Degrees/day to Radians/second Converter (°/d to rad/s)

Rate this converter

Instant calculation with 0ms overhead

Popular Converters

Live Conversion • ISO 80000-3:2019 Certified

1 Degree/day = 2.020057 × 10⁻⁷ Radian/second

1 °/d = 2.020057 × 10⁻⁷ rad/s • 1 rad/s = 4950355.34993 °/d

Decimals:

Certified Authority Value

0.00000020

rad/s

From / Input

°/d

Swap to Radian/second to Degree/day

To / Result

rad/s

Quick Values:

Conversion Formula

To convert Degree/day to Radian/second, multiply by 2.020057 × 10⁻⁷

°/d × 2.020057 × 10⁻⁷ = rad/s

Calculation: 1 °/d × 2.020057 × 10⁻⁷ = 2.020057 × 10⁻⁷ rad/s

Common Degree/day to Radian/second Calculations

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

Tap any row to calculate

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

Rule: 1 Degree/day is equal to 2.020057 × 10⁻⁷ rad/s (Radian/second)

Degree/day to Radian/second Conversion Reference Table
Conversion & Equivalent Value	Scientific Notation
0.001 °/d 2.020057 × 10⁻¹⁰ rad/s	2.02 × 10⁻¹⁰
0.01 °/d 2.020057 × 10⁻⁹ rad/s	2.02 × 10⁻⁹
0.1 °/d 2.020057 × 10⁻⁸ rad/s	2.02 × 10⁻⁸
0.5 °/d 1.010029 × 10⁻⁷ rad/s	1.01 × 10⁻⁷
1 °/d 2.020057 × 10⁻⁷ rad/s	2.02 × 10⁻⁷
2 °/d 4.040114 × 10⁻⁷ rad/s	4.04 × 10⁻⁷
5 °/d 1.010029 × 10⁻⁶ rad/s	1.01 × 10⁻⁶
10 °/d 2.020057 × 10⁻⁶ rad/s	2.02 × 10⁻⁶
20 °/d 4.040114 × 10⁻⁶ rad/s	4.04 × 10⁻⁶
25 °/d 5.050143 × 10⁻⁶ rad/s	5.05 × 10⁻⁶
50 °/d 1.010029 × 10⁻⁵ rad/s	1.01 × 10⁻⁵
100 °/d 2.020057 × 10⁻⁵ rad/s	2.02 × 10⁻⁵
250 °/d 5.050143 × 10⁻⁵ rad/s	5.05 × 10⁻⁵
500 °/d 0.000101003 rad/s	1.01 × 10⁻⁴
1000 °/d 0.000202006 rad/s	2.02 × 10⁻⁴

Radian/second to Degree/day: Reciprocal Summary

Rule: 1 Radian/second is equal to 4950355.34993 °/d (Degree/day)

Radian/second to Degree/day Conversion Reference Table
Reciprocal & Equivalent Value	Scientific Notation
1 rad/s 4950355.34993 °/d	4.95 × 10⁶
5 rad/s 2.475178 × 10⁷ °/d	2.475 × 10⁷
10 rad/s 4.950355 × 10⁷ °/d	4.95 × 10⁷
50 rad/s 2.475178 × 10⁸ °/d	2.475 × 10⁸
100 rad/s 4.950355 × 10⁸ °/d	4.95 × 10⁸

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

Degree/day References:

Earth complete daily axial rotation rate 360 °/d
Moon eastward orbital progression across night sky 13.2 °/d

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/day to Radian/second

Converting Degree/day (°/d) 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/day, converting from °/d to rad/s condenses the numerical figure. It takes 4950355.34993 Degree/day to equal a single Radian/second (1 °/d = 2.020057 × 10⁻⁷ rad/s). To convert any quantity, multiply by 2.020057 × 10⁻⁷ (or divide by 4950355.34993).

Direct Factor1 °/d = 2.020057 × 10⁻⁷ rad/s

Inverse Ratio1 rad/s = 4950355.34993 °/d

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 °/d = 2.020057 × 10⁻⁷ 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/day → Radian/second:V(rad/s) = V(°/d) × ( 2.020057 × 10⁻⁷ / 1 ) = V(°/d) × 2.020057 × 10⁻⁷

Mathematical FormulaValue in Radian/second = Value in Degree/day × 2.020057 × 10⁻⁷Direct computational formula applied for standard conversion.

Worked Example

Evaluating an input of 120 Degree/day (°/d) produces 2.424068 × 10⁻⁵ Radian/second (rad/s). In heavy-duty utility and industrial workloads, 100 °/d equals 2.020057 × 10⁻⁵ rad/s.

Inverse check: 1 rad/s = 4950355.34993 °/d.

Understanding Degree/day 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): °/d

Select Applied Shaft Torque: 250 N·m

Governing Law: P = τ × ω

Vector: [rad/s] × [N·m] → [W]

Live Calculated Bridge Equivalent:

1 °/d at Passenger Car Engine (250 N·m) = 5.0501 × 10⁻⁵ W

Equals 5.0501 × 10⁻⁸ kW • 5.050143 × 10⁻¹¹ MW • 6.7724 × 10⁻⁸ hp

SI Power

5.0501 × 10⁻⁵

Watts

Grid / Utility

5.0501 × 10⁻⁸

Kilowatts

Power Plant

5.050143 × 10⁻¹¹

Megawatts

Mechanical Rating

6.7724 × 10⁻⁸

Horsepower (Mechanical)

Metric Horsepower

6.8663 × 10⁻⁸

Metric Horsepower (PS)

HVAC Thermal Rating

0.00017

BTU/h

BTU per Hour

Step-by-Step Numerical Derivation Proof View Derivation

1. Normalize Input to SI Base Unit (rad/s):
ω = 1 °/d × 2.020057 × 10⁻⁷ = 2.020057 × 10⁻⁷ 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 = (2.020057 × 10⁻⁷ rad/s) × (250 N·m) = 5.050143 × 10⁻⁵ W
4. Convert to Standard Engineering Units:
• W: 5.050143 × 10⁻⁵ × 1 = 5.0501 × 10⁻⁵ W (Watts) • kW: 5.050143 × 10⁻⁵ × 0.001 = 5.0501 × 10⁻⁸ kW (Kilowatts) • MW: 5.050143 × 10⁻⁵ × 1 × 10⁻⁶ = 5.050143 × 10⁻¹¹ MW (Megawatts) • hp: 5.050143 × 10⁻⁵ × 0.001341 = 6.7724 × 10⁻⁸ hp (Horsepower (Mechanical)) • PS: 5.050143 × 10⁻⁵ × 0.00136 = 6.8663 × 10⁻⁸ PS (Metric Horsepower (PS)) • BTU/h: 5.050143 × 10⁻⁵ × 3.4121 = 0.00017 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 2.020057 × 10⁻⁷ radians/second (rad/s) in 1 degree/day (°/d). To calculate larger amounts manually, simply multiply your total number of degrees/day by the conversion multiplier of 2.020057 × 10⁻⁷.

The mathematical formula to convert degrees/day to radians/second is: [value] * 2.020057 × 10⁻⁷ = 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/day, you must divide your starting value by 2.020057 × 10⁻⁷. 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/day. Specifically, 1 Degree/day equals 2.020057 × 10⁻⁷ radians/second, meaning 1 Radian/second is 4950355.3499 times larger than 1 Degree/day (a difference of 6.69 orders of magnitude). Expressing measurements in degrees/day requires a larger numerical value to represent the equivalent physical magnitude.

Under standard international measurement guidelines, 1 Degree/day converts to 2.020057 × 10⁻⁷ radians/second. Precise numerical conversion factors ensure consistency across laboratory, engineering, and field data.