Simple Pendulum Period CalculatorFree online other calculator — instant results, no sign-up
Estimate a small-angle pendulum period under standard gravity.
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About the Simple Pendulum Period Calculator
The Simple Pendulum Period Calculator estimates the time for one complete small-angle swing using pendulum length and standard gravity. Enter the length in meters to obtain the period in seconds. With the default length of 1 m, the calculated period is 2.006409 s.
- Pendulum length (m)
- The pendulum length is the distance from the pivot to the bob’s center of mass, measured in meters, with a default of 1 m.
Formula and method
T = 2π√(L/g), with g = 9.80665 m/s²; for L = 1 m, T = 2π√(1/9.80665) ≈ 2.006409 s.
- TPeriod: the time for one complete oscillation, in seconds.
- LPendulum length from the pivot to the bob’s center of mass, in meters.
- gGravitational acceleration, fixed at standard gravity of 9.80665 m/s².
- πPi, the mathematical constant approximately equal to 3.14159.
The calculator divides the entered length by standard gravitational acceleration, takes the square root, and multiplies by 2π. For the default length of 1 m, this produces a period displayed as 2.006409 s.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Pendulum length1 m
Results
- Result2.006409 s
How to use the Simple Pendulum Period Calculator
- 1Measure the distance from the pendulum’s pivot to the center of mass of its bob.
- 2Express the measured length in meters.
- 3Enter a positive value in Pendulum length (m), or leave the default of 1.
- 4Run the calculation and read the Result in seconds.
- 5For the default input, check that Result is 2.006409 s, representing one complete back-and-forth swing.
Reading your result
The Result row gives the estimated period in seconds. With Pendulum length (m) set to 1, Result = 2.006409 s means the bob takes approximately that long to return to the same position while moving in the same direction. It is a full oscillation, not just a trip from one side to the other.
Limitations
The formula assumes a small angular displacement, a point-like bob, a massless inextensible suspension, a fixed pivot, and negligible air resistance and pivot friction. Larger swing angles give longer periods than this approximation predicts. Standard gravity is fixed, so local differences in gravity are not modeled. Length must be positive; zero or negative values do not represent a working simple pendulum. The displayed decimal places reflect numerical calculation, not guaranteed experimental accuracy.
Common questions
Should I measure only the string or include the bob?+
Measure from the pivot to the bob’s center of mass, not merely to the end of the string. For a uniform spherical bob, the center of mass is at its geometric center.
Why is there no input for the bob’s mass?+
Mass cancels out in the ideal simple-pendulum equation, so the small-angle period depends on length and gravity rather than bob mass.
Does 2.006409 s describe a one-way swing for the default length?+
No. For the default length of 1 m, 2.006409 s describes a complete back-and-forth oscillation. Travel from one extreme to the opposite extreme takes half the period.
Can this calculator predict a pendulum’s period on the Moon?+
Not directly. It fixes gravitational acceleration at 9.80665 m/s² rather than accepting a location-specific value. A lunar calculation would require using lunar gravity in T = 2π√(L/g).
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
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Results are estimates for informational purposes and are not financial, medical or legal advice.