Physics

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Pendulum Period Calculator.

Calculate ideal small-angle simple pendulum period.

On-device calculationNo signup
01

Set your values

Results update as you type.

Period: 2.006409 s

Period

0.000000s
Frequency: 0.498403 Hz

Frequency

0.000000Hz

Results update automatically as you type.

Use Cases

Physics homework and lab verification

Quickly compute the theoretical period for a simple pendulum experiment, allowing students to compare with measured values and verify the relationship between length and period.

Example: Enter length = 1 m and gravity = 9.81 m/s² to get a period of about 2.006 seconds.

Designing pendulum clocks or metronomes

Determine the required pendulum length to achieve a desired period, such as a 1-second period for a seconds pendulum, by adjusting the length input.

Example: For a 2-second period on Earth, set length ≈ 0.994 m.

Frequently Asked Questions

What is the pendulum period formula used by this calculator?
The calculator uses the small-angle approximation formula T = 2π√(L/g), where T is the period in seconds, L is the pendulum length in meters, and g is the acceleration due to gravity in m/s². This formula assumes the pendulum swings with a small amplitude (less than about 15 degrees).
How does gravity affect the pendulum period?
Gravity (g) is in the denominator of the formula, so a higher gravitational acceleration results in a shorter period. For example, on the Moon (g ≈ 1.62 m/s²) the same pendulum would have a longer period than on Earth (g ≈ 9.81 m/s²).
Can I use this calculator for any pendulum length?
Yes, you can enter any length in meters. However, the small-angle approximation is most accurate for lengths where the pendulum's amplitude is small. For very large amplitudes, the period becomes slightly longer than the ideal value, but this calculator provides the ideal small-angle period.

Tips & Common Mistakes

Tips

  • Use the standard gravity value 9.81 m/s² for Earth, but adjust it if you are at a high altitude or on another celestial body.
  • Ensure the pendulum length is measured from the pivot point to the center of mass of the bob, not just the string length.
  • For best accuracy, keep the initial angle small (less than 15 degrees) to satisfy the small-angle approximation.
  • Double-check your units: length must be in meters and gravity in m/s² to get the period in seconds.

Common Mistakes to Avoid

  • Using centimeters or other units for length without converting to meters, which leads to incorrect period values.
  • Forgetting that gravity is not always 9.81 m/s²; using the wrong value for your location or planet.
  • Assuming the formula works for large amplitudes; the small-angle approximation becomes less accurate as the angle increases.

Last updated: August 13, 2026