# Revolution Per Minute Converters

> Convert RPM to and from radians per second, degrees per second, hertz, and other angular velocity units

**Category:** Conversion
**Keywords:** rpm, revolution per minute, angular velocity, radians per second, hertz, frequency, conversion
**URL:** https://complete.tools/revolution-per-minute-converters

## How it calculates

The converter uses RPM as its base unit and applies mathematically precise conversion factors to translate between units. The fundamental relationships are derived from the definitions of each unit:

**RPM to Radians per Second:**
rad/s = RPM × (2π / 60)
Since one revolution equals 2π radians and there are 60 seconds in a minute, multiplying RPM by π/30 (approximately 0.10472) gives radians per second.

**RPM to Degrees per Second:**
deg/s = RPM × 6
One revolution equals 360 degrees, and dividing by 60 seconds per minute gives 6 degrees per second per RPM.

**RPM to Hertz:**
Hz = RPM / 60
Hertz measures cycles (revolutions) per second, so dividing RPM by 60 converts from per-minute to per-second.

**RPM to Revolutions per Second:**
rev/s = RPM / 60
This is equivalent to the hertz conversion since one revolution equals one cycle.

**RPM to Revolutions per Hour:**
rev/h = RPM × 60
Multiplying by 60 converts from per-minute to per-hour.

The tool also supports conversions involving radians per minute, degrees per minute, milliradians per second, gradians per second, and cycles per minute and second. All conversions maintain high precision using double-precision floating-point arithmetic and display results to eight significant figures where appropriate.

## Who should use this

Mechanical engineers designing motors, gearboxes, and rotating equipment who need to specify or verify rotational speeds in different unit systems; automotive engineers and mechanics working with engine specifications and tachometer readings; electrical engineers working with AC motor synchronous speeds and variable frequency drives; aerospace engineers calculating propeller and turbine rotational speeds; physicists and students studying rotational dynamics and angular momentum; laboratory technicians operating centrifuges and specifying separation parameters; hard drive and storage device engineers working with disk rotational speeds; manufacturing engineers programming CNC machines and spindle speeds; HVAC technicians working with fan and blower specifications; music technologists calculating turntable speeds and pitch adjustments; wind energy engineers analyzing turbine rotational behavior; and anyone converting between metric (rad/s) and practical (RPM) angular velocity units.

## Worked examples

**Example 1: Converting Engine Speed to Radians per Second**
A car engine is running at 3000 RPM. To calculate the angular velocity in radians per second:
rad/s = 3000 × (2π / 60) = 3000 × 0.10472 = 314.16 rad/s
This value is useful for calculating centripetal forces on engine components or for physics-based simulations.

**Example 2: Converting a Centrifuge Speed to Hertz**
A laboratory centrifuge operates at 12,000 RPM. To express this as frequency in hertz:
Hz = 12,000 / 60 = 200 Hz
This tells us the centrifuge completes 200 revolutions every second, which is relevant for timing and synchronization calculations.

**Example 3: Converting Angular Velocity from Physics to Practical Units**
A physics problem specifies an angular velocity of 50 rad/s. To convert this to RPM for a practical engineering application:
RPM = 50 × (60 / 2π) = 50 × 9.5493 = 477.46 RPM
This conversion helps bridge theoretical calculations with real-world motor specifications.

**Example 4: Converting Turntable Speed**
A vinyl record player operates at 33.33 RPM. To find the angular velocity in degrees per second:
deg/s = 33.33 × 6 = 200 deg/s
The turntable rotates through 200 degrees every second, completing one revolution in 1.8 seconds.

**Example 5: High-Speed Industrial Application**
A grinding wheel spins at 8,500 RPM. Converting to revolutions per second:
rev/s = 8,500 / 60 = 141.67 rev/s
This is equivalent to approximately 141.67 Hz, useful for vibration analysis and resonance calculations.

## Limitations

This converter assumes constant angular velocity and does not account for acceleration, deceleration, or varying rotational speeds. The tool provides instantaneous conversion values and cannot model time-varying rotational behavior. Precision is limited to approximately 8 significant figures due to floating-point arithmetic, which may introduce minor rounding errors in extreme precision applications. The converter does not account for physical factors such as slip in motors, gear ratios, or mechanical losses that affect actual rotational speeds in real systems. Very large or very small values may be displayed in scientific notation for readability. The tool converts between units of angular velocity only and does not calculate related quantities such as torque, angular momentum, or centripetal force. Users working with alternating current motor specifications should note that this tool converts raw RPM values and does not calculate synchronous speeds from frequency and pole count.

## FAQs

**
**Q:** What is the difference between RPM and hertz?**


**A:** RPM (revolutions per minute) and hertz (Hz) both measure rotational frequency, but on different time scales. RPM counts complete rotations per minute, while hertz counts rotations (cycles) per second. To convert RPM to hertz, divide by 60. For example, 3000 RPM equals 50 Hz.

**
**Q:** Why do physicists prefer radians per second over RPM?**


**A:** Radians provide a dimensionless ratio that simplifies many physics equations. When angular velocity is expressed in rad/s, relationships like v = ωr (linear velocity equals angular velocity times radius) work directly without conversion factors. Radians also connect naturally to trigonometric functions used in wave and oscillation analysis.

**
**Q:** How do I convert RPM to linear speed?**


**A:** First convert RPM to radians per second using this tool, then multiply by the radius: v = ω × r, where v is linear speed, ω is angular velocity in rad/s, and r is the radius. For example, a wheel with 0.3m radius spinning at 100 RPM: ω = 100 × (2π/60) = 10.47 rad/s, so v = 10.47 × 0.3 = 3.14 m/s.

**
**Q:** What RPM do common devices operate at?**


**A:** Hard drives typically spin at 5,400 or 7,200 RPM. Car engines idle around 600-1000 RPM and may reach 6,000-8,000 RPM. Washing machines spin at 800-1,600 RPM. Dental drills can exceed 400,000 RPM. Vinyl records play at 33.33, 45, or 78 RPM.

**
**Q:** Can I use this for very high speeds like in turbomachinery?**


**A:** Yes, the converter handles a wide range of values accurately. For example, gas turbine engines operating at 30,000+ RPM can be converted without issues. Results for very large or small values are displayed in scientific notation for clarity.

**
**Q:** What is the relationship between RPM and frequency for AC motors?**


**A:** For synchronous AC motors, the relationship is: RPM = (120 × frequency) / poles, where frequency is in hertz and poles is the number of magnetic poles. This tool converts the resulting RPM to other units but does not calculate synchronous speed directly from electrical frequency.

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*Generated from [complete.tools/revolution-per-minute-converters](https://complete.tools/revolution-per-minute-converters)*