Gravity pendulum input form
Choose what you want to solve for, then enter the other values. The layout uses three columns on large screens, two on medium screens, and one on mobile.
Formula used
T₀ = 2π √(L / g)
T ≈ T₀ × (1 + θ²/16 + 11θ⁴/3072)Here,
θ is in radians.
g = 4π²L × c² / T²where
c = 1 + θ²/16 + 11θ⁴/3072.
L = gT² / (4π²c²)
f = 1 / T,
ω = 2π / T,
h = L(1 - cosθ),
vₘₐₓ = √(2gh),
E = mgh
These formulas work well for classroom analysis, lab checks, and quick comparisons. For very large swing angles, a full nonlinear model is more exact.
How to use this calculator
- Select whether you want to calculate the period, gravity, or pendulum length.
- Enter the known values in SI units: meters, seconds, kilograms, and m/s².
- Add the initial release angle. A small value gives near-classical motion.
- Enter bob mass if you want weight and energy outputs.
- Choose your preferred decimal precision.
- Press Calculate to show the result block above the form.
- Review the graph, table, and export the results as CSV or PDF.
Example data table
| Example | Length (m) | Gravity (m/s²) | Angle (deg) | Corrected Period (s) | Frequency (Hz) |
|---|---|---|---|---|---|
| Lab pendulum A | 1.00 | 9.80665 | 5 | 2.007365 | 0.498166 |
| Lab pendulum B | 2.00 | 9.81 | 10 | 2.842417 | 0.351813 |
| Lab pendulum C | 0.75 | 9.79 | 15 | 1.746557 | 0.572555 |
These examples use the same correction model as the calculator.
8 FAQs
1) What does a gravity pendulum calculator measure?
It relates pendulum length, gravitational acceleration, and oscillation period. This version also estimates frequency, angular frequency, release energy, maximum speed, and angle-corrected motion for better practical analysis.
2) Why does the pendulum period depend on length?
A longer pendulum travels a bigger arc and takes more time to complete one swing. Under small-angle conditions, the period grows with the square root of length.
3) Does bob mass change the period?
For an ideal simple pendulum, mass does not change the period. Mass only affects force and energy values, such as bob weight and gravitational potential energy at release.
4) Why include the initial angle?
Small-angle formulas are common, but larger release angles slightly increase the real period. The calculator uses a correction factor, giving more realistic results for moderate swings.
5) Can I use this to estimate local gravity?
Yes. Measure pendulum length and period carefully, then solve for gravity. Better timing, accurate pivot-to-center length, and small air resistance improve the estimate.
6) What units should I enter?
Use meters for length, seconds for period, kilograms for mass, degrees for angle, and meters per second squared for gravity. The calculator assumes SI units throughout.
7) Is the graph physically exact?
The graph is idealized. It uses one corrected cycle and a simple harmonic shape for visualization. It is very useful for study and comparison, though not a full nonlinear simulation.
8) When should I avoid this model?
Avoid relying on it for extremely large angles, flexible strings, moving pivots, strong damping, or driven pendulums. Those cases need more advanced equations or numerical methods.