Revolution/min to Radian/s Converter

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Revolution/min vs Radian/s

revolution/min to radian/s metric conversion table

How to Convert RPM to RAD/S (Revolution/min to Radian/s)?

We can convert revolution/min to radian/s by using an example.

RPM to rad/s: Converting Motor Specs for Engineering Calculations

When you read a motor datasheet showing 1,750 RPM and need to calculate torque, power, or angular momentum, you must first convert to rad/s. This is because all SI physics equations expect angular velocity in radians per second. The conversion divides by 60 (minutes to seconds) and multiplies by 2π (revolutions to radians).

1. Take the rotational speed in RPM from the motor datasheet.
2. Multiply by 2π (≈ 6.2832) to convert revolutions to radians.
3. Divide by 60 to convert minutes to seconds.
4. Or simply multiply RPM by 0.10472 (which equals 2π ÷ 60).

RPM to rad/s for Common Motor Speeds

Standard motor speeds and their rad/s equivalents for engineering calculations:

Working Through RPM to rad/s Problems

RPM to rad/s Practice Problems

Try solving these on your own to test your understanding:

1. Convert 900 RPM to rad/s. (Answer: 94.25 rad/s)
2. A fan motor runs at 1,450 RPM. What is ω? (Answer: 151.84 rad/s)
3. Convert 5,000 RPM to rad/s. (Answer: 523.60 rad/s)
4. A hard drive spins at 7,200 RPM. Express in rad/s. (Answer: 753.98 rad/s)
5. Convert 120 RPM to rad/s. (Answer: 12.57 rad/s)

The Power Equation and Why rad/s Matters

Mechanical power P = τω, where τ is torque in N·m and ω is in rad/s, gives power directly in watts. If you use RPM instead, you need: P = (τ × RPM × 2π) ÷ 60, which adds error-prone factors. Converting to rad/s first keeps your calculations clean. This is especially important in electric vehicle drivetrain design where motor curves are specified in RPM but simulation software needs rad/s.

Angular Velocity in Robotics Control Systems

Robot joint controllers work in rad/s because PID loop gains are tuned in SI units. A servo motor datasheet might say "no-load speed: 5,000 RPM" but your control code needs 523.6 rad/s for velocity limits. Similarly, maximum acceleration (rad/s²) and jerk (rad/s³) limits all cascade from the base unit of rad/s. Getting this conversion right prevents dangerous overshoots in robotic arms.

Key Takeaways

• Multiply RPM by 0.10472 (or 2π/60) to get rad/s.
• 60 RPM = 2π rad/s ≈ 6.28 rad/s (one revolution per second).
• You need rad/s for power calculations: P = τω gives watts directly.
• Robotics and control systems exclusively use rad/s internally.
• Standard 4-pole motor: 1,500 RPM (50 Hz) = 157.08 rad/s.

Revolution/min to Radian/s Conversion Formula

Frequently Asked Questions