Velocity - Angular Converter

Convert angular velocity between rad/s, degrees/second, RPM, rev/s, and other rotational speed units with scientific precision.

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Angular Velocity Units Explained

Radian/Second (rad/s)

The SI unit of angular velocity. It represents the rate of change of angle measured in radians. ω = θ / t.

Common uses: International standards, physics, engineering, scientific calculations.

Degree/Second (°/s)

Angular velocity using degrees instead of radians. 1 rad/s ≈ 57.3 °/s. More intuitive for some applications.

Common uses: Mechanical specifications, surveying, navigation, everyday applications.

Revolution/Minute (rev/min or RPM)

The number of complete rotations in one minute. 1 rev/min ≈ 0.1047 rad/s. Very common in machinery.

Common uses: Motor speed, fan speed, engine RPM, rotating equipment specifications.

Revolution/Second (rev/s or Hz)

The number of complete rotations per second. 1 rev/s = 2π rad/s ≈ 6.283 rad/s. Unit of frequency.

Common uses: High-speed equipment, frequency measurements, AC power systems.

Angular Velocity Relationships

Fundamental equations for angular motion:

  • Definition: ω = θ / t (angle change / time)
  • Angular to linear: v = ω × r (linear velocity = angular × radius)
  • Conversion: 1 revolution = 2π radians
  • Period: T = 2π / ω (time for one revolution)

Common Angular Velocity Conversions

  • 1 rad/s ≈ 0.1592 rev/s ≈ 9.549 rev/min
  • 1 rev/min ≈ 0.1047 rad/s ≈ 0.01667 rev/s
  • 1 rev/s = 2π rad/s ≈ 6.283 rad/s = 60 rev/min
  • 1 degree/second ≈ 0.01745 rad/s
  • 360 degrees/second = 1 rev/s = 2π rad/s

Typical Angular Velocity Values

  • Earth's rotation: ~7.3 × 10⁻⁵ rad/s (~1/24 hour)
  • Record player: ~3.5 RPM (0.37 rad/s)
  • Typical electric motor: 1000-3600 RPM (105-377 rad/s)
  • Car engine at idle: 500-800 RPM (52-84 rad/s)
  • Car engine at high speed: 6000-8000 RPM (628-838 rad/s)
  • Jet engine: 50,000+ RPM (5,000+ rad/s)
  • Compact disc: 200-500 RPM (21-52 rad/s)

Relationship between Angular and Linear Velocity

For an object rotating about a fixed axis:

  • Linear velocity at radius r: v = ω × r
  • Angular velocity: ω = v / r
  • Example: A wheel with radius 0.5 m rotating at 100 rad/s has a linear velocity of 50 m/s at its edge

Angular Acceleration and Centripetal Acceleration

Related concepts in rotational motion:

  • Angular acceleration: α = dω/dt (change in angular velocity)
  • Centripetal acceleration: a = ω² × r (directed toward center)
  • Tangential acceleration: a_t = α × r (along the path)

Common Applications

Angular velocity conversions are essential in:

  • Motor Specifications: Motor speed in RPM
  • Vehicle Performance: Engine RPM, wheel rotation speed
  • Rotating Equipment: Fans, pumps, compressors, turbines
  • Mechanical Design: Shaft speed, gear ratios
  • Industrial Control: Speed regulation, frequency control
  • Power Transmission: Belt and pulley systems
  • Astronomy: Planetary rotation, orbital mechanics