Wheel | Pendulum


Pendulum - Calculate Length, Time, Amplitude and Angle

Calculator for a simple mathematical pendulum. This is an ideal cord pendulum with negligible friction and cord mass, which is swinging in a small angle. The weight is concentrated on one point. Then the pendulum law, which was discovered by Galileo Galilei, says that the oscillation period only depends on its length. The formula is t = 2 π √ l / g . This formula provides good values for angles up to α ≤ 5°. The larger the angle, the more inaccurate this estimation will become. From the angle, the amplitude can be calculated and from amplitude and oscillation period finally the speed at the pendulum's center can be calculated. A single oscillation begins and ends at the same state of motion, so an oscillation has the length 4a. A mathematical pendulum would swing forever, a real one is slowed down by friction. The amplitude will get lower, the oscillation period stays constant until the pendulum halts.

Please enter length or oscillation period, the other value will be calculated. When angle, amplitude or speed are entered, the other two values also will be calculated.

Length l: Pendulum
Oscillation period t:seconds
Gravitational acceleration g:m/s²

Angle α:degrees
Amplitude a:
Speed v:
Round to    decimal places.

Example: a 2 meters long pendulum has an oscillation period of 2.8 seconds. At an angle of 5°, the amplitude is 17.5 centimeters and the speed is 0.9 km/h.


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