Convert Radians per second to Degrees per second
Instantly convert Radians per second (rad/s) to Degrees per second (deg/s) with our free online calculator.
Formula: rad/s to deg/s — multiply by 57.2958
Reference Table
| Radians per second (rad/s) | Degrees per second (deg/s) |
|---|---|
| 1 | 57.2958 |
| 5 | 286.479 |
| 10 | 572.958 |
| 25 | 1432.39 |
| 50 | 2864.79 |
| 100 | 5729.58 |
How to Convert Radians per second to Degrees per second
Formula
To convert Radians per second (rad/s) to Degrees per second (deg/s): multiply by 57.2958
Step-by-Step
- Start with your value in Radians per second (rad/s).
- Multiply by 57.2958 to perform the conversion.
- The result is your value expressed in Degrees per second (deg/s).
Conversion Factor
1 rad/s = 57.2958 deg/s
Reverse Factor
1 deg/s = 0.0174533 rad/s
Worked Example
Convert 25 Radians per second to Degrees per second: 25 rad/s = 1432.39 deg/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.
About Degree per second (deg/s)
Angular velocity expressed in degrees rotated per second (1 deg/s = π/180 rad/s ≈ 0.01745 rad/s = 1/6 RPM). Deg/s is the standard reporting unit in aviation and aerospace for rotational rates: aircraft yaw / pitch / roll body-rate gyros per ARINC 429 inertial-reference unit data buses, missile guidance systems (typical airframe-rate limits 100-400 deg/s for fighter aircraft, up to 1,000 deg/s for short-range AAMs), satellite attitude-control system (ACS) reaction-wheel and CMG rates per AIAA standards, and the default unit on consumer-grade IMU (inertial measurement unit) datasheets and drone flight controllers (InvenSense MPU-6050, Bosch BMI160, ST LSM6DSL series). A standard 3-axis MEMS gyroscope chip typically measures up to ±2,000 deg/s full-scale (FSR) with programmable lower-range settings of ±250 / ±500 / ±1,000 deg/s for better noise floor at slower rates.
Quick Facts
- 1 Radian per second equals 57.2958 Degrees per second
- 1 Degree per second equals 0.0174533 Radians per second
- Radian per second is a unit of angular velocity
- Degree per second is a unit of angular velocity
- This conversion is commonly used in motor specifications, rotating machinery, and mechanical design
Common Radian per second to Degree per second Conversions
| Radians per second (rad/s) | Degrees per second (deg/s) |
|---|---|
| 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
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 Degrees per second
The Degree per second (symbol: deg/s) is a unit of angular velocity. Angular velocity expressed in degrees rotated per second (1 deg/s = π/180 rad/s ≈ 0.01745 rad/s = 1/6 RPM). Deg/s is the standard reporting unit in aviation and aerospace for rotational rates: aircraft yaw / pitch / roll body-rate gyros per ARINC 429 inertial-reference unit data buses, missile guidance systems (typical airframe-rate limits 100-400 deg/s for fighter aircraft, up to 1,000 deg/s for short-range AAMs), satellite attitude-control system (ACS) reaction-wheel and CMG rates per AIAA standards, and the default unit on consumer-grade IMU (inertial measurement unit) datasheets and drone flight controllers (InvenSense MPU-6050, Bosch BMI160, ST LSM6DSL series). A standard 3-axis MEMS gyroscope chip typically measures up to ±2,000 deg/s full-scale (FSR) with programmable lower-range settings of ±250 / ±500 / ±1,000 deg/s for better noise floor at slower rates.
Degrees per second are commonly used in motor specifications, rotating machinery, and mechanical design.
Why Convert Radians per second to Degrees per second?
Converting between Radians per second and Degrees 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 Radians per second to Degrees 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. To convert Radians per second to Degrees per second, multiply by 57.2958. For example, 25 rad/s equals 1432.39 deg/s.
How many Degrees per second are in 1 Radian per second?
There are 57.2958 Degrees per second in 1 Radian per second.
How many Radians per second are in 1 Degree per second?
There are 0.0174533 Radians per second in 1 Degree per second.
What is the formula for Radian per second to Degree per second conversion?
The formula is: multiply by 57.2958. This means 1 rad/s = 57.2958 deg/s.
Is a Radian per second bigger than a Degree per second?
No. One Radian per second is smaller than one Degree per second because 1 rad/s equals 57.2958 deg/s, which is greater than 1.
When do you need to convert between Radians per second and Degrees per second?
Angular velocity expressed in degrees rotated per second (1 deg/s = π/180 rad/s ≈ 0. Radian per second and Degree 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.