Hooke's Law Calculator
F = −kΔx
Answer
Stretch a garage-door spring or compress a pen clicker and you feel it push back—harder as you go farther. Converting between inches of stretch, lb/in spring rates, and newtons on a homework sheet is the tedious part. This calculator handles Hooke's law so you can solve for force, spring constant, or displacement without re-deriving the sign conventions each time.
How to Use This Hooke's Law Calculator
- Select a calculation mode. Solve for restoring force F, spring constant k, or displacement Δx. The output field grays out and shows (calculated).
- Enter the two known values with units from each dropdown—N/m with inches of stretch, or lbf with lb/in, all on one form.
- Click Calculate. The answer appears in the result panel and in the calculated field.
Hooke's Law Formulas and Practical Applications
Within the elastic limit, a spring's restoring force grows linearly with how far you stretch or compress it—like a rubber band that fights harder the more you pull.
F = −kΔx
k is stiffness (force per unit length). Δx is displacement from equilibrium—positive when stretched, negative when compressed. The minus sign means the force points back toward rest. Rearrange when you know different pairs: k = |F| / |Δx| and Δx = −F / k.
Example: k = 80 N/m and Δx = 0.15 m gives |F| = 12 N of restoring force. In my experience sizing suspension springs, quoting k in N/mm while measuring travel in inches is common—this tool converts internally so the numbers stay consistent.
Where Hooke's law shows up
- Mechanical design—estimate force at a known deflection for a rated spring.
- Physics labs—back-calculate k from measured force and extension data.
- Vibration basics—stiffer springs (larger k) oscillate faster for the same mass.
Standard Units and Conversion Tables
Spring constant units
| Unit | Symbol | Notes |
|---|---|---|
| Newtons per meter | N/m | SI default |
| Newtons per millimeter | N/mm | 1 N/mm = 1,000 N/m |
| Pounds per inch | lb/in | Common US spring specs |
| Pounds per foot | lb/ft | Longer spring ratings |
| Kilogram-force per meter | kgf/m | ≈ 9.81 N/m per kgf/m |
Force and displacement units
Force accepts N, dyn, kgf, kN, lbf, and ozf. Displacement accepts m, cm, mm, in, and ft. Positive Δx means stretch; negative means compression.
Frequently Asked Questions
What is Hooke's law?
F = −kΔx—restoring force is proportional to displacement and opposite in direction, valid within the elastic limit of the material.
Why is there a minus sign?
The spring always pushes back toward equilibrium—opposite to the direction you displaced it. Magnitude calculations often drop the sign; direction matters when drawing free-body diagrams.
What units does the spring constant use?
Force per unit length—typically N/m. Catalog springs may list lb/in or N/mm; pick the matching unit from the dropdown.
What happens beyond the elastic limit?
Permanent set or yield can occur and the linear law breaks down. This tool assumes elastic behavior. For energy stored in a stretched spring, use the Elastic Potential Energy Calculator. For F = ma on a moving mass, see the Newton's Second Law Calculator.