Pendulum Calculator
Calculate the period, frequency, and length of a simple pendulum. Find how pendulum length and gravity affect oscillation speed.
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How to use this calculator
T = period (seconds per oscillation), L = length of pendulum (m), g = gravitational acceleration (m/s²). The period is independent of mass and amplitude (for small angles < 15°).
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Enter the pendulum length in metres to calculate its period and frequency.
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Or enter a target period (in seconds) and the calculator finds the required length.
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Change the gravity value to simulate other planets (Moon = 1.62, Mars = 3.72).
Frequently asked questions
Does the mass of the bob affect the period?
No. For a simple pendulum (all mass concentrated at the bob, massless string), the period depends only on length and gravity. A 1 kg bob and a 10 kg bob on the same string have the same period.
What is the small-angle approximation?
The formula T = 2π√(L/g) is exact only for infinitesimally small swings. For angles below 15°, the error is less than 0.5%. For larger amplitudes, the true period is longer than the formula predicts.
How are pendulums used in clocks?
A 1-metre pendulum has a period of almost exactly 2 seconds (one "beat" per second), making it ideal for clocks. The escapement mechanism counts each swing. Modern atomic clocks have replaced pendulums, but grandfather clocks still use them for elegance and reliability.
Pendulum Calculator — Period, Frequency & Length
How to use the pendulum
This pendulum gives you instant, accurate results — no registration or download required. Enter your values above and get your result in seconds. The tool is free, works on all devices, and keeps your data private — nothing is stored or shared.
How the pendulum works
The pendulum calculator uses standard formulas used in mathematics, science, and engineering. Enter your inputs, and the tool calculates the result instantly in your browser. No server-side processing means your data stays on your device. Results update in real time as you change inputs.
The simple pendulum model
A simple pendulum consists of a point mass (bob) suspended on a massless, inextensible string. In reality, strings have mass and bobs have volume, but for most purposes the simple model is accurate. The period is completely independent of the swing amplitude for small angles — a property called isochronism, discovered by Galileo around 1602.
Pendulums on other worlds
Because T = 2π√(L/g), a pendulum swings slower where gravity is weaker. A 1 m pendulum that beats once per second on Earth would take 2.46 seconds per beat on the Moon (g = 1.62 m/s²) and 1.63 seconds per beat on Mars (g = 3.72 m/s²). This principle was used historically to measure gravity at different locations on Earth.
Pendulum: how it works
Built on well-established mathematical principles, this tool delivers accurate results for students, researchers, and professionals. Enter your values and get instant clarity without specialist software or manual arithmetic.
Who uses this tool?
Teachers, students, engineers, and data analysts use it to verify calculations, check homework, and solve problems faster. It is intuitive enough for beginners while comprehensive enough for professional use.
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Results are estimates for informational purposes only and do not constitute professional financial, medical, legal, or technical advice. Read full disclaimer →