Pendulum Calculator: Period, Frequency, and Length

This pendulum calculator finds the period, frequency, or length of a simple pendulum from the formula T = 2π√(L/g). Enter one known value, pick a planet for gravity, and the answer appears instantly with a live swinging animation.

A simple pendulum is a mass on a string that swings back and forth. For students checking homework, teachers building demos, or anyone designing a pendulum clock, this tool turns the physics into a quick calculation across three solve modes and eight celestial bodies.

Private by design: every calculation runs in your browser. No values, settings, or results are ever uploaded to a server.

How to Use the Pendulum Calculator

Choose what to solve

Select a mode at the top: Period (T) and Frequency (f) both take a length, while Length (L) takes a period.

Set the gravity

Pick a planet from the dropdown — Earth, Moon, Mars, Venus, Jupiter, Saturn, Mercury, or the Sun — or choose Custom to type your own g value in m/s².

Enter your value and unit

Type the known number and pick a unit. Length supports m, cm, ft, in, km, and yd; period supports s, ms, and min.

Read the results

Results update as you type. See the formula filled with your numbers, primary and secondary result cards, a unit conversion table, a planet comparison, and the pendulum animation swinging at the calculated period.

Features

Three Solve Modes

Switch between solving for Period (T), Frequency (f), or Length (L); the input field and formula adjust to match.

Live Formula Display

See T = 2π√(L/g) rewritten with your actual numbers, so each result shows exactly how it was found.

Eight Celestial Bodies

Preset gravity for Earth, Moon, Mars, Venus, Jupiter, Saturn, Mercury, and the Sun is built in.

Custom Gravity

Enter any gravitational acceleration in m/s² to model a moon, planet, or hypothetical environment.

Animated Pendulum

A canvas pendulum swings at the exact period you calculate, and a toggle lets you pause or resume it.

Unit Conversion Table

Every result is listed across all supported units — length, period, and frequency — at the same time.

Planet Comparison

A table shows how the period changes across every planet at once, with the selected one highlighted.

Instant Calculation

Results refresh the moment you type or change a setting — there is no calculate button to press.

Frequently Asked Questions

What is the formula for a simple pendulum?

The period is T = 2π√(L/g), where T is in seconds, L is the length in meters, and g is the gravitational acceleration in m/s². Frequency is f = 1/T, and length can be found with L = gT²/(4π²).

How do you calculate the period of a pendulum?

Choose the Period mode, enter the pendulum's length, and select a planet for gravity. The calculator applies T = 2π√(L/g) and shows the period in seconds along with the matching frequency.

How do you find pendulum length from the period?

Switch to the Length mode and enter the period. The tool rearranges the formula to L = gT²/(4π²). For example, a 1-second period on Earth needs a length of about 0.248 m (24.8 cm) — handy for a pendulum clock.

Does the period depend on the mass or amplitude?

No. For a simple pendulum with small swings, the period depends only on the length and the gravitational acceleration. The mass of the bob does not change it. The amplitude only matters at larger angles, beyond the small-angle approximation.

How does gravity affect the pendulum period?

Period is inversely related to the square root of g, so stronger gravity means a shorter, faster swing. On Jupiter (24.79 m/s²) the same pendulum swings faster than on Earth (9.807 m/s²); on the Moon (1.62 m/s²) it swings much slower. The planet comparison table shows all of these side by side.

What is the small-angle approximation?

The formula T = 2π√(L/g) is accurate for small swings, typically under about 15°. At larger angles the real period grows slightly longer than the formula predicts. This calculator uses the small-angle approximation, which covers most everyday pendulum problems.