Download your PDF
Physical Pendulum Period Calculator result sheet — free, supported by sponsors. Your download button appears in 20 seconds.
This free download is supported by sponsors — continuing in
20
Your file is generated in your browser when you choose Download — nothing is uploaded. If this calculator returns enough numeric data, the export also includes its best-fit chart alongside the readable table.
WorldCalculate result export
Physical Pendulum Period Calculator — result sheet
Calculate the small-angle period and frequency of a rigid-body physical pendulum from inertia, mass, pivot distance, and gravity.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Period=2π√(moment of inertia/(mass×gravity×pivot distance)); frequency=1/period.
The physical-pendulum model combines rotational inertia with the restoring torque produced by gravity acting at the center of mass.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Moment of inertia about pivot — kg·m²; minimum 1.0E-6; maximum 1000000000000
- Pendulum mass — kg; minimum 1.0E-6; maximum 1000000000000
- Pivot-to-center-of-mass distance — m; minimum 1.0E-6; maximum 1000000000
- Gravitational acceleration — m/s²; minimum 1.0E-6; maximum 10000
Worked example
| Input | Value |
|---|---|
| Moment of inertia about pivot | 0.2 |
| Pendulum mass | 2 |
| Pivot-to-center-of-mass distance | 0.1 |
| Gravitational acceleration | 9.80665 |
Period ≈2.006 s; frequency ≈0.4984 Hz.
Assumptions and limits
- Oscillations are small enough for the small-angle approximation.
- The body is rigid, the pivot is fixed, and the inertia is about that pivot.
- Damping, pivot friction, large-amplitude correction, and structural flexibility are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
No saved result was found. Please run the calculation first, then choose Download again.