Hooke's Law Spring Calculator
Force in a spring at a given extension, the energy stored, the sag under a mass and the natural frequency.
Results
Force
10.0000
N
Energy
0.20000
J
Extension
78.453
mm
Frequency
1.7794
Hz
What this tool does
The law holds only while the spring returns to its original length. Stretch it past the elastic limit and it takes a permanent set, after which none of these numbers apply. The natural frequency is the same relationship seen from the other side: it is what decides whether a suspension feels firm or wallowy.
Formula
F = k × x ; E = ½ k x²
Variables
| Symbol | Meaning | Unit |
|---|---|---|
k | Spring constant | N/m |
x | Extension | mm |
m | Mass | kg |
F | Force | N |
EN | Energy | J |
XM | Extension | mm |
FQ | Frequency | Hz |
Worked example
- Spring constant250 N/m
- Extension40 mm
- Mass2 kg
- Force10.0000 N
- Energy0.20000 J
- Extension78.453 mm
- Frequency1.7794 Hz
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- For work that must comply with a standard or be signed off, check the result against the applicable code and have it reviewed by a qualified engineer.