Convert Degrees per second squared to Radians per second squared
Instantly convert Degrees per second squared (deg/s²) to Radians per second squared (rad/s²) with our free online calculator.
Formula: deg/s² to rad/s² — multiply by 0.0174533
Reference Table
| Degrees per second squared (deg/s²) | Radians per second squared (rad/s²) |
|---|---|
| 1 | 0.0174533 |
| 5 | 0.0872665 |
| 10 | 0.174533 |
| 25 | 0.436332 |
| 50 | 0.872665 |
| 100 | 1.74533 |
How to Convert Degrees per second squared to Radians per second squared
Formula
To convert Degrees per second squared (deg/s²) to Radians per second squared (rad/s²): multiply by 0.0174533
Step-by-Step
- Start with your value in Degrees per second squared (deg/s²).
- Multiply by 0.0174533 to perform the conversion.
- The result is your value expressed in Radians per second squared (rad/s²).
Conversion Factor
1 deg/s² = 0.0174533 rad/s²
Reverse Factor
1 rad/s² = 57.2958 deg/s²
Worked Example
Convert 25 Degrees per second squared to Radians per second squared: 25 deg/s² = 0.436332 rad/s²
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.
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 Degree per second squared equals 0.0174533 Radians per second squared
- 1 Radian per second squared equals 57.2958 Degrees per second squared
- Degree per second squared 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 Degree per second squared to Radian per second squared Conversions
| Degrees per second squared (deg/s²) | Radians per second squared (rad/s²) |
|---|---|
| 0.01 | 0.000174533 |
| 0.1 | 0.00174533 |
| 0.25 | 0.00436332 |
| 0.5 | 0.00872665 |
| 1 | 0.0174533 |
| 2 | 0.0349066 |
| 3 | 0.0523599 |
| 5 | 0.0872665 |
| 10 | 0.174533 |
| 15 | 0.261799 |
| 20 | 0.349066 |
| 25 | 0.436332 |
| 50 | 0.872665 |
| 75 | 1.309 |
| 100 | 1.74533 |
| 250 | 4.36332 |
| 500 | 8.72665 |
| 1000 | 17.4533 |
| 5000 | 87.2665 |
| 10000 | 174.533 |
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.
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 Degrees per second squared to Radians per second squared?
Converting between Degrees per second squared 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 Degrees per second squared to Radians per second squared?
Angular acceleration expressed in degrees per second per second (1 deg/s² = π/180 rad/s² ≈ 0. To convert Degrees per second squared to Radians per second squared, multiply by 0.0174533. For example, 25 deg/s² equals 0.436332 rad/s².
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.
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.
What is the formula for Degree per second squared to Radian per second squared conversion?
The formula is: multiply by 0.0174533. This means 1 deg/s² = 0.0174533 rad/s².
Is a Degree per second squared bigger than a Radian per second squared?
Yes. One Degree per second squared is larger than one Radian per second squared because 1 deg/s² equals 0.0174533 rad/s², which is less than 1.
When do you need to convert between Degrees per second squared 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). Degree per second squared 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.