Physical Pendulum Calculator
Work out physical pendulum instantly with clear inputs, formula shown and shareable results.
About Physical Pendulum Calculator
A rigid body swinging on a pivot has period 2 pi sqrt(I/(mgd)), where d is the pivot-to-centre-of-mass distance. Unlike the simple pendulum, mass distribution matters: I/(md) is the length of a simple pendulum that would keep the same time, which is how a compound pendulum is characterised.
Formulas
Period
T = 2 pi sqrt(I / (m g d))
Equivalent length
L(eq) = I / (m d)
Worked example
With the default values below, Physical Pendulum Calculator returns Period Of Oscillation of 1.5542. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Moment of inertia about the pivotminimum 0 kg m2
- 0.45 kg m2
- Mass of the bodyminimum 0 kg
- 2.5 kg
- Distance from pivot to centre of massminimum 0 m
- 0.3 m
Results
- Period Of Oscillation
- 1.5542 s
- Frequency
- 0.6434 Hz
- Equivalent Simple Pendulum Length
- 0.6000 m
- Radius Of Gyration
- 0.4243 m
Step by step
- 1Values used
- 2Period
- 3Equivalent length
- 4Period Of Oscillation= 1.5542 s
- 5Frequency= 0.6434 Hz
- 6Equivalent Simple Pendulum Length= 0.6000 m
- 7Radius Of Gyration= 0.4243 m
Assumptions and limits
- The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
Why does a metre stick swung from its end beat faster than a metre pendulum?
Because its equivalent length is only two thirds of a metre - the mass is distributed rather than concentrated at the far end.
What is the centre of oscillation?
The point at the equivalent length from the pivot. Striking there produces no reaction at the pivot, which is the sweet spot on a bat.