Convert Radians per second to Revolutions per minute
Instantly convert Radians per second (rad/s) to Revolutions per minute (RPM) with our free online calculator.
Formula: rad/s to RPM — multiply by 9.5493
Reference Table
| Radians per second (rad/s) | Revolutions per minute (RPM) |
|---|---|
| 1 | 9.5493 |
| 5 | 47.7465 |
| 10 | 95.493 |
| 25 | 238.732 |
| 50 | 477.465 |
| 100 | 954.93 |
How to Convert Radians per second to Revolutions per minute
Formula
To convert Radians per second (rad/s) to Revolutions per minute (RPM): multiply by 9.5493
Step-by-Step
- Start with your value in Radians per second (rad/s).
- Multiply by 9.5493 to perform the conversion.
- The result is your value expressed in Revolutions per minute (RPM).
Conversion Factor
1 rad/s = 9.5493 RPM
Reverse Factor
1 RPM = 0.10472 rad/s
Worked Example
Convert 25 Radians per second to Revolutions per minute: 25 rad/s = 238.732 RPM
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.
About Revolutions per minute (RPM)
A rotational-speed unit counting complete 360° turns per minute (1 RPM = 2π/60 rad/s ≈ 0.1047 rad/s = 6°/s). RPM is the dominant everyday rotational-speed unit on tachometers, motor nameplates, and machinery specifications. Reference values: automotive engine idle 700-900 RPM, redline 6,000-9,000 RPM for naturally-aspirated gasoline cars (Honda S2000 F20C 9,000 RPM, Lexus LFA 1LR-GUE 9,500 RPM, F1 V10 engines pre-2014 18,000-20,000 RPM); turbomachinery (steam turbines 3,000 RPM for 50 Hz grid-synchronous / 3,600 RPM for 60 Hz grid; modern aeroderivative gas-turbine 3,600-9,500 RPM depending on shaft); machine tools (typical CNC milling spindle 8,000-24,000 RPM, high-speed machining 30,000-60,000 RPM); hard-disk-drive spindles 5,400 / 7,200 / 10,000 / 15,000 RPM (the last in enterprise SAS drives); ceiling fans 200-300 RPM; washing-machine spin cycles 800-1,600 RPM. Converting RPM to rad/s (multiply by π/30 ≈ 0.1047) is routine for rotor-dynamic analysis and FEA.
Quick Facts
- 1 Radian per second equals 9.5493 Revolutions per minute
- 1 Revolutions per minute equals 0.10472 Radians per second
- Radian per second is a unit of angular velocity
- Revolutions per minute is a unit of angular velocity
- This conversion is commonly used in motor specifications, rotating machinery, and mechanical design
Common Radian per second to Revolutions per minute Conversions
| Radians per second (rad/s) | Revolutions per minute (RPM) |
|---|---|
| 0.01 | 0.095493 |
| 0.1 | 0.95493 |
| 0.25 | 2.38732 |
| 0.5 | 4.77465 |
| 1 | 9.5493 |
| 2 | 19.0986 |
| 3 | 28.6479 |
| 5 | 47.7465 |
| 10 | 95.493 |
| 15 | 143.239 |
| 20 | 190.986 |
| 25 | 238.732 |
| 50 | 477.465 |
| 75 | 716.197 |
| 100 | 954.93 |
| 250 | 2387.32 |
| 500 | 4774.65 |
| 1000 | 9549.3 |
| 5000 | 47746.5 |
| 10000 | 95493 |
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.
Understanding Revolutions per minute
The Revolutions per minute (symbol: RPM) is a unit of angular velocity. A rotational-speed unit counting complete 360° turns per minute (1 RPM = 2π/60 rad/s ≈ 0.1047 rad/s = 6°/s). RPM is the dominant everyday rotational-speed unit on tachometers, motor nameplates, and machinery specifications. Reference values: automotive engine idle 700-900 RPM, redline 6,000-9,000 RPM for naturally-aspirated gasoline cars (Honda S2000 F20C 9,000 RPM, Lexus LFA 1LR-GUE 9,500 RPM, F1 V10 engines pre-2014 18,000-20,000 RPM); turbomachinery (steam turbines 3,000 RPM for 50 Hz grid-synchronous / 3,600 RPM for 60 Hz grid; modern aeroderivative gas-turbine 3,600-9,500 RPM depending on shaft); machine tools (typical CNC milling spindle 8,000-24,000 RPM, high-speed machining 30,000-60,000 RPM); hard-disk-drive spindles 5,400 / 7,200 / 10,000 / 15,000 RPM (the last in enterprise SAS drives); ceiling fans 200-300 RPM; washing-machine spin cycles 800-1,600 RPM. Converting RPM to rad/s (multiply by π/30 ≈ 0.1047) is routine for rotor-dynamic analysis and FEA.
Revolutions per minute are commonly used in motor specifications, rotating machinery, and mechanical design.
Why Convert Radians per second to Revolutions per minute?
Converting between Radians per second and Revolutions per minute 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 Radians per second to Revolutions per minute?
The SI unit of angular velocity (ISO 80000-3 §3-7), equal to the rate of change of angular displacement in radians per second. To convert Radians per second to Revolutions per minute, multiply by 9.5493. For example, 25 rad/s equals 238.732 RPM.
How many Revolutions per minute are in 1 Radian per second?
There are 9.5493 Revolutions per minute in 1 Radian per second.
How many Radians per second are in 1 Revolutions per minute?
There are 0.10472 Radians per second in 1 Revolutions per minute.
What is the formula for Radian per second to Revolutions per minute conversion?
The formula is: multiply by 9.5493. This means 1 rad/s = 9.5493 RPM.
Is a Radian per second bigger than a Revolutions per minute?
No. One Radian per second is smaller than one Revolutions per minute because 1 rad/s equals 9.5493 RPM, which is greater than 1.
When do you need to convert between Radians per second and Revolutions per minute?
A rotational-speed unit counting complete 360° turns per minute (1 RPM = 2π/60 rad/s ≈ 0. Radian per second and Revolutions per minute 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.