Pendulum Period Calculator

A simple pendulum consists of a mass (called the bob) suspended from a fixed point by a massless, inextensible string. When displaced from its equilibrium position and released, it swings back and forth in a regular, repeating motion called simple harmonic motion (SHM). The time for one complete oscillation (one full swing back and forth) is called the period (T). For small angles (less than ~15°), the period depends only on the pendulum length and the local gravitational acceleration — not on the mass of the bob or the amplitude of the swing. Our pendulum period calculator uses this small-angle approximation, which is accurate to within 0.5% for angles up to about 10°.

1. Select What to Solve For:Choose "Period (T)" to calculate the period from a known length, or "Length (L)" to find the required pendulum length for a target period. The pendulum period calculator handles both solve modes with the same interface.
2. Choose Gravity and Enter Values: Select a planetary gravity preset (Earth, Moon, Mars, and 7 more) or enter a custom gravitational acceleration in m/s². Enter the known value (length or period) and select the appropriate length unit. The pendulum period calculator converts all inputs to SI units (metres and seconds) internally before computing.
3. Read the Full Result: The pendulum period calculator displays the primary result (period or length), plus frequency, angular frequency, half-period, and oscillations per minute. The planet comparison table shows the same calculation for all 10 solar system bodies simultaneously. All calculations run locally — no data leaves your browser.

• Period (T): The time for one complete oscillation, in seconds. Calculated using T = 2π × √(L / g). This is the primary output of the pendulum period calculator when solving from length.
• Frequency (f): The number of complete oscillations per second, in Hertz. Calculated as f = 1 / T. A 1-metre pendulum on Earth has a frequency of approximately 0.498 Hz.
• Angular Frequency (ω): The rate of oscillation in radians per second, calculated as ω = 2π / T = √(g / L). Used in engineering and physics equations involving oscillatory systems.
• Required Length (L): When solving in reverse, the pendulum period calculator finds the length needed for a target period using L = g × (T / 2π)². For example, a 2-second period on Earth requires a pendulum of approximately 0.993 metres.

The pendulum period calculator uses the small-angle approximation, which assumes the pendulum swings through a small angle (less than ~15° from vertical). For larger amplitudes, the actual period is longer than the calculated value — the error is about 0.5% at 10°, 2% at 20°, and 7% at 40°. The calculator does not account for air resistance, string mass, or the finite size of the bob. Gravity values for planets are surface gravity at the equator. The Moon value (1.62 m/s²) is the mean surface gravity. For the Sun, the surface gravity (274 m/s²) is used, which is relevant for theoretical calculations only.