# Angular Velocity Converter

> Convert angular velocity between radians per second, degrees per second, revolutions per minute (RPM), and other rotational speed units

**Category:** Conversion
**Keywords:** angular velocity, radians per second, RPM, degrees per second, revolutions per second, hertz, rotation, conversion, rad/s, Hz
**URL:** https://complete.tools/velocity-angular-converter

## How it calculates

**Formula:**
```
ω₂ = ω₁ × (conversionFactor₁ / conversionFactor₂)
```

**Where:**
- **ω₁** = Input angular velocity value in the source unit
- **ω₂** = Output angular velocity value in the target unit
- **conversionFactor** = Factor to convert each unit to rad/s (the base unit)

**Base Conversion Factors (to rad/s):**
- **rad/s** = 1 (base unit)
- **deg/s** = π / 180 rad/s ≈ 0.01745
- **RPM** = 2π / 60 rad/s ≈ 0.10472
- **rev/s** = 2π rad/s ≈ 6.28319
- **Hz** = 2π rad/s ≈ 6.28319 (same as rev/s, cycles per second)
- **rad/min** = 1 / 60 rad/s ≈ 0.01667
- **rad/hr** = 1 / 3600 rad/s ≈ 0.000278
- **deg/min** = π / 10800 rad/s ≈ 0.000291
- **deg/hr** = π / 648000 rad/s ≈ 0.00000485

**Example Calculation:**
Converting 100 RPM to rad/s:
- First, multiply by the RPM conversion factor: 100 × (2π / 60)
- Result: 100 × 0.10472 = 10.472 rad/s

**Example Converting Between Units:**
Converting 3600 deg/hr to RPM:
- Convert to rad/s: 3600 × (π / 648000) = 0.01745 rad/s
- Convert to RPM: 0.01745 / (2π / 60) = 0.1667 RPM

## Who should use this

- **Mechanical Engineers**: Engineers designing rotating machinery such as motors, turbines, gears, and flywheels frequently need to convert between RPM (common in industry) and rad/s (used in mathematical calculations and simulations).

- **Physics Students and Researchers**: Angular velocity is fundamental to rotational mechanics. Students studying circular motion, torque, and angular momentum need to convert between different unit systems used in textbooks and laboratory equipment.

- **Automotive Professionals**: Engine speeds are typically measured in RPM, but calculations for wheel rotation, differential analysis, and drivetrain design often require conversions to other angular velocity units.

- **Aerospace Engineers**: Satellite orientation, gyroscope calibration, and propeller design all involve angular velocity calculations that may use different unit conventions depending on the application.

- **Robotics Developers**: Robot joint movements and motor control systems often specify angular velocities in various units. Converting between deg/s for user-friendly displays and rad/s for control algorithms is a common task.

- **Manufacturing Technicians**: CNC machine operators and technicians working with lathes, mills, and other rotating equipment need to understand and convert between different speed specifications.

- **Astronomers**: Earth's rotation, planetary motion, and satellite tracking involve angular velocities often expressed in degrees per hour or radians per hour for precise calculations.

## Real-world examples

**Electric Motors:**
A standard household ceiling fan operates at approximately 200 RPM on its highest setting. Converting this to rad/s for engineering calculations: 200 RPM = 20.94 rad/s. When designing the motor controller, engineers need this value in rad/s to calculate torque requirements and power consumption.

**Vehicle Wheels:**
A car traveling at 100 km/h with 65 cm diameter tires has wheels rotating at approximately 817 RPM. To calculate the angular acceleration needed for braking, engineers convert this to rad/s: 817 RPM = 85.6 rad/s. This conversion is essential for anti-lock braking system (ABS) calibration.

**Industrial Centrifuges:**
Laboratory centrifuges can spin at 15,000 RPM to separate blood components. In rad/s, this equals 1,571 rad/s. Medical equipment engineers use rad/s for stress calculations on the centrifuge rotor and sample containers.

**Lathe and CNC Machines:**
A metal lathe cutting steel might operate at 1,200 RPM for a specific cutting speed. Machinists often need to convert this to surface speed using the formula v = ω × r, where ω must be in rad/s: 1,200 RPM = 125.7 rad/s.

**Wind Turbines:**
Large wind turbines rotate slowly, typically at 10-20 RPM. At 15 RPM, the angular velocity is 1.57 rad/s. Engineers use this to calculate tip speed ratios and optimize blade efficiency.

**Hard Disk Drives:**
Traditional hard drives spin at 5,400 or 7,200 RPM. A 7,200 RPM drive has an angular velocity of 754 rad/s. This high speed requires precise bearing design and careful consideration of gyroscopic effects.

## How to use

1. **Enter your angular velocity value** in the input field. You can enter any positive or negative number, including decimal values. Negative values represent clockwise rotation when viewed from a standard reference frame.

2. **Select the input unit** from the dropdown menu. Choose the unit that matches your source measurement, whether that is rad/s, deg/s, RPM, rev/s, or any of the other supported units.

3. **View all converted values** instantly displayed in the results grid. Each card shows the equivalent angular velocity in a different unit, making it easy to find the value you need.

4. **Identify your input unit** by looking for the highlighted result card. The card corresponding to your selected input unit is displayed with a larger variant to help you track which unit you started with.

5. **Reference the quick guide** at the bottom of the tool for common conversion relationships. This includes the fundamental relationship that 1 revolution equals 2π radians equals 360 degrees.

**Practical Tips:**
- When working with motors and machinery, RPM is typically the most intuitive unit for human understanding, while rad/s is preferred for mathematical calculations.
- For very slow rotations like those in astronomy, deg/hr or rad/hr provide more manageable numbers.
- Remember that angular velocity is a vector quantity in three dimensions, but this converter handles the magnitude (scalar) portion of the measurement.

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*Generated from [complete.tools/velocity-angular-converter](https://complete.tools/velocity-angular-converter)*