Angular frequency describes how fast something rotates or oscillates in radians per second. It appears in every wave and vibration formula, from pendulums and springs to AC circuits (ω = 2π × 50 Hz ≈ 314 rad/s).
How to use the Angular Frequency Calculator
- Object
- Angular displacement Δθ
- Time taken Δt
- Time period T
- Frequency f
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose rotating or oscillating. For oscillations enter either the period or the frequency.
Tips
- Rotational formulas mirror linear ones: torque ↔ force, moment of inertia ↔ mass, ω ↔ v.
- Angles in formulas are in radians; 1 revolution = 2π rad.
- rpm ÷ 60 × 2π gives rad/s – or simply use the unit menu.
- The moment of inertia depends on both the mass and how far it is from the axis.
Common mistakes to avoid
- Using rpm directly in ω-based formulas.
- Confusing centripetal (real) and centrifugal (apparent) force.
- Using diameter in place of radius.
Inputs explained
| Field | What to enter |
|---|---|
| Object | Choose one: Rotating (angle and time), Oscillating – from the period, Oscillating – from the frequency |
| Angular displacement Δθ | Units: rad, °, rev |
| Time taken Δt | Units: s, ms, min, h, days |
| Time period T | Units: s, ms, min, h, days |
| Frequency f | Units: Hz, kHz, MHz, GHz, THz, rpm |
What each result means
- Frequency = [Angular frequency ω]÷(2×pi)
- Period = 2×pi÷[Angular frequency ω]
Example values
How the main result changes when Angular displacement Δθ changes and everything else stays at the example values above:
| Angular displacement Δθ (rad) | Angular frequency ω (rad/s) |
|---|---|
| 5 | 314.1593 |
| 7.5 | 314.1593 |
| 10 | 314.1593 |
| 12.5 | 314.1593 |
| 15 | 314.1593 |
| 20 | 314.1593 |
Formula
ω = Δθ/Δt · ω = 2π/T = 2π·fWorked example
Inputs — Object: Oscillating – from the period; Time period T: 0.02 s.
Results — Angular frequency ω = 314.15927 rad/s; Frequency = 50 Hz; Period = 0.02 s.
Key terms
- Angular frequency
- 2π times the frequency.
Frequently asked questions
What is the difference between frequency and angular frequency?
ω = 2πf; f counts cycles per second, ω radians per second.
What is ω for 50 Hz mains?
About 314.16 rad/s.
How do I convert rpm to rad/s?
Multiply by 2π/60 ≈ 0.1047.
Is angular frequency the same as angular velocity?
Numerically yes for uniform rotation; ω for oscillations is a rate of phase change.
What formula does the Angular Frequency Calculator use?
ω = Δθ/Δt · ω = 2π/T = 2π·f.