The Period Of A Pendulum Calculator
A pendulum's period depends on just two things: how long it is and how strong gravity is. Neither the mass hanging on the end nor a small swing angle changes the answer.
Period
2.0064
- Frequency
- 0.4984
- Angular frequency
- 3.1316
- Swings per minute
- 29.9042
- Length of a seconds pendulum
- 0.9936
Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.
The formula this calculator uses
T = 2 x pi x sqrt(L / g)
- T
- The period, the time for one complete swing there and back
- L
- The length of the pendulum from pivot to centre of mass
- g
- The acceleration of gravity, 9.80665 m/s^2 at standard gravity
- pi
- About 3.14159, from the circular motion of the swing
How to check the result by hand
- 1
Divide the length by gravity
One metre divided by 9.80665 is 0.101972 seconds squared. Keeping the units straight here is what makes the square root come out in seconds.
- 2
Take the square root
The square root of 0.101972 is 0.31933 seconds. This is the time scale of the swing, and it grows with the square root of the length.
- 3
Multiply by two pi
0.31933 times 6.283185 is 2.0064 seconds, the period of a 1 metre pendulum. Roughly two seconds, which is a useful rule of thumb.
- 4
Cross check against the seconds pendulum
A two second period needs a length of 0.993621 metres, just six millimetres short of a metre. If your answer is far from that, a unit conversion went wrong.
For worked examples, common mistakes and the limits of this formula, read the full How To Calculate The Period Of A Pendulum page.