Convert Revolutions Per Minute (rpm) to Radians Per Second (rad/s)

What Is a Revolution Per Minute?

RPM measures rotational speed in complete revolutions per minute. Standard for engines, turbines, and rotating machinery.

What Is a Radian Per Second?

Radians per second (rad/s) is the SI unit of angular velocity. One revolution = 2π radians, making rad/s the natural unit for physics and engineering.

Revolution Per Minute to Radian Per Second Formula

The conversion formula is:

rad/s = RPM × 2π ÷ 60 ≈ RPM × 0.10472

Derived from: 1 RPM = 1 rev/min = 2π rad / 60 s ≈ 0.10472 rad/s.

Worked Example

Convert 3000 revolution per minute (3,000 RPM motor):

1. Calculate: 3000 → 314.16 radian per second

Common Use Cases

This conversion is essential wherever mechanical specifications meet physics calculations:

• Electric motor control: Motor datasheets specify speed in RPM (e.g., 1,500 RPM or 3,000 RPM), but control algorithms using torque equations (τ = Iα) require angular velocity in rad/s. A 3,000 RPM motor operates at 314.16 rad/s.
• Mechanical engineering: Shaft design, gear ratio calculations, and centrifugal force analysis use the formula F = mω²r, where ω must be in rad/s. Converting from the RPM specification on a machine nameplate is a standard engineering step.
• Robotics and servo systems: Industrial robots specify joint speeds in RPM or degrees/second, but inverse kinematics algorithms work in rad/s. A servo rated at 60 RPM has an angular velocity of 6.283 rad/s (exactly 2π).
• Physics and dynamics: Textbook problems involving angular momentum (L = Iω), rotational kinetic energy (½Iω²), and centripetal acceleration (a = ω²r) all require ω in rad/s, not RPM.