Pendulum period calculator
Period of a simple pendulum from its length.
Fill in the fields and the result will appear here automatically.
Find the full out-and-back period of a simple pendulum in the small-angle approximation. Measure length from the pivot to the centre of mass of a compact bob. A full 1 s period needs about 24.84 cm at g=9.80665 m/s²; a traditional seconds pendulum takes 1 s for half a swing, has a full 2 s period and is about 99.36 cm long.
How it works
Formula and logic
T = 2π√(L/g); frequency = 1/T.
Example
A one-metre string swings with a period of 2.006 s — nearly two seconds, not one.
Fields and units
- String length — m
- Acceleration of gravity — m/s²
How to use
- — Gravity is adjustable: 1.62 on the Moon, 3.72 m/s² on Mars.
- — The mass of the bob does not affect the period — it is not in the formula.
- — No angle is entered, so large-amplitude period growth is not computed. Mass cancels in this simple-pendulum model.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- OpenStax: small-angle pendulum
- Limitation
- Compact bob, massless inextensible suspension, small angles and constant g; no air drag or damping. This is the full period, not the time between opposite turning points.
FAQ
Why does mass not affect the period?
A heavier bob is pulled harder but is exactly that much harder to accelerate. Mass enters both the force and the inertia, so it cancels — just as it does in free fall.
How long is a seconds pendulum?
The traditional name means a 1 s half-period, hence a full 2 s period. L=gT²/(4π²) gives 0.9936 m at g=9.80665 m/s². The calculator’s “Length for a 1 s period” row uses a full period and gives one quarter of that length, 0.2484 m.
Why only small swings?
It uses sinθ≈θ with θ in radians. Error grows continuously with amplitude; there is no sharp 15° boundary. The full nonlinear period depends on amplitude and is not computed here.
How was g measured with a pendulum?
By measuring length and period and solving the formula. The method reached a fraction of a per cent and revealed that gravity is weaker at the equator than at the poles.