Degree/second to Radian/hour (°/s to rad/h) Calculator & Formula

Rate this converter

Instant calculation with 0ms overhead

Popular Converters

Live Conversion • ISO 80000-3:2019 Certified

1 Degree/second = 62.83185307 Radian/hour

1 °/s = 62.831853 rad/h • 1 rad/h = 0.0159155 °/s

Decimals:

Certified Authority Value

62.83185307

rad/h

From / Input

°/s

Swap to Radian/hour to Degree/second

To / Result

rad/h

Quick Values:

Conversion Formula

To convert Degree/second to Radian/hour, multiply by 62.83185307

°/s × 62.83185307 = rad/h

Calculation: 1 °/s × 62.83185307 = 62.83185307 rad/h

Common Degree/second to Radian/hour Calculations

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

Tap any row to calculate

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

Rule: 1 Degree/second is equal to 62.831853 rad/h (Radian/hour)

Degree/second to Radian/hour Conversion Reference Table
Conversion & Equivalent Value	Scientific Notation
0.001 °/s 0.0628319 rad/h	6.283 × 10⁻²
0.01 °/s 0.628319 rad/h	6.283 × 10⁻¹
0.1 °/s 6.283185 rad/h	6.283 × 10⁰
0.5 °/s 31.415927 rad/h	3.142 × 10¹
1 °/s 62.831853 rad/h	6.283 × 10¹
2 °/s 125.663706 rad/h	1.257 × 10²
5 °/s 314.159265 rad/h	3.142 × 10²
10 °/s 628.318531 rad/h	6.283 × 10²
20 °/s 1256.637061 rad/h	1.257 × 10³
25 °/s 1570.796327 rad/h	1.571 × 10³
50 °/s 3141.592654 rad/h	3.142 × 10³
100 °/s 6283.185307 rad/h	6.283 × 10³
250 °/s 15707.963268 rad/h	1.571 × 10⁴
500 °/s 31415.926536 rad/h	3.142 × 10⁴
1000 °/s 62831.853072 rad/h	6.283 × 10⁴

Radian/hour to Degree/second: Reciprocal Summary

Rule: 1 Radian/hour is equal to 0.0159155 °/s (Degree/second)

Radian/hour to Degree/second Conversion Reference Table
Reciprocal & Equivalent Value	Scientific Notation
1 rad/h 0.0159155 °/s	1.592 × 10⁻²
5 rad/h 0.0795775 °/s	7.958 × 10⁻²
10 rad/h 0.159155 °/s	1.592 × 10⁻¹
50 rad/h 0.795775 °/s	7.958 × 10⁻¹
100 rad/h 1.591549 °/s	1.592 × 10⁰

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

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/hour References:

Minute hand on traditional analog clock rotational velocity 6.28 rad/h
Hour hand on traditional analog clock rotational velocity 0.524 rad/h
Earth diurnal axial rotation angular rate (15 degrees/hour) 0.262 rad/h

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

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

How to Convert Degree/second to Radian/hour

Converting Degree/second (°/s) to Radian/hour (rad/h) is a core calculation in Angular Velocity, which measures the rotational speed and rate of angular displacement per unit of time. Because Degree/second represents a larger magnitude than Radian/hour, converting from °/s to rad/h expands the numerical figure. Exactly 1 Degree/second encompasses 62.831853 Radian/hour. To convert any quantity, multiply the value in Degree/second by 62.831853.

Direct Factor1 °/s = 62.831853 rad/h

Inverse Ratio1 rad/h = 0.0159155 °/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 °/s = 0.0174533 radian per second (rad/s)

2. Target SI Bridge (k_target):1 rad/h = 0.000277778 radian per second (rad/s)

Step-by-step substitution for Degree/second → Radian/hour:V(rad/h) = V(°/s) × ( 0.0174533 / 0.000277778 ) = V(°/s) × 62.831853

Mathematical FormulaValue in Radian/hour = Value in Degree/second × 62.83185307Direct computational formula applied for standard conversion.

Worked Example

Evaluating an input of 24 Degree/second (°/s) produces 1507.964474 Radian/hour (rad/h). In heavy-duty utility and industrial workloads, 240 °/s equals 15079.644737 rad/h.

Inverse check: 1 rad/h = 0.0159155 °/s.

Understanding Degree/second and Radian/hour

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 62.83185307 radians/hour (rad/h) in 1 degree/second (°/s). To calculate larger amounts manually, simply multiply your total number of degrees/second by the conversion multiplier of 62.83185307.

The mathematical formula to convert degrees/second to radians/hour is: [value] * 62.83185307 = radians/hour. 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/hour back to degrees/second, you must divide your starting value by 62.83185307. Our bidirectional tool automatically computes this inverse equation the moment you type into the radian/hour input field.

1 Degree/second is larger than 1 Radian/hour. Specifically, 1 Degree/second equals exactly 62.83185307 radians/hour, making it 62.8319 times larger (a difference of 1.80 orders of magnitude). Therefore, quantities expressed in radians/hour require a larger numerical value to represent the same physical amount.

Under standard international measurement guidelines, 1 Degree/second converts to 62.83185307 radians/hour. Precise numerical conversion factors ensure consistency across laboratory, engineering, and field data.

There is exactly 62.8319 Radian/hour in one Degree/second. Expressed mathematically, 1 °/s = 62.8319 rad/h.

To execute the conversion from Degree/second to Radian/hour, multiply the rate by 62.8319. The formula is: V(rad/h) = V(°/s) × 62.8319.

To convert in reverse, multiply the Radian/hour value by 0.0159155. The formula equates to: V(°/s) = V(rad/h) × 0.0159155.

This is critical for converting rapid rotational adjustments mapping within a single second (like servomotor stabilization loops) into aggregate long-duration operational envelopes expressed in radians per hour.