Answer first
What this calculator tells you
Calculate a spring's force and stored energy from its spring constant and stretch. Check the load a spring carries or the energy it stores at a given stretch. Formula: Force = k × x; stored elastic energy = ½ × k × x². At the worked-example inputs, the spring force (n) is 30. Holding every other input steady, moving spring constant (n/m) from 160 to 240 moves the result from 24 to 36.
Transparent method
The formula
Check the load a spring carries or the energy it stores at a given stretch.
Worked example
Example inputs
How to interpret the result
A spring pushes back with a force in proportion to how far it is stretched, and stores energy in proportion to the square of that stretch. A spring of 200 newtons per meter pulled 0.15 meters pulls back with 30 newtons and holds 2.25 joules. Doubling the stretch doubles the force but quadruples the stored energy, which is why a wide stretch is so much harder to release safely.
At the worked-example inputs the spring force (n) is 30. It rises with spring constant (n/m) and stretch or compression (m).
These are textbook formulas for ideal conditions: no air resistance, no friction, gravity of 9.81 meters per second squared and gases that behave ideally. Real results differ, so treat them as first estimates and use the units the formulas expect (meters, kilograms, seconds).
Before you rely on it
What to check
Keep the stretch inside the spring's working range. Past it, the spring deforms for good and the straight-line rule no longer applies.
The common error
Where people go wrong with hooke's law calculator
Entering the spring's total length instead of the change in length. The formula uses only how far it moves from its resting length.
Sensitivity evidence
How spring constant (n/m) changes the spring force (n)
Holding every other input at the worked-example value, moving spring constant (n/m) from 160 to 240 moves the spring force (n) from 24 to 36: a spread of 12, or 40% of the worked-example result.
| Spring constant (N/m) | Spring force (N) | Stored energy (J) |
|---|---|---|
| 160 | 24 | 1.8 |
| 180 | 27 | 2 |
| 200worked example | 30 | 2.3 |
| 220 | 33 | 2.5 |
| 240 | 36 | 2.7 |
Every input, tested
Which input moves the spring force (n) most
Of the 2 inputs, spring constant (n/m) moves the spring force (n) most (6 across the range tested) and stretch or compression (m) moves it least (6).
| Input | Tested from | To | Spring force (N) at each end | Swing |
|---|---|---|---|---|
| Spring constant (N/m) | 180 | 220 | 27 to 33 | 6 (20%) |
| Stretch or compression (m) | 0.14 | 0.17 | 28 to 34 | 6 (20%) |
Two variables at once
Spring force (N) by spring constant (n/m) and stretch or compression (m)
Across the grid the spring force (n) runs from 19.2 to 43.2. Moving spring constant (n/m) from 160 to 240 shifts it by 12 at the middle column, and moving stretch or compression (m) from 0.12 to 0.18 shifts it by 12 at the middle row, so neither is the bigger lever here.
| Spring constant (N/m) \ Stretch or compression (m) | 0.12 | 0.15 | 0.18 |
|---|---|---|---|
| 160 | 19.2 | 24 | 28.8 |
| 180 | 21.6 | 27 | 32.4 |
| 200 | 24 | 30 | 36 |
| 220 | 26.4 | 33 | 39.6 |
| 240 | 28.8 | 36 | 43.2 |
The highlighted cell is the worked example: 30.
Step by step
The worked example, input by input
| Input | Value used | What it means |
|---|---|---|
| Spring constant (N/m) | 200 | Enter the spring constant (n/m) used in this calculation. |
| Stretch or compression (m) | 0.15 | Enter the stretch or compression (m) used in this calculation. |
| Spring force (N) | 30 | |
| Stored energy (J) | 2.3 | |
Inputs, definitions and assumptions
Spring constant (N/m)
Enter the spring constant (n/m) used in this calculation. The prefilled worked-example value is 200.
Stretch or compression (m)
Enter the stretch or compression (m) used in this calculation. The prefilled worked-example value is 0.15.
How to use this calculator
- 1Verify the inputs. Gather spring constant (n/m) and stretch or compression (m) from your own documents; the prefilled values are examples.
- 2Save a baseline. The worked example puts the spring force (n) at 30. Store your own version of it as Scenario A.
- 3Test one change. Start with spring constant (n/m), the input with the biggest effect here: moving spring constant (n/m) from 180 to 220 takes the spring force (n) from 27 to 33, a swing of 20% of the worked-example figure.
- 4Check the extremes. At half the example spring constant (n/m) (100) the spring force (n) is 15; at double (400) it is 60.
People also ask
Frequently asked questions
How do you calculate hooke's law?
Force = k × x; stored elastic energy = ½ × k × x². At the worked-example inputs the spring force (n) is 30.
What does the hooke's law result mean?
Check the load a spring carries or the energy it stores at a given stretch. At the worked-example inputs the spring force (n) is 30. It rises with spring constant (n/m) and stretch or compression (m).
How much does spring constant (n/m) change the spring force (n)?
Holding every other input at the worked-example value, moving spring constant (n/m) from 160 to 240 moves the spring force (n) from 24 to 36, a spread of 12.
What are the limits of this hooke's law calculator?
These are textbook formulas for ideal conditions: no air resistance, no friction, gravity of 9.81 meters per second squared and gases that behave ideally. Real results differ, so treat them as first estimates and use the units the formulas expect (meters, kilograms, seconds). The tables on this page test spring constant (n/m) only from 160 to 240; a value outside that range is not tabulated here.
Which input moves the spring force (n) most in the hooke's law calculator?
Ranked by how far each moves the spring force (n) across the range tested: spring constant (n/m) (6, 20%) and stretch or compression (m) (6, 20%).
If I double spring constant (n/m) in the hooke's law calculator, does the spring force (n) double?
Doubling it from 200 to 400 takes the spring force (n) from 30 to 60, which is 2.00 times the worked-example figure. So the result scales almost exactly in proportion. Halving it to 100 gives 15.
How much does stretch or compression (m) matter in the hooke's law calculator?
The worked example uses 0.15. With the other inputs left at the worked example, moving stretch or compression (m) from 0.14 to 0.17 takes the spring force (n) from 28 to 34, a swing of 20% of the worked-example figure.
Which inputs change the stored energy (j) in the hooke's law calculator?
At the worked-example inputs it is 2.3. Spring constant (n/m) takes it from 2 to 2.5 and stretch or compression (m) takes it from 2 to 2.9.
What is the difference between speed and velocity?
Speed is how fast something moves. Velocity is speed with a direction. A car circling a track at a steady 30 mph has a constant speed and a changing velocity, because its direction keeps changing.
Sources and evidence
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