Waves & Oscillations
Pendulum Period Calculator
Calculate period, frequency or length for a simple pendulum on any planet.
Result
Period (T)
—
s
Frequency (f)
—
Hz
Length (L)
—
m
Step-by-Step Solution
The Simple Pendulum
A simple pendulum consists of a mass (the bob) attached to a string of fixed length, free to swing back and forth. For small angles (less than about 15°), the motion is approximately simple harmonic, and the period depends only on the length of the string and the local gravitational field strength — not on the mass of the bob or the amplitude of the swing.
T = 2π√(L/g)
T = period (s) | L = length (m) | g = gravity (m/s²)
Variables Explained
| Symbol | Name | Unit | Notes |
|---|---|---|---|
| T | Period | s | Time for one complete oscillation (out and back) |
| f | Frequency | Hz | Number of oscillations per second; f = 1/T |
| L | String Length | m | Measured from pivot to centre of mass of bob |
| g | Gravity | m/s² | 9.81 on Earth; varies on other planets |
💡 The pendulum clock was the most accurate timepiece in the world for nearly 300 years (1656–1930s). Christiaan Huygens invented it in 1656 using the isochronous property of pendulums.
Frequently Asked Questions
Does the pendulum mass affect the period?
No. For a simple pendulum, the period T = 2π√(L/g) has no mass term. This is because gravitational force and inertia both scale with mass, so the effects cancel. Only length and gravity matter.
What is the period of a 1-metre pendulum on Earth?
T = 2π√(1/9.81) = 2π × 0.3193 ≈ 2.006 seconds. This is why a 1-metre pendulum was historically used as a "seconds pendulum" — it takes about 1 second to swing each way.
Why does the formula only work for small angles?
For large angles, the restoring force is no longer proportional to displacement. The full equation involves a more complex series expansion. For angles under 15°, the simple formula is accurate to within 0.5%.