Pendulum Calculator
Period and frequency of a simple pendulum — or the length for a target period.
Quick answer
- Formula: T = 2π √(L ÷ g); L = g × (T ÷ 2π)²; f = 1 ÷ T
- Worked example — Period: 2.0064 s (full example below).
Pendulum Calculator
| Period | 2.0064 s |
| Frequency | 0.4984 Hz |
| Length | 1.0000 m |
A 1 m pendulum has a period of about 2.006 s and frequency 0.498 Hz — the principle behind longcase (grandfather) clocks.
For small swings, a pendulum's period depends only on its length and gravity — not on its mass or (to first approximation) its swing amplitude. This calculator uses that small-angle approximation.
Use period mode to find the period and frequency from the length, or length mode to design a pendulum with a desired period (a 1 m pendulum ticks at just over 2 seconds per full swing). Gravity is g = 9.80665 m/s².
The formula
Worked example
A 1 m pendulum has a period of about 2.006 s and frequency 0.498 Hz — the principle behind longcase (grandfather) clocks.
The example is pre-loaded in the result panel — press Calculate with your own numbers to replace it.
Frequently asked questions
Why doesn't the bob's mass matter?
Gravity accelerates all masses equally, and the restoring effect scales with mass in the same way, so mass cancels out of the period formula. Only length and g remain.
What is a 'seconds pendulum'?
A pendulum with a 2-second period (1 second each way), historically used in precision clocks. Its length is about 0.994 m at standard gravity — use length mode with T = 2 to verify.
Category: Science calculators
Sources & methodology
This calculator applies the formula shown on this page exactly as written, using the standard definitions for its inputs. Results are computed from the values you enter — no data is stored — and are rounded only for display.
Content last reviewed by CalcHub Editorial.
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