Angular Velocity Converter

Rotational Dynamics: Angular vs. Linear Velocity

Angular velocity (ω) quantifies how fast an object rotates around a fixed central axis in terms of angular displacement per unit time.

Relationship Between Angular and Linear Speed

Points further from the axis of rotation travel faster linearly than points close to the hub:

• Linear Velocity (v): \ (proportional to distance from the center).

• Centripetal Force: \ (forces acting on blades and tires grow quadratically with rotational speed).

How to Use This Calculator

Enter your Angular Speed / Rotational Velocity (e.g. 3600), From Unit — choose from Revolutions per Minute (RPM), Radians per Second (rad/s, Base SI), Degrees per Second (°/s), To Primary Target Unit — choose from Radians per Second (rad/s), RPM, Degrees per Second (°/s), and Rotating Radius (r in meters, for Tangential Velocity) (e.g. 0.30 (approx tire radius)). Results update instantly as you type — adjust any value to compare scenarios.

The Formula

Universal angular velocity (ω) and rotational kinematics formulas: to Radians/sec: ω = RPM × (2π) / (60) = RPM × (π) / (30) ≈ RPM × 0.104719755/sec to RPM: RPM = ω × (60) / (2π) = ω × (30) / (π) ≈ ω × 9.54929658 Linear Speed: v = ω × r Centripetal Acceleration: a_c = ω^2 × r = (v^2) / (r)

Worked Example

For example, an electric motor spinning at 3,600 RPM with a 0.30-meter (11.8 in) radius pulley: . In other angular units, this is \ and . The outer pulley rim moves at a tangential speed of .

Understanding Your Result

Speed benchmarks for reference: typical car 0–60 mph in 5–8 seconds (average), performance sports car under 4 seconds, Tesla Model S Plaid under 2 seconds. Running pace: sub-6 min/mile is competitive amateur; 8–10 min/mile is average recreational runner. Cycling: 12–16 mph average recreational; 18–22 mph intermediate. Velocity calculations assume constant acceleration — real-world values vary due to friction, air resistance, and grade changes.