Angular velocity measures rotation rate. A car wheel at 100 km/h turns at about 85 rad/s (800 rpm); the Earth turns at 7.29 × 10⁻⁵ rad/s. Linear speed grows with distance from the axis: v = ω·r.
How to use the Angular Velocity Calculator
- Method
- Angle change Δα
- Time t
- Velocity v
- Radius r
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose the method and enter your values. Use the unit menu to show the result in rpm or Hz.
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 |
|---|---|
| Method | Choose one: Angle difference and time, Linear (tangential) velocity and radius |
| Angle change Δα | Units: °, rad, rev |
| Time t | Units: s, ms, min, h, days |
| Velocity v | Units: m/s, km/h, mph, ft/s, knots, km/s |
| Radius r | Units: m, cm, mm, km, in, ft … |
What each result means
- In rpm = [Angular velocity ω]
- Period of one turn = 2×pi÷[Angular velocity ω]
Example values
How the main result changes when Angle change Δα changes and everything else stays at the example values above:
| Angle change Δα (°) | Angular velocity ω (rad/s) |
|---|---|
| 180 | 1.5708 |
| 270 | 2.3562 |
| 360 | 3.1416 |
| 450 | 3.927 |
| 540 | 4.7124 |
| 720 | 6.2832 |
Formula
ω = Δα/t · ω = v/rWorked example
Inputs — Method: Angle difference and time; Angle change Δα: 360 °; Time t: 2 s.
Results — Angular velocity ω = 3.14159 rad/s; In rpm = 30 rpm; Period of one turn = 2 s.
Key terms
- Angular velocity
- Rate of change of angle.
Frequently asked questions
How fast does the Earth rotate?
7.29 × 10⁻⁵ rad/s – one turn per sidereal day.
How do I convert rpm to rad/s?
Multiply by π/30.
Do all points of a rigid wheel have the same ω?
Yes – but points farther out move faster.
Is angular velocity a vector?
Yes, pointing along the rotation axis.
What formula does the Angular Velocity Calculator use?
ω = Δα/t · ω = v/r.