Spring Constant Calculator
Find spring stiffness and stored energy.
How far the spring stretches or compresses.
Results update as you type.
How it works
The spring constant measures how stiff a spring is, and this spring constant calculator finds it from the force applied and the resulting displacement, then reports the elastic potential energy the spring stores. A high spring constant means a stiff spring that needs a large force to stretch even a little, while a low constant describes a soft, easily deformed spring. The value is expressed in newtons per metre. This property matters across mechanical and structural design: vehicle suspensions, mattress support, retractable pens, door mechanisms, weighing scales, and vibration isolators all depend on choosing the right stiffness. Too stiff and the ride is harsh; too soft and the spring bottoms out. A spring constant calculator lets you confirm the stiffness from a simple force-and-stretch measurement instead of guessing. The formula works because Hooke's law says the restoring force of a spring grows in direct proportion to its displacement, so the ratio of force to stretch is a fixed constant for that spring. The stored energy follows as one-half the constant times displacement squared, the area under the force-distance graph. Engineers, product designers, and physics students use a spring constant calculator to size springs and predict how much energy they will hold.
k = force ÷ displacement
Hooke's law states that the force a spring exerts is proportional to how far it is stretched or compressed, so dividing force by displacement gives the constant of proportionality k, the stiffness. The stored elastic energy is one-half k times displacement squared, because the force builds up linearly from zero as the spring deforms, and energy is the area under that force-versus-distance line.
Source:Standard physics (Hooke's law)
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Worked example
How to use this calculator
- 1
Enter your values
Enter applied force and displacement.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Spring constant updates instantly as you type — no button to press.
Frequently asked questions
What is the spring constant?
The spring constant, written k, measures a spring's stiffness. It equals the force needed to stretch or compress the spring divided by how far it moves, and is expressed in newtons per metre. A large value means a stiff spring that resists deformation strongly, while a small value means a soft, flexible spring. It is a fixed property of each spring, set by its material, coil diameter, wire thickness, and number of turns.
What is Hooke's law?
Hooke's law states that the force a spring exerts is directly proportional to its displacement from the resting position, as long as the spring is not stretched too far. Written F equals k times x, it means doubling the stretch doubles the force. The law holds within the elastic limit; beyond that point the spring deforms permanently and the simple linear relationship no longer describes its behaviour.
How is the stored energy calculated?
Elastic potential energy equals one-half the spring constant multiplied by the displacement squared. Because the restoring force rises linearly from zero as the spring deforms, the energy is the triangular area under the force-versus-distance line. This is why stretching a spring twice as far stores four times the energy. That stored energy is released when the spring returns to its natural length.
What are the units of the spring constant?
The spring constant is measured in newtons per metre in SI units, meaning the number of newtons of force required to stretch the spring by one metre. In imperial work you may see pounds per inch instead. To keep this calculator accurate, enter force in newtons and displacement in metres. A displacement given in centimetres should be divided by 100 before entering it.
Does Hooke's law work for every spring?
Hooke's law applies only within a spring's elastic range, where deformation is reversible and proportional to force. Stretch a spring beyond its elastic limit and it deforms permanently, so force no longer rises linearly and the constant no longer applies. Real springs also have a maximum load. For accurate results, stay within the manufacturer's specified working range where the linear relationship reliably holds.