Radian/second to Degree/second (rad/s to °/s) Converter & Formula

Rate this converter

Instant calculation with 0ms overhead

Popular Converters

Live Conversion • ISO 80000-3:2019 Certified

1 Radian/second = 57.29577951 Degree/second

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

Decimals:

Certified Authority Value

57.29577951

°/s

From / Input

rad/s

Swap to Degree/second to Radian/second

To / Result

°/s

Quick Values:

Conversion Formula

To convert Radian/second to Degree/second, multiply by 57.29577951

rad/s × 57.29577951 = °/s

Calculation: 1 rad/s × 57.29577951 = 57.29577951 °/s

Common Radian/second to Degree/second Calculations

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

Tap any row to calculate

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

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

Radian/second to Degree/second Conversion Reference Table
Conversion & Equivalent Value	Scientific Notation
0.001 rad/s 0.0572958 °/s	5.73 × 10⁻²
0.01 rad/s 0.572958 °/s	5.73 × 10⁻¹
0.1 rad/s 5.729578 °/s	5.73 × 10⁰
0.5 rad/s 28.64789 °/s	2.865 × 10¹
1 rad/s 57.29578 °/s	5.73 × 10¹
2 rad/s 114.591559 °/s	1.146 × 10²
5 rad/s 286.478898 °/s	2.865 × 10²
10 rad/s 572.957795 °/s	5.73 × 10²
20 rad/s 1145.91559 °/s	1.146 × 10³
25 rad/s 1432.394488 °/s	1.432 × 10³
50 rad/s 2864.788976 °/s	2.865 × 10³
100 rad/s 5729.577951 °/s	5.73 × 10³
250 rad/s 14323.944878 °/s	1.432 × 10⁴
500 rad/s 28647.889757 °/s	2.865 × 10⁴
1000 rad/s 57295.779513 °/s	5.73 × 10⁴

Degree/second to Radian/second: Reciprocal Summary

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

Degree/second to Radian/second Conversion Reference Table
Reciprocal & Equivalent Value	Scientific Notation
1 °/s 0.0174533 rad/s	1.745 × 10⁻²
5 °/s 0.0872665 rad/s	8.727 × 10⁻²
10 °/s 0.174533 rad/s	1.745 × 10⁻¹
50 °/s 0.872665 rad/s	8.727 × 10⁻¹
100 °/s 1.745329 rad/s	1.745 × 10⁰

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

Real-World Context & Everyday Benchmarks

Tap to load into converter

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

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

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

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

How to Convert Radian/second to Degree/second

Converting Radian/second (rad/s) to Degree/second (°/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 represents a larger magnitude than Degree/second, converting from rad/s to °/s expands the numerical figure. Exactly 1 Radian/second encompasses 57.29578 Degree/second. To convert any quantity, multiply the value in Radian/second by 57.29578.

Direct Factor1 rad/s = 57.29578 °/s

Inverse Ratio1 °/s = 0.0174533 rad/s

Conversion ScaleDirect Proportional Magnitude Expansion

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 rad/s = 1 radian per second (rad/s)

2. Target SI Bridge (k_target):1 °/s = 0.0174533 radian per second (rad/s)

Step-by-step substitution for Radian/second → Degree/second:V(°/s) = V(rad/s) × ( 1 / 0.0174533 ) = V(rad/s) × 57.29578

Mathematical FormulaValue in Degree/second = Value in Radian/second × 57.29577951Direct computational formula applied for standard conversion.

Worked Example

To convert 12 Radian/second (rad/s) to Degree/second (°/s): multiply 12 by 57.29578 to get 687.549354 °/s. At an industrial engineering scale, 1000 rad/s converts to 57295.779513 °/s.

Inverse check: 1 °/s = 0.0174533 rad/s.

Understanding Radian/second and Degree/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): rad/s

Select Applied Shaft Torque: 250 N·m

Governing Law: P = τ × ω

Vector: [rad/s] × [N·m] → [W]

Live Calculated Bridge Equivalent:

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

Equals 0.25 kW • 0.00025 MW • 0.3353 hp

SI Power

250

Watts

Grid / Utility

0.25

Kilowatts

Power Plant

0.00025

Megawatts

Mechanical Rating

0.3353

Horsepower (Mechanical)

Metric Horsepower

0.3399

Metric Horsepower (PS)

HVAC Thermal Rating

853.04

BTU/h

BTU per Hour

Step-by-Step Numerical Derivation Proof View Derivation

1. Normalize Input to SI Base Unit (rad/s):
ω = 1 rad/s × 1 = 1 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 = (1 rad/s) × (250 N·m) = 250 W
4. Convert to Standard Engineering Units:
• W: 250 × 1 = 250 W (Watts) • kW: 250 × 0.001 = 0.25 kW (Kilowatts) • MW: 250 × 1 × 10⁻⁶ = 0.00025 MW (Megawatts) • hp: 250 × 0.001341 = 0.3353 hp (Horsepower (Mechanical)) • PS: 250 × 0.00136 = 0.3399 PS (Metric Horsepower (PS)) • BTU/h: 250 × 3.4121 = 853.04 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 57.29577951 degrees/second (°/s) in 1 radian/second (rad/s). To calculate larger amounts manually, simply multiply your total number of radians/second by the conversion multiplier of 57.29577951.

The mathematical formula to convert radians/second to degrees/second is: [value] * 57.29577951 = degrees/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 degrees/second back to radians/second, you must divide your starting value by 57.29577951. Our bidirectional tool automatically computes this inverse equation the moment you type into the degree/second input field.

1 Radian/second is larger than 1 Degree/second. Specifically, 1 Radian/second equals exactly 57.29577951 degrees/second, making it 57.2958 times larger (a difference of 1.76 orders of magnitude). Therefore, quantities expressed in degrees/second require a larger numerical value to represent the same physical amount.

Under standard international measurement guidelines, 1 Radian/second converts to 57.29577951 degrees/second. Precise numerical conversion factors ensure consistency across laboratory, engineering, and field data.

Under ISO 80000 angular velocity standards, 1 rad/s is exactly equal to 57.2958 °/s.

To determine the value in Degree/second, multiply the Radian/second measurement by the conversion factor of 57.2958. The exact equation is: V(°/s) = V(rad/s) × 57.2958.

To convert inversely from Degree/second to Radian/second, multiply the value by 0.0174533. The exact formula is: V(rad/s) = V(°/s) × 0.0174533.

In rotational mechanics and robotics, a standard servo motor rotating at a velocity of π rad/s (3.14159 rad/s) operates at exactly 180 °/s, representing one half-rotation per second.