Solve period problems using mass, length, gravity, frequency. Switch methods easily and inspect every calculated step. Create graphs, save outputs, and verify examples with confidence.
T = 1 / f
Use this when frequency is already known. Period is the reciprocal of frequency.
T = 2π / ω
Use this when angular velocity is known in radians per second.
T = 2π√(L / g)
This assumes small swing angles and a light string with negligible air resistance.
T = 2π√(m / k)
This assumes an ideal spring and no damping.
T = 2π√(r³ / GM)
This assumes a circular orbit around a central body.
These sample rows help you validate expected outputs.
| Mode | Inputs | Expected Period (s) | Notes |
|---|---|---|---|
| Frequency | f = 2 Hz | 0.5000 | Reciprocal of frequency. |
| Angular Velocity | ω = 12.5664 rad/s | 0.5000 | Equivalent to 2 Hz motion. |
| Simple Pendulum | L = 1 m, g = 9.81 m/s² | 2.0061 | Small-angle approximation. |
| Mass-Spring | m = 0.5 kg, k = 200 N/m | 0.3142 | Ideal spring system. |
| Orbital | r = 7000 km, M = Earth | 5828.5166 | Near-Earth circular orbit example. |
Period is the time needed for one complete cycle of repeating motion. It is commonly measured in seconds and is the inverse of frequency.
They are reciprocals. If frequency increases, period decreases. The relationship is T = 1 / f when frequency is given in hertz.
Use it for a simple pendulum with a small swing angle, constant gravity, and a light string. Large angles need a more advanced model.
It is best for ideal undamped motion. Real springs with damping or friction may have slightly different behavior and a changing amplitude over time.
Stronger gravity pulls the pendulum back faster, shortening the period. Weaker gravity makes the motion slower, increasing the period.
Larger orbits cover more distance and move under weaker gravitational pull, so the full orbit takes longer to complete.
Yes. You can display the final period in seconds, milliseconds, minutes, or hours, while the calculator also keeps a base value in seconds.
Yes. It is useful for homework, lab checks, demonstrations, and quick verification of standard period equations in physics.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.