Formula used
- U = ½ · k · x² (energy stored at displacement x)
- ΔU = ½ · k · (x₂² − x₁²) (energy change between two positions)
- F = k · x (spring force magnitude; sign follows x)
- x = √(2U / k), k = 2U / x² (rearranged solves)
- Optional ideal outputs: v = √(2U/m), ω = √(k/m), f = ω/(2π), T = 1/f
How to use this calculator
- Select a calculation mode that matches your goal.
- Enter spring constant k and choose its unit.
- Enter displacement x, or x₁ and x₂ for a change.
- If solving, provide energy U and its unit.
- Optionally enter mass to estimate vmax and oscillation.
- Click Calculate, then export to CSV or PDF if needed.
Example data table
| k (N/m) | x (m) | Energy U (J) | Force F (N) | Notes |
|---|---|---|---|---|
| 120 | 0.05 | 0.1500 | 6.0 | Light spring, small compression |
| 250 | 0.08 | 0.8000 | 20.0 | General lab setup |
| 500 | 0.10 | 2.5000 | 50.0 | Stiffer spring, moderate travel |
| 800 | 0.03 | 0.3600 | 24.0 | Short travel, higher stiffness |
| 1500 | 0.12 | 10.8000 | 180.0 | High energy storage scenario |
All example energies use U = ½·k·x².