# Angular Frequency Calculator

URL: https://speedycalculator.com/calculators/physics/angular-frequency/
Last updated: 2026-10-30

> The angular frequency calculator finds ω for a rotating object from the angle turned and time, or for an oscillation from its period or frequency – in rad/s, rpm and Hz.

## Inputs

- Object
- Angular displacement Δθ (rad, °, rev)
- Time taken Δt (s, ms, min, h, days)
- Time period T (s, ms, min, h, days)
- Frequency f (Hz, kHz, MHz, GHz, THz, rpm)

## Results

- Angular frequency ω
- Frequency
- Period

## Formula

```
ω = Δθ/Δt · ω = 2π/T = 2π·f
```

## Explanation

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

FieldWhat to enterObjectChoose one: Rotating (angle and time), Oscillating – from the period, Oscillating – from the frequencyAngular displacement ΔθUnits: rad, °, revTime taken ΔtUnits: s, ms, min, h, daysTime period TUnits: s, ms, min, h, daysFrequency fUnits: 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)5314.15937.5314.159310314.159312.5314.159315314.159320314.1593

## Worked 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.

## FAQ

**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.


## Sources

- [OpenStax – University Physics Volume 1](https://openstax.org/details/books/university-physics-volume-1)
- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)