Convert Degrees per second to Radians per second
Instantly convert Degrees per second (deg/s) to Radians per second (rad/s) with our free online calculator.
Formula: deg/s to rad/s — multiply by 0.0174533
Reference Table
| Degrees per second (deg/s) | Radians per second (rad/s) |
|---|---|
| 1 | 0.0174533 |
| 5 | 0.0872665 |
| 10 | 0.174533 |
| 25 | 0.436332 |
| 50 | 0.872665 |
| 100 | 1.74533 |
How to Convert Degrees per second to Radians per second
Formula
To convert Degrees per second (deg/s) to Radians per second (rad/s): multiply by 0.0174533
Step-by-Step
- Start with your value in Degrees per second (deg/s).
- Multiply by 0.0174533 to perform the conversion.
- The result is your value expressed in Radians per second (rad/s).
Conversion Factor
1 deg/s = 0.0174533 rad/s
Reverse Factor
1 rad/s = 57.2958 deg/s
Worked Example
Convert 25 Degrees per second to Radians per second: 25 deg/s = 0.436332 rad/s
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.
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.
Quick Facts
- 1 Degree per second equals 0.0174533 Radians per second
- 1 Radian per second equals 57.2958 Degrees per second
- Degree per second is a unit of angular velocity
- Radian per second is a unit of angular velocity
- This conversion is commonly used in motor specifications, rotating machinery, and mechanical design
Common Degree per second to Radian per second Conversions
| Degrees per second (deg/s) | Radians per second (rad/s) |
|---|---|
| 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
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.
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.
Why Convert Degrees per second to Radians per second?
Converting between Degrees per second and Radians 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 Degrees per second to Radians per second?
Angular velocity expressed in degrees rotated per second (1 deg/s = π/180 rad/s ≈ 0. To convert Degrees per second to Radians per second, multiply by 0.0174533. For example, 25 deg/s equals 0.436332 rad/s.
How many Radians per second are in 1 Degree per second?
There are 0.0174533 Radians per second in 1 Degree per second.
How many Degrees per second are in 1 Radian per second?
There are 57.2958 Degrees per second in 1 Radian per second.
What is the formula for Degree per second to Radian per second conversion?
The formula is: multiply by 0.0174533. This means 1 deg/s = 0.0174533 rad/s.
Is a Degree per second bigger than a Radian per second?
Yes. One Degree per second is larger than one Radian per second because 1 deg/s equals 0.0174533 rad/s, which is less than 1.
When do you need to convert between Degrees per second and Radians 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. Degree per second and Radian 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.