Pendulum Period Calculator
Calculate the period, frequency, and length for any simple pendulum.
⏱️ Physics📐 T = 2π × √(L/g)
Pendulum length (m)
Gravity (m/s²)
Please enter valid values.
Formula & Reference
| Variable | Formula | Units |
|---|---|---|
| Pendulum Period Calculator | T = 2π × √(L/g) | seconds |
Step-by-Step Examples
Example 1
1-Meter Pendulum
L=1.0 m, g=9.81 m/s².
- T = 2π × √(1/9.81) = 2.007 s
✓ T = 2.007 s
Example 2
Grandfather Clock
Target T=2s — what length?
- L = g(T/2π)² = 9.81×(2/2π)² = 0.993 m ≈ 1 m
✓ L ≈ 0.993 m
Example 3
Moon Pendulum
L=1.0 m, g=1.62 m/s² (Moon).
- T = 2π × √(1/1.62) = 4.93 s — much slower!
✓ T = 4.93 s
Real-World Applications
Physics Students
Master simple harmonic motion.
Horologists
Design clock pendulums.
Teachers
Demonstrate gravity measurement.
Geophysicists
Measure local gravity variations.
Common Mistakes to Avoid
⚠️
Beyond small angle
Formula only accurate below ~15°. Larger angles need elliptic integrals.
⚠️
Ignoring air resistance
Friction reduces period slightly and causes decay.
Frequently Asked Questions
Why doesn't mass affect period? ▾
Gravitational and inertial mass cancel. Heavy and light pendulums of same length have identical periods.
How was g first measured? ▾
By measuring T and L precisely: g = 4π²L/T².
What is SHM? ▾
Simple Harmonic Motion — restoring force proportional to displacement.