Physics
Pendulum period
Find period or length for a small-angle pendulum.
Your measurements
Number formats & units
Use decimal dots in datasets. Single values also accept decimal commas and scientific notation such as 1.2e-3 or 1.2 × 10⁻³.
Calculated locally. No account or uploads.
Result & working
ExampleThe calculator is loading. You can read the worked example below.
Download results
Excel and CSV files can be imported into Google Sheets.
More results
Show calculation steps
Interpretation & assumptions
Copy & export
Formula & example
The relationship
What the variables mean
| Symbol | Meaning |
|---|---|
| Time for one full oscillation, in seconds. | |
| Distance from the pivot to the center of the bob, in meters. | |
| Local gravitational acceleration; default 9.81 m/s². |
Worked example
- Solve for
- Period T
- Pendulum length L
- 1
- Length unit
- m
- Gravitational acceleration g (m/s²)
- 9.81
2.006067 s
Follow the example steps
- Length in SI = 1 × 1 = 1 m
- T = 2π√(L/g) = 2π√(1/9.81) = 2.006067 s
Common mistakes
Convert the pendulum length to metres.
Incorrect approach
L = 25 cm: T = 2π√(25/9.81)
Correct approach
L = 0.25 m: T = 2π√(0.25/9.81) ≈ 1.003 s
More checks before you submit
- 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.
Method notes
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.