Degrees/hour to Radians/second Converter (°/h to rad/s)

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Live Conversion • ISO 80000-3:2019 Certified

1 Degree/hour = 4.84813681 × 10⁻⁶ Radian/second

1 °/h = 4.848137 × 10⁻⁶ rad/s • 1 rad/s = 206264.806247 °/h

Decimals:

Certified Authority Value

0.00000485

rad/s

From / Input

°/h

Swap to Radian/second to Degree/hour

To / Result

rad/s

Quick Values:

Conversion Formula

To convert Degree/hour to Radian/second, multiply by 4.84813681 × 10⁻⁶

°/h × 4.84813681 × 10⁻⁶ = rad/s

Calculation: 1 °/h × 4.84813681 × 10⁻⁶ = 4.84813681 × 10⁻⁶ rad/s

Common Degree/hour to Radian/second Calculations

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

Tap any row to calculate

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

Rule: 1 Degree/hour is equal to 4.848137 × 10⁻⁶ rad/s (Radian/second)

Degree/hour to Radian/second Conversion Reference Table
Conversion & Equivalent Value	Scientific Notation
0.001 °/h 4.848137 × 10⁻⁹ rad/s	4.848 × 10⁻⁹
0.01 °/h 4.848137 × 10⁻⁸ rad/s	4.848 × 10⁻⁸
0.1 °/h 4.848137 × 10⁻⁷ rad/s	4.848 × 10⁻⁷
0.5 °/h 2.424068 × 10⁻⁶ rad/s	2.424 × 10⁻⁶
1 °/h 4.848137 × 10⁻⁶ rad/s	4.848 × 10⁻⁶
2 °/h 9.696274 × 10⁻⁶ rad/s	9.696 × 10⁻⁶
5 °/h 2.424068 × 10⁻⁵ rad/s	2.424 × 10⁻⁵
10 °/h 4.848137 × 10⁻⁵ rad/s	4.848 × 10⁻⁵
20 °/h 9.696274 × 10⁻⁵ rad/s	9.696 × 10⁻⁵
25 °/h 0.000121203 rad/s	1.212 × 10⁻⁴
50 °/h 0.000242407 rad/s	2.424 × 10⁻⁴
100 °/h 0.000484814 rad/s	4.848 × 10⁻⁴
250 °/h 0.00121203 rad/s	1.212 × 10⁻³
500 °/h 0.00242407 rad/s	2.424 × 10⁻³
1000 °/h 0.00484814 rad/s	4.848 × 10⁻³

Radian/second to Degree/hour: Reciprocal Summary

Rule: 1 Radian/second is equal to 206264.806247 °/h (Degree/hour)

Radian/second to Degree/hour Conversion Reference Table
Reciprocal & Equivalent Value	Scientific Notation
1 rad/s 206264.806247 °/h	2.063 × 10⁵
5 rad/s 1031324.031235 °/h	1.031 × 10⁶
10 rad/s 2062648.062471 °/h	2.063 × 10⁶
50 rad/s 1.031324 × 10⁷ °/h	1.031 × 10⁷
100 rad/s 2.062648 × 10⁷ °/h	2.063 × 10⁷

View Complete 15-Row Radian/second to Degree/hour 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/hour (°/h) and Radian/second (rad/s):

Degree/hour References:

Earth rotational speed relative to celestial stars 15 °/h
Minute hand rotational speed on traditional wall clock 360 °/h
Hour hand rotational speed on standard 12-hour clock 30 °/h

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/hour to Radian/second

Converting Degree/hour (°/h) 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/hour, converting from °/h to rad/s condenses the numerical figure. It takes 206264.806247 Degree/hour to equal a single Radian/second (1 °/h = 4.848137 × 10⁻⁶ rad/s). To convert any quantity, multiply by 4.848137 × 10⁻⁶ (or divide by 206264.806247).

Direct Factor1 °/h = 4.848137 × 10⁻⁶ rad/s

Inverse Ratio1 rad/s = 206264.806247 °/h

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 °/h = 4.848137 × 10⁻⁶ 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/hour → Radian/second:V(rad/s) = V(°/h) × ( 4.848137 × 10⁻⁶ / 1 ) = V(°/h) × 4.848137 × 10⁻⁶

Mathematical FormulaValue in Radian/second = Value in Degree/hour × 4.84813681 × 10⁻⁶Direct computational formula applied for standard conversion.

Worked Example

To convert 24 Degree/hour (°/h) to Radian/second (rad/s): multiply 24 by 4.848137 × 10⁻⁶ to get 0.000116355 rad/s. At an industrial engineering scale, 1000 °/h converts to 0.00484814 rad/s.

Inverse check: 1 rad/s = 206264.806247 °/h.

Understanding Degree/hour 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): °/h

Select Applied Shaft Torque: 250 N·m

Governing Law: P = τ × ω

Vector: [rad/s] × [N·m] → [W]

Live Calculated Bridge Equivalent:

1 °/h at Passenger Car Engine (250 N·m) = 0.001212 W

Equals 1.212 × 10⁻⁶ kW • 1.212034 × 10⁻⁹ MW • 1.6254 × 10⁻⁶ hp

SI Power

0.001212

Watts

Grid / Utility

1.212 × 10⁻⁶

Kilowatts

Power Plant

1.212034 × 10⁻⁹

Megawatts

Mechanical Rating

1.6254 × 10⁻⁶

Horsepower (Mechanical)

Metric Horsepower

1.6479 × 10⁻⁶

Metric Horsepower (PS)

HVAC Thermal Rating

0.0041

BTU/h

BTU per Hour

Step-by-Step Numerical Derivation Proof View Derivation

1. Normalize Input to SI Base Unit (rad/s):
ω = 1 °/h × 4.84813681 × 10⁻⁶ = 4.84813681 × 10⁻⁶ 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 = (4.84813681 × 10⁻⁶ rad/s) × (250 N·m) = 0.00121203 W
4. Convert to Standard Engineering Units:
• W: 0.00121203 × 1 = 0.001212 W (Watts) • kW: 0.00121203 × 0.001 = 1.212 × 10⁻⁶ kW (Kilowatts) • MW: 0.00121203 × 1 × 10⁻⁶ = 1.212034 × 10⁻⁹ MW (Megawatts) • hp: 0.00121203 × 0.001341 = 1.6254 × 10⁻⁶ hp (Horsepower (Mechanical)) • PS: 0.00121203 × 0.00136 = 1.6479 × 10⁻⁶ PS (Metric Horsepower (PS)) • BTU/h: 0.00121203 × 3.4121 = 0.0041 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 4.84813681 × 10⁻⁶ radians/second (rad/s) in 1 degree/hour (°/h). To calculate larger amounts manually, simply multiply your total number of degrees/hour by the conversion multiplier of 4.84813681 × 10⁻⁶.

The mathematical formula to convert degrees/hour to radians/second is: [value] * 4.84813681 × 10⁻⁶ = 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/hour, you must divide your starting value by 4.84813681 × 10⁻⁶. 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/hour. Specifically, 1 Degree/hour equals 4.84813681 × 10⁻⁶ radians/second, meaning 1 Radian/second is 206264.8062 times larger than 1 Degree/hour (a difference of 5.31 orders of magnitude). Expressing measurements in degrees/hour requires a larger numerical value to represent the equivalent physical magnitude.

Under standard international measurement guidelines, 1 Degree/hour converts to 4.84813681 × 10⁻⁶ radians/second. Precise numerical conversion factors ensure consistency across laboratory, engineering, and field data.