select a preset to populate the spring constant field.

Spring type preset

Note: spring constants vary widely by design. These are illustrative values for reference.

Results

Spring Force
-
newtons (N)

Spring Constant

N/m

Displacement

metres (m)

Elastic PE

joules (J)

Calculation Breakdown

Solve for-

Spring constant (k)-

Displacement (x)-

Spring force (F)-

Formula applied-

Elastic potential energy-

Worked Example (Default Values)

Spring constant (k)200 N/m

Displacement (x)0.05 m (5 cm)

Formula: F = k x x200 x 0.05

Spring force (F)10.00 N

Elastic PE: 0.5 x k x x²0.5 x 200 x 0.05²

Elastic potential energy0.25 J

What is Hooke's Law?

Hooke's Law, named after the English scientist Robert Hooke who published it in 1678, describes the behaviour of elastic materials under deformation. It states that the force a spring exerts is directly proportional to the distance it is displaced from its natural (rest) position. The relationship is written as:

F = k × x

Where:

F = restoring force in newtons (N)
k = spring constant (also called stiffness coefficient) in newtons per metre (N/m)
x = displacement from natural length in metres (m)

The force F is the restoring force that acts in the opposite direction to the displacement. When you stretch a spring, it pulls back; when you compress it, it pushes back. This is why Hooke's Law is sometimes written as F = -kx, with the negative sign indicating the opposing direction. For magnitude calculations (how strong is the spring force?), you use F = kx.

The Spring Constant (k)

The spring constant k describes how stiff a spring is. A high k value means the spring is stiff and requires a large force to stretch it a small amount. A low k value means the spring is soft and stretches easily with a small force.

Spring Type	Typical k Value	Notes
Slinky toy	~1 to 10 N/m	Very soft, long extension
Pen click spring	~150 N/m	Small, stiff for its size
Typical physics lab spring	100 to 400 N/m	General demonstration use
Trampoline springs	~2,500 N/m	Stiff, high load capacity
Automotive coil spring	15,000 to 30,000 N/m	Must support vehicle weight

Elastic Potential Energy

When a spring is stretched or compressed, it stores energy. This stored energy is called elastic potential energy (also called spring potential energy) and is given by:

E = 0.5 × k × x²

The energy is in joules (J). Notice that energy depends on the square of displacement, so doubling the stretch quadruples the stored energy. This is why compressed springs can release energy quickly and powerfully, as in spring-loaded mechanisms, toys, and shock absorbers.

The Elastic Limit

Hooke's Law holds only within the elastic limit of a spring. If you stretch a spring beyond this point, the spring deforms permanently and no longer returns to its original length. The relationship between force and displacement becomes non-linear. In practical applications, springs are always designed to operate well within their elastic limit to ensure reliable, repeatable behaviour.

Rearranging Hooke's Law

You can rearrange the formula to solve for any of the three variables:

To find force: F = k × x
To find spring constant: k = F / x
To find displacement: x = F / k

This calculator handles all three arrangements. Select what you want to solve for, enter the other two values, and the result updates instantly.

Related Calculators

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Angular Velocity Calculator: rotational speed and frequency.

Sources and method: Hooke, R. (1678). De Potentia Restitutiva. The formula F = kx and elastic potential energy E = 0.5kx² are standard results from classical mechanics. Spring constant examples are illustrative only; actual values depend on spring geometry and material.

This calculator provides results based on ideal Hooke's Law behaviour within the elastic limit. Real springs may deviate from this model when subjected to high loads, temperature extremes, or fatigue. For engineering applications, consult manufacturer specifications and appropriate standards.