`L = g*(T/(2pi))^2`

Enter a value for all fields

The Length of a Pendulum calculator computes the length (L) of a simple pendulum based on the period (T) of the pendulum arm and the acceleration due to gravity (g).

INSTRUCTIONS: Choose units and enter the following:

• (T)  This is the period of the pendulum
• (g)  This is the acceleration due to gravity.

Length(L): The calculator returns the length in meters.  However this can be automatically converted to compatible units via the pull-down menu.

The Math / Science

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

The formula for the length of a simple pendulum is:

     `L = g* (T/(2π))^2`

where:

• L is the Length of the pendulum
• T is the period of the pendulum
• g is the acceleration due to gravity

Related Calculators

• Acceleration Due to Gravity
• Angular Frequency of Pendulum
• Period of a Pendulum
• Angular Frequency of Pendulum (Any gravity)
• Frequency 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 13.34