Degree/second to Radian/second (°/s to rad/s) Angular Velocity Calculator

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Live Conversion • ISO 80000-3:2019 Certified

1 Degree/second = 0.017453293 Radian/second

1 °/s = 0.0174533 rad/s • 1 rad/s = 57.29578 °/s

Decimals:

Certified Authority Value

0.01745329

rad/s

From / Input

°/s

Swap to Radian/second to Degree/second

To / Result

rad/s

Quick Values:

Conversion Formula

To convert Degree/second to Radian/second, multiply by 0.017453293

°/s × 0.017453293 = rad/s

Calculation: 1 °/s × 0.017453293 = 0.017453293 rad/s

Common Degree/second to Radian/second Calculations

Quick-lookup reference table showing calculated equivalents for standard increments between Degree/second (°/s) and Radian/second (rad/s).

Tap any row to calculate

Degree/second to Radian/second: Primary Direct Table (15 Steps)

Rule: 1 Degree/second is equal to 0.0174533 rad/s (Radian/second)

Degree/second to Radian/second Conversion Reference Table
Conversion & Equivalent Value	Scientific Notation
0.001 °/s 1.745329 × 10⁻⁵ rad/s	1.745 × 10⁻⁵
0.01 °/s 0.000174533 rad/s	1.745 × 10⁻⁴
0.1 °/s 0.00174533 rad/s	1.745 × 10⁻³
0.5 °/s 0.00872665 rad/s	8.727 × 10⁻³
1 °/s 0.0174533 rad/s	1.745 × 10⁻²
2 °/s 0.0349066 rad/s	3.491 × 10⁻²
5 °/s 0.0872665 rad/s	8.727 × 10⁻²
10 °/s 0.174533 rad/s	1.745 × 10⁻¹
20 °/s 0.349066 rad/s	3.491 × 10⁻¹
25 °/s 0.436332 rad/s	4.363 × 10⁻¹
50 °/s 0.872665 rad/s	8.727 × 10⁻¹
100 °/s 1.745329 rad/s	1.745 × 10⁰
250 °/s 4.363323 rad/s	4.363 × 10⁰
500 °/s 8.726646 rad/s	8.727 × 10⁰
1000 °/s 17.453293 rad/s	1.745 × 10¹

Radian/second to Degree/second: Reciprocal Summary

Rule: 1 Radian/second is equal to 57.29578 °/s (Degree/second)

Radian/second to Degree/second Conversion Reference Table
Reciprocal & Equivalent Value	Scientific Notation
1 rad/s 57.29578 °/s	5.73 × 10¹
5 rad/s 286.478898 °/s	2.865 × 10²
10 rad/s 572.957795 °/s	5.73 × 10²
50 rad/s 2864.788976 °/s	2.865 × 10³
100 rad/s 5729.577951 °/s	5.73 × 10³

View Complete 15-Row Radian/second to Degree/second Table

Real-World Context & Everyday Benchmarks

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To help contextualize these units in everyday life, science, and engineering, here are verified real-world reference points for Degree/second (°/s) and Radian/second (rad/s):

Degree/second References:

Second hand movement rate on standard analog clock 6 °/s
Human smooth pursuit eye tracking maximum visual velocity 30 °/s
Aerobatic competition stunt airplane maximum roll rate 360 °/s

Radian/second References:

Planet Earth rotational angular velocity on its polar axis 7.27E-5 rad/s
Four-pole AC induction electric motor synchronous speed at 60Hz 188.5 rad/s

Tap any benchmark above to automatically calculate its exact equivalent in Radian/second.

ISQ Dimension: [T⁻¹] Coherent SI Unit: radian per second (rad/s) Classical Mechanics & Dimensional Metrology

How to Convert Degree/second to Radian/second

Converting Degree/second (°/s) to Radian/second (rad/s) is a core calculation in Angular Velocity, which measures the rotational speed and rate of angular displacement per unit of time. Because Radian/second is a broader physical scale than Degree/second, converting from °/s to rad/s condenses the numerical figure. It takes 57.29578 Degree/second to equal a single Radian/second (1 °/s = 0.0174533 rad/s). To convert any quantity, multiply by 0.0174533 (or divide by 57.29578).

Direct Factor1 °/s = 0.0174533 rad/s

Inverse Ratio1 rad/s = 57.29578 °/s

Conversion ScaleDirect Proportional Magnitude Compression

First-Principles SI Derivation ProofNIST SP 811 / ISO 80000 Compliance

Mathematical Conversion Derivation via Coherent SI Base Unit

Under the International System of Quantities (ISQ), dimensional conversion between non-SI units is rigorously resolved by bridging through the coherent SI base unit (radian per second (rad/s)) without arbitrary rounding:

V_{\text{target}} = V_{\text{source}} \times \left( \frac{k_{\text{source} \to \text{SI}}}{k_{\text{target} \to \text{SI}}} \right)

Universal Dimensional Conversion Law (ISO 80000 / NIST SP 811)

1. Source SI Bridge (k_source):1 °/s = 0.0174533 radian per second (rad/s)

2. Target SI Bridge (k_target):1 rad/s = 1 radian per second (rad/s)

Step-by-step substitution for Degree/second → Radian/second:V(rad/s) = V(°/s) × ( 0.0174533 / 1 ) = V(°/s) × 0.0174533

Mathematical FormulaValue in Radian/second = Value in Degree/second × 0.017453293Direct computational formula applied for standard conversion.

Worked Example

Converting 75 °/s yields an exact output of 1.308997 rad/s in Radian/second. Under higher industrial throughput, 100 °/s translates to 1.745329 rad/s.

Inverse check: 1 rad/s = 57.29578 °/s.

Understanding Degree/second and Radian/second

Domain Metrology & Engineering Applications

Governing Law & Equation

Rotational Kinematics Relation (ω = dθ/dt)

Measurement Instrumentation

Rigorously quantified in laboratory and field settings using optical non-contact tachometers, stroboscopes, and resolver feedback transducers.

Primary Industry Sectors

Applied across electric motor drives, wind turbine generator monitoring, centrifuge engineering, and automotive drivetrains under international metrology standard ISO 80000-3:2019.

Institutional Metrology & Standard Authority:

Formulas, conversion coefficients, and base definitions on this page strictly adhere to the ISO 80000-3:2019 and the BIPM SI Brochure (9th Edition). Governed by Rotational Kinematics Relation (ω = dθ/dt) under ISO 80000 dimensional vector [T⁻¹].

Multi-Variable Engineering Bridge Drivetrain Engineering & Shaft Power

Angular Velocity to Mechanical Power Bridge (Watts • Kilowatts • Horsepower)

Calculate total shaft power output P = τ × ω across standard torque load ratings, bridging rotational velocity [T⁻¹] with power [M L² T⁻³].

Input Rotational Angular Velocity (ω): °/s

Select Applied Shaft Torque: 250 N·m

Governing Law: P = τ × ω

Vector: [rad/s] × [N·m] → [W]

Live Calculated Bridge Equivalent:

1 °/s at Passenger Car Engine (250 N·m) = 4.3633 W

Equals 0.004363 kW • 4.363323 × 10⁻⁶ MW • 0.005851 hp

SI Power

4.3633

Watts

Grid / Utility

0.004363

Kilowatts

Power Plant

4.363323 × 10⁻⁶

Megawatts

Mechanical Rating

0.005851

Horsepower (Mechanical)

Metric Horsepower

0.005932

Metric Horsepower (PS)

HVAC Thermal Rating

14.89

BTU/h

BTU per Hour

Step-by-Step Numerical Derivation Proof View Derivation

1. Normalize Input to SI Base Unit (rad/s):
ω = 1 °/s × 0.01745329 = 0.01745329 rad/s
2. Apply Engineering Parameter (τ):
Selected condition: Passenger Car Engine (250 N·m) at τ = 250 N·m
3. Execute Governing Physical Law in SI Units:
P = τ × ω = (0.01745329 rad/s) × (250 N·m) = 4.363323 W
4. Convert to Standard Engineering Units:
• W: 4.363323 × 1 = 4.3633 W (Watts) • kW: 4.363323 × 0.001 = 0.004363 kW (Kilowatts) • MW: 4.363323 × 1 × 10⁻⁶ = 4.363323 × 10⁻⁶ MW (Megawatts) • hp: 4.363323 × 0.001341 = 0.005851 hp (Horsepower (Mechanical)) • PS: 4.363323 × 0.00136 = 0.005932 PS (Metric Horsepower (PS)) • BTU/h: 4.363323 × 3.4121 = 14.89 BTU/h (BTU per Hour)

Explore Full Torque Converter →

Engineering Substance / Operating Standard	Parameter Value (N·m)	Reference State / Condition	Typical Industrial & Engineering Application
Automation Servo Motor (2 N·m)	`2`	2.0 N·m	Packaging & robotics joint servo
Passenger Car Engine (250 N·m)	`250`	250.0 N·m	Typical 2.0L turbo automobile engine
Commercial Diesel Semi Truck (1,200 N·m)	`1200`	1,200 N·m	Heavy freight turbo diesel engine
Marine Propulsion Shaft (25,000 N·m)	`25000`	25,000 N·m	Container vessel direct drive shaft

Frequently Asked Questions

There are exactly 0.017453293 radians/second (rad/s) in 1 degree/second (°/s). To calculate larger amounts manually, simply multiply your total number of degrees/second by the conversion multiplier of 0.017453293.

The mathematical formula to convert degrees/second to radians/second is: [value] * 0.017453293 = radians/second. Rather than doing the math manually, you can use our high-precision online calculator to process this exact equation instantly without rounding errors.

To perform the reverse calculation from radians/second back to degrees/second, you must divide your starting value by 0.017453293. Our bidirectional tool automatically computes this inverse equation the moment you type into the radian/second input field.

1 Radian/second is larger than 1 Degree/second. Specifically, 1 Degree/second equals 0.017453293 radians/second, meaning 1 Radian/second is 57.2958 times larger than 1 Degree/second (a difference of 1.76 orders of magnitude). Expressing measurements in degrees/second requires a larger numerical value to represent the equivalent physical magnitude.

Under standard international measurement guidelines, 1 Degree/second converts to 0.017453293 radians/second. Precise numerical conversion factors ensure consistency across laboratory, engineering, and field data.

There are approximately 0.0174532925 rad/s in 1 °/s. The exact theoretical conversion factor is derived from π / 180 rad/s, which evaluates to 0.0174533 rad/s to seven significant figures.

To convert angular velocity from degree/second (V(°/s)) to radian/second (V(rad/s)), multiply by π / 180 (0.0174532925): V(rad/s) = V(°/s) × 0.0174533 For example, 90 °/s × 0.0174532925 = 1.5707963 rad/s (0.5π rad/s).

To convert radian/second (V(rad/s)) to degree/second (V(°/s)), multiply by 180 / π (57.2957795): V(°/s) = V(rad/s) × 57.2958 For instance, 3.14159265 rad/s × 57.2957795 = 180 °/s.

While degrees/second (°/s) are commonly used in industrial gyroscopes and automotive steering instrumentation, the SI unit radian/second (rad/s) directly relates rotational speed to linear velocity via v = ω r without requiring degree-to-radian scale factors in kinematic equations.