Convert RPM per second to Radians per second squared
Instantly convert RPM per second (RPM/s) to Radians per second squared (rad/s²) with our free online calculator.
Formula: RPM/s to rad/s² — multiply by 0.10472
Reference Table
| RPM per second (RPM/s) | Radians per second squared (rad/s²) |
|---|---|
| 1 | 0.10472 |
| 5 | 0.523599 |
| 10 | 1.0472 |
| 25 | 2.61799 |
| 50 | 5.23599 |
| 100 | 10.472 |
How to Convert RPM per second to Radians per second squared
Formula
To convert RPM per second (RPM/s) to Radians per second squared (rad/s²): multiply by 0.10472
Step-by-Step
- Start with your value in RPM per second (RPM/s).
- Multiply by 0.10472 to perform the conversion.
- The result is your value expressed in Radians per second squared (rad/s²).
Conversion Factor
1 RPM/s = 0.10472 rad/s²
Reverse Factor
1 rad/s² = 9.5493 RPM/s
Worked Example
Convert 25 RPM per second to Radians per second squared: 25 RPM/s = 2.61799 rad/s²
About RPM per second (RPM/s)
The change in rotational speed in revolutions per minute, per second (1 RPM/s = 2π/60 rad/s² ≈ 0.1047 rad/s² = 6 deg/s²). RPM/s is the standard motor-drive specification for acceleration ramp programming: a servo-motor catalog spec of '0 to 3,000 RPM in 0.5 seconds' translates to a 6,000 RPM/s acceleration limit. CNC machine-tool controllers (Siemens 840D, Fanuc 30i / 31i, Haas NGC) expose spindle and axis ramp-rate limits in RPM/s for programmable acceleration profiles; EV traction-motor inverters (Tesla Drive Unit, Cascadia Motion CM200) advertise peak acceleration in RPM/s as a key performance spec; industrial Variable-Frequency-Drive (VFD) parameters (ABB ACS880, Allen-Bradley PowerFlex 755, Siemens SINAMICS G120) all expose acceleration / deceleration ramp times that internally compute RPM/s limits per IEC 61800-4 adjustable-speed-drive standards. Convert RPM/s to rad/s² by multiplying by π/30; to deg/s² by multiplying by 6.
About Radian per second squared (rad/s²)
The SI unit of angular acceleration (ISO 80000-3 §3-8) — the rate of change of angular velocity with respect to time (α = dω/dt). rad/s² is the universal working unit in rotational dynamics: the rotational form of Newton's second law τ = I·α (torque equals mass moment of inertia times angular acceleration) is dimensionally consistent only when α is in rad/s². Used extensively in: robotics motion planning (joint-trajectory generation with bounded velocity AND acceleration per ROS MoveIt! and KUKA KRL controllers), vehicle drivetrain spin-up simulations (clutch-engagement transient analysis), rotor balancing per ISO 21940 (residual-unbalance limits trigger speed-up / coast-down acceleration testing), control-system tuning (motor controllers expose acceleration limits in rad/s² for ramp-rate programming), and FEA rotating-machinery transient analysis (Abaqus/Standard, ANSYS Workbench Transient Structural). Reference values: a typical industrial servo motor commanded acceleration 100-1,000 rad/s²; an automotive engine free-revving acceleration 200-500 rad/s²; a hard-drive spindle spin-up 200-500 rad/s². 1 rad/s² ≈ 9.549 RPM/s.
Quick Facts
- 1 RPM per second equals 0.10472 Radians per second squared
- 1 Radian per second squared equals 9.5493 RPM per second
- RPM per second is a unit of angular acceleration
- Radian per second squared is a unit of angular acceleration
- This conversion is commonly used in motor control, robotics, and rotational dynamics
Common RPM per second to Radian per second squared Conversions
| RPM per second (RPM/s) | Radians per second squared (rad/s²) |
|---|---|
| 0.01 | 0.0010472 |
| 0.1 | 0.010472 |
| 0.25 | 0.0261799 |
| 0.5 | 0.0523599 |
| 1 | 0.10472 |
| 2 | 0.20944 |
| 3 | 0.314159 |
| 5 | 0.523599 |
| 10 | 1.0472 |
| 15 | 1.5708 |
| 20 | 2.0944 |
| 25 | 2.61799 |
| 50 | 5.23599 |
| 75 | 7.85398 |
| 100 | 10.472 |
| 250 | 26.1799 |
| 500 | 52.3599 |
| 1000 | 104.72 |
| 5000 | 523.599 |
| 10000 | 1047.2 |
Understanding RPM per second
The RPM per second (symbol: RPM/s) is a unit of angular acceleration. The change in rotational speed in revolutions per minute, per second (1 RPM/s = 2π/60 rad/s² ≈ 0.1047 rad/s² = 6 deg/s²). RPM/s is the standard motor-drive specification for acceleration ramp programming: a servo-motor catalog spec of '0 to 3,000 RPM in 0.5 seconds' translates to a 6,000 RPM/s acceleration limit. CNC machine-tool controllers (Siemens 840D, Fanuc 30i / 31i, Haas NGC) expose spindle and axis ramp-rate limits in RPM/s for programmable acceleration profiles; EV traction-motor inverters (Tesla Drive Unit, Cascadia Motion CM200) advertise peak acceleration in RPM/s as a key performance spec; industrial Variable-Frequency-Drive (VFD) parameters (ABB ACS880, Allen-Bradley PowerFlex 755, Siemens SINAMICS G120) all expose acceleration / deceleration ramp times that internally compute RPM/s limits per IEC 61800-4 adjustable-speed-drive standards. Convert RPM/s to rad/s² by multiplying by π/30; to deg/s² by multiplying by 6.
RPM per second are commonly used in motor control, robotics, and rotational dynamics.
Understanding Radians per second squared
The Radian per second squared (symbol: rad/s²) is a unit of angular acceleration. The SI unit of angular acceleration (ISO 80000-3 §3-8) — the rate of change of angular velocity with respect to time (α = dω/dt). rad/s² is the universal working unit in rotational dynamics: the rotational form of Newton's second law τ = I·α (torque equals mass moment of inertia times angular acceleration) is dimensionally consistent only when α is in rad/s². Used extensively in: robotics motion planning (joint-trajectory generation with bounded velocity AND acceleration per ROS MoveIt! and KUKA KRL controllers), vehicle drivetrain spin-up simulations (clutch-engagement transient analysis), rotor balancing per ISO 21940 (residual-unbalance limits trigger speed-up / coast-down acceleration testing), control-system tuning (motor controllers expose acceleration limits in rad/s² for ramp-rate programming), and FEA rotating-machinery transient analysis (Abaqus/Standard, ANSYS Workbench Transient Structural). Reference values: a typical industrial servo motor commanded acceleration 100-1,000 rad/s²; an automotive engine free-revving acceleration 200-500 rad/s²; a hard-drive spindle spin-up 200-500 rad/s². 1 rad/s² ≈ 9.549 RPM/s.
Radians per second squared are commonly used in motor control, robotics, and rotational dynamics.
Why Convert RPM per second to Radians per second squared?
Converting between RPM per second and Radians per second squared is a frequent requirement for engineers, scientists, and students working with angular acceleration 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 acceleration conversion is essential.
Frequently Asked Questions
How do I convert RPM per second to Radians per second squared?
The change in rotational speed in revolutions per minute, per second (1 RPM/s = 2π/60 rad/s² ≈ 0. To convert RPM per second to Radians per second squared, multiply by 0.10472. For example, 25 RPM/s equals 2.61799 rad/s².
How many Radians per second squared are in 1 RPM per second?
There are 0.10472 Radians per second squared in 1 RPM per second.
How many RPM per second are in 1 Radian per second squared?
There are 9.5493 RPM per second in 1 Radian per second squared.
What is the formula for RPM per second to Radian per second squared conversion?
The formula is: multiply by 0.10472. This means 1 RPM/s = 0.10472 rad/s².
Is a RPM per second bigger than a Radian per second squared?
Yes. One RPM per second is larger than one Radian per second squared because 1 RPM/s equals 0.10472 rad/s², which is less than 1.
When do you need to convert between RPM per second and Radians per second squared?
The SI unit of angular acceleration (ISO 80000-3 §3-8) — the rate of change of angular velocity with respect to time (α = dω/dt). RPM per second and Radian per second squared are both angular acceleration 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.