Quick answer
Hooke's law gives the spring constant k = F ÷ x, and the stored energy is E = ½kx². A 10 N force that stretches a spring 0.05 m gives k = 200 N/m and stores 0.25 J.
Enter the force and extension. The calculator returns the spring constant and the stored energy.
Related tools: Gear Ratio Calculator: Gear ratio, output speed and torque multiplication. Transmission Gear Ratio Calculator: Vehicle speed from engine rpm, gear ratio, final drive and tire size. Gear Speed Calculator: Output speed and ratio of a gear pair.
How to use the Spring Constant Calculator
- Enter force (N) (above 0).
- Enter extension (m) (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Force | A number, in N | > 0 |
| Extension | A number, in m | > 0 |
Formula and method
Formula
k = F ÷ x; E = ½ k x²
IEEE-754 double precision; shown to at most 6 decimal places.
Linear elastic spring (Hooke's law).
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Force = 10; Extension = 0.05.
| Result | Value |
|---|---|
| Spring constant | 200 N/m |
| Stored energy | 0.25 |
Example 2
Inputs: Force = 4.9; Extension = 0.1.
| Result | Value |
|---|---|
| Spring constant | 49 N/m |
| Stored energy | 0.245 |
The first line is the headline result (spring constant). Below it the spring Constant Calculator lists stored energy, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
Elastic limit
The law holds only within the elastic limit. Beyond it the spring deforms permanently. A stiffer spring has a larger k: doubling the force for the same extension doubles k.
Springs in combination
Springs in parallel add their constants (k = k₁ + k₂), while springs in series combine as 1/k = 1/k₁ + 1/k₂. Energy stored grows with the square of the extension: doubling the stretch stores four times as much.
How the result changes with force
Holding every other input at the first worked example, this table changes only force. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Force | Spring constant | Stored energy |
|---|---|---|
| 5 | 100 N/m | 0.125 |
| 10 | 200 N/m | 0.25 |
| 20 | 400 N/m | 0.5 |
| 40 | 800 N/m | 1 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Extension: entering "0" shows "Extension must be greater than 0." beside that field and no result.
Choosing between the Spring Constant Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Gear Ratio Calculator](/engineering/gear-ratio-calculator/) | driving gear teeth and driven gear teeth | Gear ratio |
| [Transmission Gear Ratio Calculator](/engineering/transmission-gear-ratio-calculator/) | transmission gear ratio, final drive ratio and tire diameter | Vehicle speed |
| [Gear Speed Calculator](/engineering/gear-speed-calculator/) | driver gear teeth, driven gear teeth and input speed | Output speed |
| [Belt Length Calculator](/construction/belt-length-calculator/) | large pulley diameter, small pulley diameter and center distance | Belt length |
| [Days Until Spring](/date-calendar/days-until-spring/) | today's date and hemisphere | Days until |
Background: structural and wiring estimates
Structural and electrical results are only as good as their assumptions. Bending stress is the bending moment divided by the section modulus, and an allowable stress is the yield strength divided by a safety factor that depends on the governing design code and the type of load. For a single-phase or DC run the voltage drop uses the round-trip length: V = 2 × L × R per unit length × I.
Recommended limits, such as keeping branch-circuit voltage drop around 3%, differ between sources and code editions. These pages are estimates: follow the applicable code and a qualified engineer or electrician for real work.
Assumptions and limitations
- Within the elastic limit
Use results as engineering estimates and check them against the governing standards, safety factors and a qualified engineer's judgement before relying on them.
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for extension to confirm this.
Frequently asked questions
What are the units of k?
k is in newtons per metre (N/m); the example's 10 N for 0.05 m gives 200 N/m.
How do I find the extension for a given load?
Rearrange Hooke's law to x = F ÷ k: a 20 N load on a 200 N/m spring stretches it 0.1 m.
Is the force linear?
Yes within the elastic range.
What does the Spring Constant Calculator calculate?
Hooke's law spring constant and stored energy. It returns Spring constant and Stored energy.
What formula does the Spring Constant Calculator use?
k = F ÷ x; E = ½ k x². Linear elastic spring (Hooke's law).
What do I need to enter in the spring Constant Calculator?
You enter Force (N) and Extension (m).
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Within the elastic limit.
What is an example of a spring Constant result?
With force 10 and extension 0.05, the spring constant is 200 N/m.
Can I rely on this calculator for a decision?
Use results as engineering estimates and check them against the governing standards, safety factors and a qualified engineer's judgement before relying on them. For this calculator in particular: Within the elastic limit.
Related calculators
- Gear Ratio Calculator — Gear ratio, output speed and torque multiplication.
- Transmission Gear Ratio Calculator — Vehicle speed from engine rpm, gear ratio, final drive and tire size.
- Gear Speed Calculator — Output speed and ratio of a gear pair.
- Belt Length Calculator — Open-belt length for two pulleys.
- Days Until Spring — Days until the astronomical start of spring.
- Ohm's Law Calculator — Solve voltage, current or resistance.
Sources
- OpenStax, University Physics Volume 1 (Rice University): mechanics
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.