Convert Radians Per Second (rad/s) to Revolutions Per Minute (rpm)
1 radian per second equals 9.5493 revolutions per minute.
Radian Per Second to Revolution Per Minute Converter
How to Convert Radian Per Second to Revolution Per Minute
1 radian per second = 9.5493 revolutions per minute
Revolution Per Minute = Radian Per Second × 9.5493
Example: 1 rad/s × 9.5493 = 9.5493 rpm
Reverse Conversion
To convert revolutions per minute back to radians per second:
- Remember, 1 revolution per minute equals 0.10472 radians per second.
- To convert 9.5493 rpm to rad/s, multiply
9.5493 x 0.10472, resulting in1 rad/s.
Common Radian Per Second to Revolution Per Minute Conversions
| Radian Per Second | Revolution Per Minute | Actions |
|---|---|---|
| 12 radians per second | 4.77465 revolutions per minute | |
| 1 radian per second | 9.5493 revolutions per minute | |
| 2 radians per second | 19.0986 revolutions per minute | |
| 5 radians per second | 47.7465 revolutions per minute |
| Radian Per Second | Revolution Per Minute | Actions |
|---|---|---|
| 10 radians per second | 95.493 revolutions per minute | |
| 50 radians per second | 477.465 revolutions per minute | |
| 100 radians per second | 954.93 revolutions per minute | |
| 200 radians per second | 1909.86 revolutions per minute |
Radians per second to revolutions per minute Conversion Table
Reference table with common radians per second to revolutions per minute conversions. All values calculated with high precision.
Radians Per Second to Revolutions Per Minute Table
0.0001 to 12
Radians Per Second to Revolutions Per Minute Table
1 to 100000
Revolutions Per Minute to Radians Per Second Table
0.001 to 5
Revolutions Per Minute to Radians Per Second Table
10 to 1000000
Definition of Radian Per Second
Radian per Second: Angular Frequency Unit
The radian per second (symbol: rad/s) is the SI unit of angular velocity and angular frequency. While hertz counts complete cycles, radians per second measures the rate of change of angular position. One complete cycle equals 2π radians, so the angular frequency ω (omega) relates to ordinary frequency f by ω = 2πf.
Conversions to Other Units of Measurement:
- Hertz (Hz): 1 rad/s equals 1/(2π) Hz (approximately 0.15915 Hz). To convert angular frequency to ordinary frequency, divide by 2π.
- Revolution per Minute (rpm): 1 rad/s equals 30/π rpm (approximately 9.5493 rpm). This conversion is essential for converting between physics notation and engineering notation.
- Revolution per Second (rps): 1 rad/s equals 1/(2π) rps (approximately 0.15915 rps).
Angular frequency is preferred in physics because it simplifies many equations. For example, the energy of a quantum is E = ℏω (where ℏ is the reduced Planck constant), and simple harmonic motion is described by x = A·sin(ωt).
- Definition
- SI unit of angular velocity; the rate of change of angular position in radians per second.
- Key relationship
- ω = 2πf (angular frequency = 2π × ordinary frequency)
- Common equivalents
- 1 rad/s = 1/(2π) Hz ≈ 0.15915 Hz
- 1 rad/s = 30/π rpm ≈ 9.5493 rpm
- 2π rad/s = 1 Hz (exact)
- Sources
Definition of Revolution Per Minute
Revolution per Minute: Rotational Speed Unit
The revolution per minute (symbol: rpm or r/min) is a unit of rotational frequency expressing the number of complete turns in one minute. It is one of the most widely used units in mechanical engineering, automotive, and industrial applications. From car engines to hard drives, rpm is the standard way to express how fast something spins.
Conversions to Other Units of Measurement:
- Hertz (Hz): 1 rpm equals exactly 1/60 Hz (approximately 0.01667 Hz). A car engine at 3,000 rpm operates at 50 Hz.
- Radian per Second (rad/s): 1 rpm equals π/30 rad/s (approximately 0.10472 rad/s). This conversion is essential in dynamics and control engineering.
- Revolution per Second (rps): 1 rpm equals 1/60 rps. At 7,200 rpm (a common hard drive speed), the disk spins 120 times per second.
Common rpm values: ceiling fans (50-300 rpm), car engines at idle (600-1000 rpm), hard drives (5,400-15,000 rpm), jet engines (10,000-25,000 rpm), dental drills (up to 400,000 rpm).
- Definition
- Unit of rotational frequency; number of complete revolutions per minute.
- Exact factors
- 1 rpm = 1/60 Hz = π/30 rad/s
- Common equivalents
- 1 rpm = 1/60 Hz ≈ 0.01667 Hz
- 1 rpm = π/30 rad/s ≈ 0.10472 rad/s
- 60 rpm = 1 Hz (exact)
- Sources
About the Radian Per Second
In electrical engineering, the angular frequency ω = 2πf simplifies many calculations. For a 50 Hz power grid, ω ≈ 314.16 rad/s; for 60 Hz, ω ≈ 376.99 rad/s. These values appear constantly in power system analysis, motor control, and signal processing.
Earth rotates at approximately 7.292 × 10⁻⁵ rad/s (one revolution per sidereal day of 23 hours, 56 minutes). This angular velocity is fundamental in calculating the Coriolis effect for weather patterns and long-range ballistics.
About the Revolution Per Minute
Vinyl records play at standardized speeds: 33⅓ rpm for LP albums, 45 rpm for singles, and 78 rpm for early shellac records. These speeds were chosen to balance audio quality with playing time and were standardized by the 1950s.
A Formula 1 engine can rev to over 15,000 rpm (limited by regulations), while a diesel truck engine typically operates between 1,200-1,800 rpm. Hard drives commonly spin at 5,400 or 7,200 rpm, with enterprise drives reaching 15,000 rpm.
Frequently Asked Questions
How many revolutions per minute are in one radian per second?
One radian per second equals 9.5493 revolutions per minute. To convert, multiply the radian per second value by 9.5493. For the reverse, divide the revolution per minute value by 9.5493 (or multiply by 0.10472).
What is 10 radians per second in revolutions per minute?
10 radians per second = 95.493 revolutions per minute. This is one of the most commonly searched conversions for this pair.
How precise is the radian per second-to-revolution per minute conversion?
The factor 9.5493 is accurate to 6 significant figures, derived from international measurement standards. Our calculator uses full precision internally.
Looking for the reverse? Convert Revolution Per Minute to Radian Per Second
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Related in other categories:
- Minutes to Hours — RPM = revolutions per minute
- Radians to Degrees — Angular frequency: ω = 2πf
