Calculating your period is straightforward once you know the Pendulum Period formula and what each input means. This guide explains the method in plain language, walks through a manual calculation, and gives worked examples you can follow — then you can do it instantly with the Pendulum Period Calculator.
What is Pendulum Period?
The Pendulum Period calculation tells you your period from a few simple inputs. The figure you are solving for here is the period.
The Pendulum Period formula
The core formula is:
Period = 2 × 3.141592653589793 × √(Pendulum length ÷ Gravity)Here is what each input means:
- Pendulum length — a value measured in m. Example: 1 m.
- Gravity — a value measured in m/s². Example: 9.81 m/s².
How to calculate it step by step
- Write down the pendulum length (for example, 1 m).
- Write down the gravity (for example, 9.81 m/s²).
- Apply the formula above to get your period.
- Double-check the result with the Pendulum Period Calculator.
Worked examples
Example 1
| Input / Output | Value |
|---|---|
| Pendulum length | 1 m |
| Gravity | 9.81 m/s² |
| Period | 2.0061 |
| Frequency | 0.4985 |
With pendulum length of 1 m and gravity of 9.81 m/s², the period works out to 2.0061.
Example 2
With pendulum length of 2 m and gravity of 9.81 m/s², the period works out to 2.8370.
| Result | Value |
|---|---|
| Period | 2.8370 |
| Frequency | 0.3525 |
Example 3
With pendulum length of 5 m and gravity of 9.81 m/s², the period works out to 4.4857.
| Result | Value |
|---|---|
| Period | 4.4857 |
| Frequency | 0.2229 |
Tips for an accurate result
- Keep your units consistent — mixing, say, months with years or grams with kilograms is the most common source of error.
- Round only at the very end. Rounding inputs early can shift the final answer noticeably.
- Re-run the numbers whenever an input changes, rather than estimating from an old result.
Prefer not to do the maths by hand? — the Pendulum Period Calculator does it instantly, for free, with the formula and a worked example built in.
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