Physics
Pendulum Period & Length Calculator
Find the period of a simple pendulum, or work backwards to its length, using the small-angle model.
Your measurements
Start with the example, or enter your own values. Use a dot for decimals and e for scientific notation.
Calculated locally. No account or uploads.
Result & working
ExampleThe calculator is loading. You can read the worked example below.
Step-by-step working
The formula
T = 2π√(L/g)
L = g(T/2π)²
| Symbol | Meaning |
|---|---|
| T | Time for one full oscillation, in seconds. |
| L | Distance from the pivot to the center of the bob, in meters. |
| g | Local gravitational acceleration; default 9.81 m/s². |
When to use this calculator
Use this for a small-amplitude pendulum whose bob is approximately a point mass, with a light string and negligible damping. The approximation sin θ ≈ θ requires θ in radians and works best for small amplitudes.
Measure several complete oscillations and divide the total time by their count to estimate T. At larger amplitudes the real period is longer than this formula predicts. A swinging uniform rod is a physical pendulum and needs a different model.
Worked example
The calculator opens with these example values. All steps below are available even with JavaScript disabled.
- Length in SI = 1 × 1 = 1 m
- T = 2π√(L/g) = 2π√(1/9.81) = 2.006067 s
2.006067 s
Common mistakes
- Measure length to the bob’s center, not to the end of the string.
- A trip from one extreme to the opposite extreme is half a period.
- Convert centimeters to meters before applying the formula.