`f = 1/(2pi)sqrt((9.80665 m/s^2) / L )`

Enter a value for all fields

The Frequency of a Pendulum calculator computes the frequency (ƒ) of a simple pendulum based on the length (L) of the pendulum.

INSTRUCTIONS: Choose the preferred length units and enter the following:

• (L) Length of Pendulum

Frequency (ƒ): The calculator returns the frequency of the pendulum per minute.  However, this can be automatically converted to other frequency units via the pull-down menu.

The Math / Science

This formula is accurate given that the amplitude is small.  The formula uses the acceleration due to gravity (9.80665 m/s²).

This equation is derived from the general form of the equation of f=ω/(2π) where ω=`sqrt(g/L)`. After substituting for ω, we get the equation as given above.

See also

• Angular Frequency of Pendulum [version designed specifically for problems involving the Earth's gravity approximation at sea level]
• Angular Frequency of Pendulum (Any gravity)
• Period of Pendulum
• Restoring Force on Pendulum
• Restoring Torque on Physical Pendulum

References

Young, Hugh and Freeman, Roger.  University Physics With Modern Physics.  Addison-Wesley, 2008. 12th Edition, (ISBN-13: 978-0321500625 ISBN-10: 0321500628 ) Pg 437, eq 13.33