Convert Radians per second squared to Degrees per second squared
Instantly convert Radians per second squared (rad/s²) to Degrees per second squared (deg/s²) with our free online calculator.
Formula: rad/s² to deg/s² — multiply by 57.2958
Reference Table
| Radians per second squared (rad/s²) | Degrees per second squared (deg/s²) |
|---|---|
| 1 | 57.2958 |
| 5 | 286.479 |
| 10 | 572.958 |
| 25 | 1432.39 |
| 50 | 2864.79 |
| 100 | 5729.58 |
How to Convert Radians per second squared to Degrees per second squared
Formula
To convert Radians per second squared (rad/s²) to Degrees per second squared (deg/s²): multiply by 57.2958
Step-by-Step
- Start with your value in Radians per second squared (rad/s²).
- Multiply by 57.2958 to perform the conversion.
- The result is your value expressed in Degrees per second squared (deg/s²).
Conversion Factor
1 rad/s² = 57.2958 deg/s²
Reverse Factor
1 deg/s² = 0.0174533 rad/s²
Worked Example
Convert 25 Radians per second squared to Degrees per second squared: 25 rad/s² = 1432.39 deg/s²
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.
About Degree per second squared (deg/s²)
Angular acceleration expressed in degrees per second per second (1 deg/s² = π/180 rad/s² ≈ 0.01745 rad/s² = 1/6 RPM/s). deg/s² is the standard reporting unit in aerospace navigation and aviation control-system design where rotation rates are also reported in deg/s for consistency: spacecraft, missile, and satellite attitude-control rate-loop tuning per AIAA standards; aviation autopilot pitch / roll / yaw inner-loop PID tuning per FAA AC 25-7C transport-aircraft handling-qualities specifications; aerobatic-airframe maneuver-load calculations (typical aerobatic-category aircraft pitch acceleration limits 100-300 deg/s²); and consumer IMU/gyro datasheets for expected drift and step-response characterization per IEEE 952 inertial-sensor terminology. Drone flight-controller PID gains on the rate loop (Betaflight, ArduPilot, PX4) are often tuned in deg/s² for pilot-intuitive stability and reflex-response tuning.
Quick Facts
- 1 Radian per second squared equals 57.2958 Degrees per second squared
- 1 Degree per second squared equals 0.0174533 Radians per second squared
- Radian per second squared is a unit of angular acceleration
- Degree per second squared is a unit of angular acceleration
- This conversion is commonly used in motor control, robotics, and rotational dynamics
Common Radian per second squared to Degree per second squared Conversions
| Radians per second squared (rad/s²) | Degrees per second squared (deg/s²) |
|---|---|
| 0.01 | 0.572958 |
| 0.1 | 5.72958 |
| 0.25 | 14.3239 |
| 0.5 | 28.6479 |
| 1 | 57.2958 |
| 2 | 114.592 |
| 3 | 171.887 |
| 5 | 286.479 |
| 10 | 572.958 |
| 15 | 859.437 |
| 20 | 1145.92 |
| 25 | 1432.39 |
| 50 | 2864.79 |
| 75 | 4297.18 |
| 100 | 5729.58 |
| 250 | 14323.9 |
| 500 | 28647.9 |
| 1000 | 57295.8 |
| 5000 | 286479 |
| 10000 | 572958 |
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.
Understanding Degrees per second squared
The Degree per second squared (symbol: deg/s²) is a unit of angular acceleration. Angular acceleration expressed in degrees per second per second (1 deg/s² = π/180 rad/s² ≈ 0.01745 rad/s² = 1/6 RPM/s). deg/s² is the standard reporting unit in aerospace navigation and aviation control-system design where rotation rates are also reported in deg/s for consistency: spacecraft, missile, and satellite attitude-control rate-loop tuning per AIAA standards; aviation autopilot pitch / roll / yaw inner-loop PID tuning per FAA AC 25-7C transport-aircraft handling-qualities specifications; aerobatic-airframe maneuver-load calculations (typical aerobatic-category aircraft pitch acceleration limits 100-300 deg/s²); and consumer IMU/gyro datasheets for expected drift and step-response characterization per IEEE 952 inertial-sensor terminology. Drone flight-controller PID gains on the rate loop (Betaflight, ArduPilot, PX4) are often tuned in deg/s² for pilot-intuitive stability and reflex-response tuning.
Degrees per second squared are commonly used in motor control, robotics, and rotational dynamics.
Why Convert Radians per second squared to Degrees per second squared?
Converting between Radians per second squared and Degrees 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 Radians per second squared to Degrees 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). To convert Radians per second squared to Degrees per second squared, multiply by 57.2958. For example, 25 rad/s² equals 1432.39 deg/s².
How many Degrees per second squared are in 1 Radian per second squared?
There are 57.2958 Degrees per second squared in 1 Radian per second squared.
How many Radians per second squared are in 1 Degree per second squared?
There are 0.0174533 Radians per second squared in 1 Degree per second squared.
What is the formula for Radian per second squared to Degree per second squared conversion?
The formula is: multiply by 57.2958. This means 1 rad/s² = 57.2958 deg/s².
Is a Radian per second squared bigger than a Degree per second squared?
No. One Radian per second squared is smaller than one Degree per second squared because 1 rad/s² equals 57.2958 deg/s², which is greater than 1.
When do you need to convert between Radians per second squared and Degrees per second squared?
Angular acceleration expressed in degrees per second per second (1 deg/s² = π/180 rad/s² ≈ 0. Radian per second squared and Degree 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.