Hooke's law calculator
Spring force, extension or rate, plus the energy stored.
Fill in the fields and the result will appear here automatically.
Solve the linear relation between deformation, holding force and spring rate. Here F=kx is the external force holding the spring in position; the spring’s restoring force is −kx. With k>0, doubling deformation doubles the force and quadruples stored energy. The element’s linear range must be known separately; it need not cover the whole elastic range.
How it works
Formula and logic
For holding force F=kx, deformation x=F/k, and rate k=F/x. The spring’s restoring force has the opposite sign, −kx. Stored energy U=kx²/2=Fx/2 is nonnegative. Finding k requires nonzero deformation and a force of the same sign; F=x=0 does not determine a spring rate.
Example
For k=200 N/m and extension x=0.05 m, the holding force is +10 N. The spring force is −10 N and stored energy is 0.25 J.
Fields and units
- What to find — list option
- Spring rate — N/m
- Extension or compression — m
- Force — N
How to use
- — Choose which of the three quantities you are after.
- — Give the extension in metres: 5 cm is 0.05.
- — Enter the two visible known quantities; the unknown appears in the result. Positive x means extension and negative x compression; F here points in the same direction as x.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- OpenStax: linear spring and restoring force
- Limitation
- Ideal linear spring with no preload in the stated range. Coil contact, nonlinearity, plastic deformation and component load suitability are not checked.
FAQ
How is this different from Newton's second law?
Hooke’s law relates an element’s force to its deformation; Newton’s second law relates net force to acceleration. They can be used together: the spring force −kx enters the force balance, for example m·a=−kx for an ideal attached mass with no other forces.
Why does the energy grow faster than the force?
Because force is linear in deformation while energy is quadratic. Twice the compression gives twice the force and four times the energy.
How far does the law hold?
Only within the element’s proportional F–x range. An elastic deformation may already be nonlinear, while plastic deformation is irreversible. A value of k alone does not tell this calculator the deformation limit.
What does a negative sign mean?
This model uses the same k for both signs of x. That is an assumption, not a property of every real spring: preload and coil contact change the relation. Stored energy remains nonnegative for either sign.