Angular Velocity Calculator
Angular velocity is how fast something rotates: ω = θ ÷ t. Compute it from an angle and a time, or convert between RPM and rad/s — tangential rim speed included.
Example: with Mode Angle ÷ time (ω = θ ÷ t) · Angle turned (θ) 360 · Angle unit degrees · Time (seconds) 4 · Value to convert (RPM / rad/s modes) 300 · Radius in m (optional, rim speed) 0.5 → Angular velocity: 1.57 rad/s.
Computed by the calculator below using its default values. Change any input to see your own numbers.
⚙️ Check spin speeds with a laser tachometer
Check it outAngular velocity formula and RPM conversion
The angular velocity formula is ω = θ ÷ t: angle turned divided by time, in radians per second. A wheel that turns 360° (2π = 6.2832 rad) in 4 s has ω = 6.2832 ÷ 4 = 1.57 rad/s — which is 90° per second, or 15 RPM. Angular speed is the same calculation; “velocity” just adds the rotation direction.
To convert RPM to rad/s, multiply by 2π/60 ≈ 0.10472 (300 RPM = 31.42 rad/s); multiply rad/s by 60/2π ≈ 9.5493 to go back. Tangential velocity — how fast a point on the rim actually moves — is v = ω × r: at 300 RPM, a point 0.5 m from the axis travels 31.42 × 0.5 ≈ 15.7 m/s. That’s why longer blades have much faster tips at the same RPM.
How it’s calculated
ω = θ ÷ t with the angle converted to radians first (360° = 2π rad; 1 revolution = 2π rad). Conversions: rad/s = RPM × 2π ÷ 60; RPM = rad/s × 60 ÷ 2π; deg/s = rad/s × 180 ÷ π. Tangential speed v = ω × r with the radius in meters, giving m/s.
Results update as you type and are estimates, not professional advice — verify important decisions with a qualified professional.
Common mistakes
- Dividing degrees by time and calling it rad/s — convert the angle to radians first (multiply degrees by π/180).
- Mixing up RPM and rad/s — 100 RPM is only 10.47 rad/s; the factor is 2π/60.
- Using diameter instead of radius for tangential speed — v = ωr wants the distance from the axis.
Frequently asked questions
How do you find angular velocity?
Divide the angle turned (in radians) by the time: ω = θ ÷ t. Half a turn (π ≈ 3.1416 rad) in 2 s is about 1.57 rad/s.
How do I convert RPM to rad/s?
Multiply RPM by 2π/60 ≈ 0.10472. An engine idling at 800 RPM spins at about 83.8 rad/s.
What is tangential velocity?
The straight-line speed of a point on a rotating object: v = ω × r. At 10 rad/s, a point 0.3 m from the axis moves 3 m/s.
Is angular speed the same as angular velocity?
Angular speed is the magnitude; angular velocity is a vector that also names the rotation axis and direction. Numerically both come from ω = θ ÷ t.
How many rad/s is one revolution per second?
One revolution is 2π radians, so 1 rev/s = 6.2832 rad/s = 60 RPM.