Mechanics
Elastic Potential Energy
The work stored in the spring by stretching or compressing it.
The Formula
U = 0.5 k x squared
The work stored in the spring by stretching or compressing it.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| U | Stored energy | — | Energy held in the spring, in joules. |
| k | Spring constant | — | Stiffness of the spring, in newtons per metre. |
| x | Displacement | — | Distance from the natural length, in metres. |
What Each Symbol Means
U
Stored energy
Energy held in the spring, in joules.
k
Spring constant
Stiffness of the spring, in newtons per metre.
x
Displacement
Distance from the natural length, in metres.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate a spring force page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate A Spring Force, filed under Science. Every number the guide produces comes from substituting into this one line.