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

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Live Conversion • ISO 80000-3:2019 Certified

1 Radian/day = 1.15740741 × 10⁻⁵ Radian/second

1 rad/d = 1.157407 × 10⁻⁵ rad/s • 1 rad/s = 86,400 rad/d

Decimals:

Certified Authority Value

0.00001157

rad/s

From / Input

rad/d

Swap to Radian/second to Radian/day

To / Result

rad/s

Quick Values:

Conversion Formula

To convert Radian/day to Radian/second, multiply by 1.15740741 × 10⁻⁵

rad/d × 1.15740741 × 10⁻⁵ = rad/s

Calculation: 1 rad/d × 1.15740741 × 10⁻⁵ = 1.15740741 × 10⁻⁵ rad/s

Common Radian/day to Radian/second Calculations

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

Tap any row to calculate

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

Rule: 1 Radian/day is equal to 1.157407 × 10⁻⁵ rad/s (Radian/second)

Radian/day to Radian/second Conversion Reference Table
Conversion & Equivalent Value	Scientific Notation
0.001 rad/d 1.157407 × 10⁻⁸ rad/s	1.157 × 10⁻⁸
0.01 rad/d 1.157407 × 10⁻⁷ rad/s	1.157 × 10⁻⁷
0.1 rad/d 1.157407 × 10⁻⁶ rad/s	1.157 × 10⁻⁶
0.5 rad/d 5.787037 × 10⁻⁶ rad/s	5.787 × 10⁻⁶
1 rad/d 1.157407 × 10⁻⁵ rad/s	1.157 × 10⁻⁵
2 rad/d 2.314815 × 10⁻⁵ rad/s	2.315 × 10⁻⁵
5 rad/d 5.787037 × 10⁻⁵ rad/s	5.787 × 10⁻⁵
10 rad/d 0.000115741 rad/s	1.157 × 10⁻⁴
20 rad/d 0.000231481 rad/s	2.315 × 10⁻⁴
25 rad/d 0.000289352 rad/s	2.894 × 10⁻⁴
50 rad/d 0.000578704 rad/s	5.787 × 10⁻⁴
100 rad/d 0.00115741 rad/s	1.157 × 10⁻³
250 rad/d 0.00289352 rad/s	2.894 × 10⁻³
500 rad/d 0.00578704 rad/s	5.787 × 10⁻³
1000 rad/d 0.0115741 rad/s	1.157 × 10⁻²

Radian/second to Radian/day: Reciprocal Summary

Rule: 1 Radian/second is equal to 86,400 rad/d (Radian/day)

Radian/second to Radian/day Conversion Reference Table
Reciprocal & Equivalent Value	Scientific Notation
1 rad/s 86400 rad/d	8.64 × 10⁴
5 rad/s 432000 rad/d	4.32 × 10⁵
10 rad/s 864000 rad/d	8.64 × 10⁵
50 rad/s 4320000 rad/d	4.32 × 10⁶
100 rad/s 8640000 rad/d	8.64 × 10⁶

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

Radian/day References:

Earth axial rotation angular velocity (one full turn) 6.28 rad/d
Moon synchronous orbital angular speed around Earth 0.23 rad/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 Radian/day to Radian/second

Converting Radian/day (rad/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 Radian/day, converting from rad/d to rad/s condenses the numerical figure. It takes 86400 Radian/day to equal a single Radian/second (1 rad/d = 1.157407 × 10⁻⁵ rad/s). To convert any quantity, multiply by 1.157407 × 10⁻⁵ (or divide by 86400).

Direct Factor1 rad/d = 1.157407 × 10⁻⁵ rad/s

Inverse Ratio1 rad/s = 86400 rad/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 rad/d = 1.157407 × 10⁻⁵ 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 Radian/day → Radian/second:V(rad/s) = V(rad/d) × ( 1.157407 × 10⁻⁵ / 1 ) = V(rad/d) × 1.157407 × 10⁻⁵

Mathematical FormulaValue in Radian/second = Value in Radian/day × 1.15740741 × 10⁻⁵Direct computational formula applied for standard conversion.

Worked Example

Converting 15 rad/d yields an exact output of 0.000173611 rad/s in Radian/second. Under higher industrial throughput, 5000 rad/d translates to 0.0578704 rad/s.

Inverse check: 1 rad/s = 86400 rad/d.

Understanding Radian/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): rad/d

Select Applied Shaft Torque: 250 N·m

Governing Law: P = τ × ω

Vector: [rad/s] × [N·m] → [W]

Live Calculated Bridge Equivalent:

1 rad/d at Passenger Car Engine (250 N·m) = 0.002894 W

Equals 2.8935 × 10⁻⁶ kW • 2.893519 × 10⁻⁹ MW • 3.8803 × 10⁻⁶ hp

SI Power

0.002894

Watts

Grid / Utility

2.8935 × 10⁻⁶

Kilowatts

Power Plant

2.893519 × 10⁻⁹

Megawatts

Mechanical Rating

3.8803 × 10⁻⁶

Horsepower (Mechanical)

Metric Horsepower

3.9341 × 10⁻⁶

Metric Horsepower (PS)

HVAC Thermal Rating

0.0099

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/d × 1.15740741 × 10⁻⁵ = 1.15740741 × 10⁻⁵ 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 = (1.15740741 × 10⁻⁵ rad/s) × (250 N·m) = 0.00289352 W
4. Convert to Standard Engineering Units:
• W: 0.00289352 × 1 = 0.002894 W (Watts) • kW: 0.00289352 × 0.001 = 2.8935 × 10⁻⁶ kW (Kilowatts) • MW: 0.00289352 × 1 × 10⁻⁶ = 2.893519 × 10⁻⁹ MW (Megawatts) • hp: 0.00289352 × 0.001341 = 3.8803 × 10⁻⁶ hp (Horsepower (Mechanical)) • PS: 0.00289352 × 0.00136 = 3.9341 × 10⁻⁶ PS (Metric Horsepower (PS)) • BTU/h: 0.00289352 × 3.4121 = 0.0099 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 1.15740741 × 10⁻⁵ radians/second (rad/s) in 1 radian/day (rad/d). To calculate larger amounts manually, simply multiply your total number of radians/day by the conversion multiplier of 1.15740741 × 10⁻⁵.

The mathematical formula to convert radians/day to radians/second is: [value] * 1.15740741 × 10⁻⁵ = 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 radians/day, you must divide your starting value by 1.15740741 × 10⁻⁵. 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 Radian/day. Specifically, 1 Radian/day equals 1.15740741 × 10⁻⁵ radians/second, meaning 1 Radian/second is 86400 times larger than 1 Radian/day (a difference of 4.94 orders of magnitude). Expressing measurements in radians/day requires a larger numerical value to represent the equivalent physical magnitude.

Under standard international measurement guidelines, 1 Radian/day converts to 1.15740741 × 10⁻⁵ radians/second. Precise numerical conversion factors ensure consistency across laboratory, engineering, and field data.