Convert Revolutions per second to Radians per second
Instantly convert Revolutions per second (rev/s) to Radians per second (rad/s) with our free online calculator.
Formula: rev/s to rad/s — multiply by 6.28319
Reference Table
| Revolutions per second (rev/s) | Radians per second (rad/s) |
|---|---|
| 1 | 6.28319 |
| 5 | 31.4159 |
| 10 | 62.8319 |
| 25 | 157.08 |
| 50 | 314.159 |
| 100 | 628.319 |
How to Convert Revolutions per second to Radians per second
Formula
To convert Revolutions per second (rev/s) to Radians per second (rad/s): multiply by 6.28319
Step-by-Step
- Start with your value in Revolutions per second (rev/s).
- Multiply by 6.28319 to perform the conversion.
- The result is your value expressed in Radians per second (rad/s).
Conversion Factor
1 rev/s = 6.28319 rad/s
Reverse Factor
1 rad/s = 0.159155 rev/s
Worked Example
Convert 25 Revolutions per second to Radians per second: 25 rev/s = 157.08 rad/s
About Revolution per second (rev/s)
Rotational speed expressed in full turns per second (1 rev/s = 60 RPM = 2π rad/s ≈ 6.283 rad/s = 360 deg/s). Rev/s is used in specialized contexts where RPM feels too slow or where the per-second timebase matches the calculation's other time units. Common applications: laboratory centrifuges (Beckman Coulter Avanti J-26 max rotor speed ~5,000 RPM = 83 rev/s; Sorvall RC-6+ ~16,000 RPM = 267 rev/s; ultracentrifuges like Beckman Optima MAX 150,000 RPM = 2,500 rev/s for protein and nucleic-acid separation), automotive turbochargers (small passenger-car turbos run 150,000-250,000 RPM = 2,500-4,200 rev/s; truck/marine turbos slower at 30,000-80,000 RPM), high-speed grinding spindles and dental drills (200,000-400,000 RPM = 3,300-6,700 rev/s), and inertial-confinement-fusion target-rotation rigs. 1 rev/s = 60 RPM = 2π rad/s ≈ 6.28 rad/s.
About Radian per second (rad/s)
The SI unit of angular velocity (ISO 80000-3 §3-7), equal to the rate of change of angular displacement in radians per second. rad/s is the native unit of every physics and engineering formula involving rotational motion: rotational power P = τ·ω (torque × angular velocity), angular momentum L = I·ω (moment of inertia × ω), rotational kinetic energy KE = ½·I·ω², centripetal acceleration a = ω²·r, and the time-derivative form of angular position θ(t) where ω = dθ/dt. Mechanical engineering (drivetrain dynamics, turbomachinery analysis per ASME PTC 6), robotics control loops (PID position-loop tuning in radians per second for joint actuators), gyroscope output (MEMS rate gyros report rad/s natively on the I²C/SPI register), and physics simulations (Bullet Physics, Newton Dynamics, PhysX) all work in rad/s. Reference values: Earth's rotation 7.27 × 10⁻⁵ rad/s (one full turn per 24 h ≈ 86,164 s sidereal day); a typical automotive crankshaft at 6,000 RPM = 628 rad/s; helicopter rotor 30-40 rad/s. 1 rad/s ≈ 9.5493 RPM.
Quick Facts
- 1 Revolution per second equals 6.28319 Radians per second
- 1 Radian per second equals 0.159155 Revolutions per second
- Revolution per second is a unit of angular velocity
- Radian per second is a unit of angular velocity
- This conversion is commonly used in motor specifications, rotating machinery, and mechanical design
Common Revolution per second to Radian per second Conversions
| Revolutions per second (rev/s) | Radians per second (rad/s) |
|---|---|
| 0.01 | 0.0628319 |
| 0.1 | 0.628319 |
| 0.25 | 1.5708 |
| 0.5 | 3.14159 |
| 1 | 6.28319 |
| 2 | 12.5664 |
| 3 | 18.8496 |
| 5 | 31.4159 |
| 10 | 62.8319 |
| 15 | 94.2478 |
| 20 | 125.664 |
| 25 | 157.08 |
| 50 | 314.159 |
| 75 | 471.239 |
| 100 | 628.319 |
| 250 | 1570.8 |
| 500 | 3141.59 |
| 1000 | 6283.19 |
| 5000 | 31415.9 |
| 10000 | 62831.9 |
Understanding Revolutions per second
The Revolution per second (symbol: rev/s) is a unit of angular velocity. Rotational speed expressed in full turns per second (1 rev/s = 60 RPM = 2π rad/s ≈ 6.283 rad/s = 360 deg/s). Rev/s is used in specialized contexts where RPM feels too slow or where the per-second timebase matches the calculation's other time units. Common applications: laboratory centrifuges (Beckman Coulter Avanti J-26 max rotor speed ~5,000 RPM = 83 rev/s; Sorvall RC-6+ ~16,000 RPM = 267 rev/s; ultracentrifuges like Beckman Optima MAX 150,000 RPM = 2,500 rev/s for protein and nucleic-acid separation), automotive turbochargers (small passenger-car turbos run 150,000-250,000 RPM = 2,500-4,200 rev/s; truck/marine turbos slower at 30,000-80,000 RPM), high-speed grinding spindles and dental drills (200,000-400,000 RPM = 3,300-6,700 rev/s), and inertial-confinement-fusion target-rotation rigs. 1 rev/s = 60 RPM = 2π rad/s ≈ 6.28 rad/s.
Revolutions per second are commonly used in motor specifications, rotating machinery, and mechanical design.
Understanding Radians per second
The Radian per second (symbol: rad/s) is a unit of angular velocity. The SI unit of angular velocity (ISO 80000-3 §3-7), equal to the rate of change of angular displacement in radians per second. rad/s is the native unit of every physics and engineering formula involving rotational motion: rotational power P = τ·ω (torque × angular velocity), angular momentum L = I·ω (moment of inertia × ω), rotational kinetic energy KE = ½·I·ω², centripetal acceleration a = ω²·r, and the time-derivative form of angular position θ(t) where ω = dθ/dt. Mechanical engineering (drivetrain dynamics, turbomachinery analysis per ASME PTC 6), robotics control loops (PID position-loop tuning in radians per second for joint actuators), gyroscope output (MEMS rate gyros report rad/s natively on the I²C/SPI register), and physics simulations (Bullet Physics, Newton Dynamics, PhysX) all work in rad/s. Reference values: Earth's rotation 7.27 × 10⁻⁵ rad/s (one full turn per 24 h ≈ 86,164 s sidereal day); a typical automotive crankshaft at 6,000 RPM = 628 rad/s; helicopter rotor 30-40 rad/s. 1 rad/s ≈ 9.5493 RPM.
Radians per second are commonly used in motor specifications, rotating machinery, and mechanical design.
Why Convert Revolutions per second to Radians per second?
Converting between Revolutions per second and Radians per second is a frequent requirement for engineers, scientists, and students working with angular velocity values. Different industries and regions favour different unit systems, so having a dependable conversion tool saves time and prevents errors in technical calculations. Whether you are verifying a specification sheet, cross-checking simulation results, or preparing a report for an international audience, accurate angular velocity conversion is essential.
Frequently Asked Questions
How do I convert Revolutions per second to Radians per second?
Rotational speed expressed in full turns per second (1 rev/s = 60 RPM = 2π rad/s ≈ 6. To convert Revolutions per second to Radians per second, multiply by 6.28319. For example, 25 rev/s equals 157.08 rad/s.
How many Radians per second are in 1 Revolution per second?
There are 6.28319 Radians per second in 1 Revolution per second.
How many Revolutions per second are in 1 Radian per second?
There are 0.159155 Revolutions per second in 1 Radian per second.
What is the formula for Revolution per second to Radian per second conversion?
The formula is: multiply by 6.28319. This means 1 rev/s = 6.28319 rad/s.
Is a Revolution per second bigger than a Radian per second?
No. One Revolution per second is smaller than one Radian per second because 1 rev/s equals 6.28319 rad/s, which is greater than 1.
When do you need to convert between Revolutions per second and Radians per second?
The SI unit of angular velocity (ISO 80000-3 §3-7), equal to the rate of change of angular displacement in radians per second. Revolution per second and Radian per second are both angular velocity units, so conversion comes up whenever one source of information uses one unit and another uses the other — a classic cross-reference challenge in engineering, trade, travel, and everyday life.