What Is the Spring Constant?
The spring constant (k) quantifies the stiffness of a spring. A large k means the spring is stiff and requires more force for a given stretch. A small k means the spring is soft. It is fundamental to understanding spring behaviour in mechanics, engineering, and physics.
Hooke’s Law: F = kx
Hooke's law states that the restoring force of an ideal spring is directly proportional to displacement from equilibrium. It works for small deformations within the elastic limit.
Finding the Spring Constant: k = F / x
Apply a known force, measure the resulting displacement, and divide. This is the standard experimental method for determining k.
Elastic Potential Energy: U = ½kx²
The energy stored in a stretched or compressed spring. You can also rearrange to find k = 2U/x² if you know the stored energy and displacement.
Spring Constant Units
| Unit | To N/m |
|---|---|
| 1 N/cm | 100 N/m |
| 1 N/mm | 1 000 N/m |
| 1 kN/m | 1 000 N/m |
| 1 lbf/in | ≈ 175.13 N/m |
How to Use the Calculator
- Choose what to find: k, force, displacement, k from energy, or elastic PE.
- Enter known values with units.
- Click Calculate.
- Review the result and formula steps.
Example Calculations
10 N stretches spring 5 cm
k = 10 / 0.05 = 200 N/m
k = 200 N/m, x = 0.1 m
F = 200 × 0.1 = 20 N, U = ½ × 200 × 0.1² = 1 J
U = 2 J, x = 0.2 m → k
k = 2 × 2 / 0.2² = 100 N/m
Common Mistakes
- Using total spring length instead of displacement from equilibrium.
- Using cm without converting to metres.
- Applying Hooke's law beyond the elastic limit.
- Confusing spring constant with spring force.
- Forgetting to square displacement when computing energy.
Accuracy and Limitations
This calculator assumes an ideal linear spring obeying Hooke's law. Real springs can be non-linear, especially at large deformations. Springs have an elastic limit beyond which permanent deformation occurs. Temperature, fatigue, and manufacturing tolerances affect real springs. This tool is educational.
FAQ
What is the spring constant?›
The spring constant (k) measures how stiff a spring is. It is the force needed to stretch or compress the spring by one unit of length (e.g., 1 metre).
What is Hooke's law?›
F = kx. The force exerted by or on an ideal spring is proportional to displacement from equilibrium.
What unit is the spring constant in?›
SI: N/m. Other units include N/cm, N/mm, kN/m, and lbf/in.
How do I find k from force and extension?›
k = F / x. Divide the applied force by the resulting extension or compression.
How do I find k from energy and displacement?›
k = 2U / x². This uses the elastic PE formula rearranged.
Does Hooke's law work for large deformations?›
No. Hooke’s law is only valid within the elastic limit. Beyond that, the spring deforms permanently.
Can k be negative?›
No. The spring constant is always positive for a real spring.
What is a typical spring constant?›
It varies enormously: a soft toy spring might be 10 N/m, a car suspension spring ~20 000 N/m.
Sources
Author & technical reviewer
Manish Kumar
PhysicsCalcs tools are reviewed with an educational focus: clear formulas, transparent assumptions, and practical context for students and science learners.
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