Case 1
- Spring constant k
- 200N/m
- Displacement x
- 0.1m
20.00N
Open with these valuesHooke's Law Calculator
20.00N
Result: 20.00 NA spring pushes back in proportion to how far you move it: 200 N/m stretched 10 cm pulls with 20 N. The answer is the magnitude — the textbook form F = −kx carries a minus only to say the force points back towards the rest position. It holds while the spring stays elastic.
The numbers at a glance
Held fixed: Spring constant k 200.000 N/m.
| Displacement x (m) | Result (N) |
|---|---|
| 0.0000 | 0.00 |
| 0.0250 | 5.00 |
| 0.0500 | 10.00 |
| 0.0750 | 15.00 |
| 0.1000Your value | 20.00 |
| 0.1250 | 25.00 |
| 0.1500 | 30.00 |
| 0.1750 | 35.00 |
| 0.2000 | 40.00 |
Worked examples
Case 2
- Spring constant k
- 100N/m
- Displacement x
- 0.5m
50.00N
Open with these valuesCase 3
- Spring constant k
- 1000N/m
- Displacement x
- 0.05m
50.00N
Open with these valuesHow it's calculated
F = k × x
- StepEnter the spring constant in newtons per metre — the stiffness of that one spring.
- StepEnter how far it is stretched or compressed, in metres; 10 cm is 0.1.
- ResultRead the magnitude of the restoring force in newtons.
Reference table
| Constant, displacement | What it is | Force |
|---|---|---|
| 50, 1 | A soft spring pulled a full metre | 50 |
| 100, 0.5 | A light spring, 50 cm | 50 |
| 200, 0 | At rest — no displacement, no force | 0 |
| 200, 0.1 | A medium spring, 10 cm | 20 |
| 1000, 0.05 | A stiff spring, 5 cm | 50 |
Questions
What is Hooke's law?
The force a spring exerts is proportional to how far it is stretched or compressed from rest: F = k × x. A spring of 200 N/m pulled 0.1 m gives 20 N. It describes springs, beams and many materials under small loads.
Why is the textbook version written F = −kx?
The minus sign records the direction: the force points back towards the rest position, opposite to the displacement. Its magnitude is still k × x, and that is what this calculator returns.
What units does Hooke's law use?
Newtons per metre for the constant, metres for the displacement, newtons for the force. These are coherent SI units, so no conversion is needed — but convert centimetres first, since 10 cm is 0.1 m.
How much energy is stored in the spring?
Half the constant times the displacement squared: PE = ½ × k × x². The same 200 N/m spring at 0.1 m stores 1 joule. Because the displacement is squared, the energy grows faster than the force as you pull further.
When does Hooke's law stop working?
Beyond the elastic limit of the material. Past that point the spring deforms permanently, the force is no longer proportional to the displacement, and the constant you measured before no longer applies.
Sources and last check
Information, not professional advice.