Angular Velocity Calculator
A rotation expressed every way — revolutions per minute, radians per second, degrees per second, period and frequency — with the linear speed and centripetal acceleration at a chosen radius, and the rpm that would give a target tip speed.
Angular velocity is angle turned per unit time; one revolution is 2π radians or 360°, so rpm times 2π over 60 is radians per second.
How the angular velocity calculator works
Angular velocity is angle turned per unit time; one revolution is 2π radians or 360°, so rpm times 2π over 60 is radians per second. A point at radius r moves at ω r and accelerates toward the center at ω² r — the reason rotating machinery has a speed limit set by its radius. The period is the time for one turn; the frequency is turns per second.
Formula: ω = 2π × rpm / 60; v = ω r; a = ω² r; T = 2π / ω
Worked examples
| Inputs | Angular velocity (rad/s) | Note |
|---|---|---|
| 3,000 rpm at 150 mm | 314.1593 | 47 m/s, 1,500 g |
| A vinyl record | 3.4906 | half a meter a second |
| A centrifuge | 1,256.6371 | over 12,000 g |
FAQFrequently asked questions
How do I convert rpm to radians per second?
Multiply by 2π and divide by 60 — or, near enough, multiply by 0.1047. 3,000 rpm is 314 rad/s.
What is the difference between angular and linear speed?
Angular speed is how fast the whole thing turns; linear speed is how fast a point on it moves, which grows with radius. The hub and the rim share the angular speed and nothing else.
Why does centripetal acceleration grow so fast?
Because it goes with the square of the angular velocity. Doubling the rpm quadruples the inward pull, which is why rotating parts are rated by rpm and radius.
What tip speeds are typical?
Grinding wheels run to about 50 m/s, fan blades 60 to 100, jet turbines over 400 — the limit set by the strength of the material against its own centripetal load.
What is a rad/s in everyday terms?
About 9.55 rpm. A second hand turns at 0.105 rad/s; a car engine at idle around 80.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Institute of Standards and Technology — the US measurement authority
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.