Calculation
F = k · x
Double deflection doubles force while the spring remains linear.
F = k·x
Spring Force Calculator (Hooke's Law)
Double deflection doubles force while the spring remains linear.
MINTSI
02
Result
Select a target and calculate.
Understand the inputs
- Spring force F — The spring's restoring force, opposing the deflection x (Hooke's law).
- Spring rate k — The spring rate (also called spring constant or stiffness) – how much force is needed per metre of deflection. Source: the spring's datasheet, or determine it yourself as the slope of the force-deflection curve (measure two force-deflection pairs and form ΔF/Δx).
- Deflection x — The deflection relative to the spring's unloaded (free) length – not the absolute length itself. Sign depends on spring type and the chosen convention: usually positive for compression or extension away from the free position.
Example
1,000 N/m · 0.1 m = 100 N.
Assumptions and limits
Linear spring without hysteresis, buckling or coil bind.
Understand Spring Force Calculator (Hooke's Law)
This calculator finds the missing quantity among spring force F, spring rate k and deflection x from the other two, for a linear spring under Hooke's law. It explains why spring scales and mechanical bathroom scales work at all — and where this simple linear relationship stops applying.
What does this quantity describe?
Hooke's law describes a linear spring's restoring force as proportional to its deflection: F = k·x. Spring rate k states how much force is needed per metre of deflection, and stays constant for a given spring within its linear-elastic range.
A mechanical bathroom scale uses exactly this principle: an internal spring compresses under body weight, and its deflection is translated by a dial mechanism into a weight reading. Because deflection is directly proportional to applied force, twice the deflection corresponds exactly to twice the weight.
Formula and variables
F = k · x
F = k · xk = F / xx = F / k
| Symbol / input | Meaning |
|---|---|
| Spring force F | The spring's restoring force, opposing the deflection x (Hooke's law). |
| Spring rate k | The spring rate (also called spring constant or stiffness) – how much force is needed per metre of deflection. Source: the spring's datasheet, or determine it yourself as the slope of the force-deflection curve (measure two force-deflection pairs and form ΔF/Δx). |
| Deflection x | The deflection relative to the spring's unloaded (free) length – not the absolute length itself. Sign depends on spring type and the chosen convention: usually positive for compression or extension away from the free position. |
Choose the inputs correctly
Enter two of the three quantities. Spring force requires rate and deflection, rate requires force and deflection, deflection requires force and rate. The formula applies only within the spring's linear-elastic range.
How to use the calculator
Select the target quantity and enter the two known values with units. For very large deflections, check whether the spring still operates in its linear range or is already approaching coil bind (solid height).
Worked example
Given k = 1,000 N/m and x = 0.1 m, substitution gives F = 1,000 N/m · 0.1 m = 100 N.
Understand the result and units
A spring force of 100 N means a restoring force of 100 N acts at this deflection. Doubling deflection to 0.2 m doubles force to 200 N at the same spring rate — as long as the spring stays within its linear-elastic range.
Spring force in newtons (N), spring rate in N/m (or N/mm for very stiff springs), deflection in metres or millimetres. Make sure spring rate and deflection use compatible length units.
Typical applications
Hooke's law is used to design spring scales, suspension springs, valve springs, safety relief valves, and for rough force estimates in elastic components.
Assumptions, limits and common mistakes
The formula applies only within the linear-elastic range, where force and deflection are proportional (the proportional limit). Beyond this limit, the spring responds nonlinearly or takes permanent set; for compression springs, reaching solid height additionally causes a sharp jump in force.
Common mistake: Do not apply Hooke's law uncritically over a spring's entire possible deflection range — beyond the proportional limit the relationship is no longer linear. Also, do not simply add spring rates for springs arranged in parallel or series without applying the correct combination rule (parallel: rates add; series: reciprocals add).
Frequently asked questions
Why does a mechanical bathroom scale work?
Because the internal spring's deflection is proportional to the applied force (body weight). The dial mechanism translates that proportional deflection into a weight reading.
What happens if a spring is loaded beyond its proportional limit?
The linear relationship F = k·x no longer holds; the spring may take permanent set, or its coils may touch (solid height), causing a sharply nonlinear rise in force.
How do spring rates combine for multiple springs?
For springs in parallel, rates add directly; for springs in series, their reciprocals add instead, similar to electrical resistors.