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
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.
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