Angular Velocity Converter: rad/s, °/s, r/min & More

What is angular velocity?

Angular velocity is the rate at which an object rotates—how much angle it sweeps per unit time. It’s the rotational analogue of linear speed: instead of meters per second (m/s), you have radians per second (rad/s), degrees per second (°/s), or revolutions per minute (RPM). In physics and engineering, angular velocity (often written ω) appears in dynamics of rotating bodies, motors, turbines, gears, and anything that spins. The SI unit is radian per second (rad/s); the radian is dimensionless (length/length), so angular velocity has dimension 1/time (s⁻¹).

This converter lets you switch between 12 common ways to express angular velocity: radians per second, minute, hour, and day; degrees per second, minute, hour, and day; and revolutions per second, minute, hour, and day. Every value is normalized to rad/s under the hood, so conversions are consistent and you can mix units (e.g. convert from RPM to degrees per second in one step).

How angular velocity conversion works

To convert between any two angular velocity units, we first express both in rad/s. Multiply your value by the source unit’s factor (how many rad/s one unit equals), then divide by the target unit’s factor:

Example: convert 100 RPM to rad/s. One revolution per minute = 2π/60 rad/s, so 100 r/min = 100 × (2π/60) ≈ 10.47 rad/s. Another example: convert 30 degrees per second to rad/s. One °/s = π/180 rad/s, so 30 °/s = 30 × (π/180) = π/6 ≈ 0.524 rad/s. The tool above does this for all 12 units so you don’t have to remember the factors.

Key Angular Velocity Units Explained

Each unit’s factor to rad/s — what this angular velocity converter uses. 1 revolution = 2π radians; 1° = π/180 radians. Time divisors (per second, per minute, per hour, per day) give the conversion to rad/s.

Radians vs degrees vs revolutions: when to use which

Radians per second (rad/s) are the SI unit and are preferred in physics, calculus, and rotational dynamics because derivatives and integrals of angle work cleanly (e.g. ω = dθ/dt). Textbook formulas for torque, moment of inertia, and angular momentum use rad/s. Degrees per second (°/s) are common in navigation, robotics, and when hardware or displays use degrees (e.g. pan/tilt rates in °/s). Revolutions per minute (RPM or r/min) are the standard in motors, pumps, fans, and machinery—nameplate data and datasheets often give RPM, so converting RPM to rad/s is a frequent need when plugging into physics equations. Revolutions per day (r/d) or radians per day (rad/d) show up in astronomy and very slow rotations (e.g. Earth’s spin). This converter supports all of these so you can switch between specs and formulas without error.

Who uses an angular velocity converter?

Mechanical and electrical engineers convert motor nameplate RPM to rad/s for torque–speed calculations, or degree per second for servo specs. Students and educators use it to check homework (e.g. “convert 3600 RPM to rad/s”) and to relate textbook formulas (in rad/s) to real-world specs (in RPM or °/s). Robotics and automation often work in °/s or °/min for joint rates; converting to rad/s is needed when interfacing with dynamics libraries. Astronomy and geodesy sometimes use rad/day or °/day for slow rotations (e.g. Earth’s angular velocity ≈ 2π rad/day). HVAC and pump engineers see RPM on nameplates and may need rad/s for power or flow calculations. All conversions run in your browser—no data is sent to a server—so you can use it offline or on sensitive specs.

Why radian per second is the SI unit

The radian is the SI derived unit for plane angle. By definition, one radian is the angle subtended at the center of a circle by an arc equal in length to the radius, so the radian is dimensionless (length/length = 1). Angular velocity is angle per time, so its dimension is 1/time—the same as frequency. The SI unit is therefore rad/s (or s⁻¹ when the radian is omitted). The BIPM and CGPM adopt the radian and rad/s for coherent derived units; degrees and revolutions are accepted for use with SI but are not part of the coherent set. Using rad/s keeps formulas like v = rω (linear speed = radius × angular velocity) and P = τω (power = torque × angular velocity) dimensionally consistent. This converter uses rad/s as the internal base so every result is traceable to SI.

Common angular velocity conversions at a glance

Handy reference for rad/s to r/min, °/s to rad/s, and other everyday angular velocity conversions.

Avoiding common mistakes

The most common error is mixing units without converting: e.g. using RPM in a formula that expects rad/s, or plugging degrees per second into an equation written for rad/s. Always convert to a single unit (we recommend rad/s for physics) before combining with radius, torque, or moment of inertia. Another pitfall is confusing angular velocity (ω, in rad/s or °/s) with angular frequency (often also ω, in rad/s)—they’re numerically the same for rotation, but “frequency” can mean cycles per second (Hz), so 1 r/s = 2π rad/s = 1 Hz when “cycle” is one revolution. When in doubt, use this converter to express everything in rad/s, then apply your formulas.

Angular Velocity Conversion FAQ