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

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Live Conversion • ISO 80000-3:2019 Certified

1 Radian/second = 13750.98708314 Revolution/day

1 rad/s = 13750.987083 rev/d • 1 rev/d = 7.272205 × 10⁻⁵ rad/s

Decimals:

Certified Authority Value

13750.98708314

rev/d

From / Input

rad/s

Swap to Revolution/day to Radian/second

To / Result

rev/d

Quick Values:

Conversion Formula

To convert Radian/second to Revolution/day, multiply by 13750.98708314

rad/s × 13750.98708314 = rev/d

Calculation: 1 rad/s × 13750.98708314 = 13750.98708314 rev/d

Common Radian/second to Revolution/day Calculations

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

Tap any row to calculate

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

Rule: 1 Radian/second is equal to 13750.987083 rev/d (Revolution/day)

Radian/second to Revolution/day Conversion Reference Table
Conversion & Equivalent Value	Scientific Notation
0.001 rad/s 13.750987 rev/d	1.375 × 10¹
0.01 rad/s 137.509871 rev/d	1.375 × 10²
0.1 rad/s 1375.098708 rev/d	1.375 × 10³
0.5 rad/s 6875.493542 rev/d	6.875 × 10³
1 rad/s 13750.987083 rev/d	1.375 × 10⁴
2 rad/s 27501.974166 rev/d	2.75 × 10⁴
5 rad/s 68754.935416 rev/d	6.875 × 10⁴
10 rad/s 137509.870831 rev/d	1.375 × 10⁵
20 rad/s 275019.741663 rev/d	2.75 × 10⁵
25 rad/s 343774.677078 rev/d	3.438 × 10⁵
50 rad/s 687549.354157 rev/d	6.875 × 10⁵
100 rad/s 1375098.708314 rev/d	1.375 × 10⁶
250 rad/s 3437746.770785 rev/d	3.438 × 10⁶
500 rad/s 6875493.54157 rev/d	6.875 × 10⁶
1000 rad/s 1.375099 × 10⁷ rev/d	1.375 × 10⁷

Revolution/day to Radian/second: Reciprocal Summary

Rule: 1 Revolution/day is equal to 7.272205 × 10⁻⁵ rad/s (Radian/second)

Revolution/day to Radian/second Conversion Reference Table
Reciprocal & Equivalent Value	Scientific Notation
1 rev/d 7.272205 × 10⁻⁵ rad/s	7.272 × 10⁻⁵
5 rev/d 0.00036361 rad/s	3.636 × 10⁻⁴
10 rev/d 0.000727221 rad/s	7.272 × 10⁻⁴
50 rev/d 0.0036361 rad/s	3.636 × 10⁻³
100 rev/d 0.00727221 rad/s	7.272 × 10⁻³

View Complete 15-Row Revolution/day to Radian/second 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/second (rad/s) and Revolution/day (rev/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

Revolution/day References:

Earth diurnal rotation cycle relative to celestial background 1 rev/d
International Space Station ISS low Earth orbits per day 15.5 rev/d
Geostationary communications satellite orbital revolution rate 1 rev/d

Tap any benchmark above to automatically calculate its exact equivalent in Revolution/day.

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

How to Convert Radian/second to Revolution/day

Converting Radian/second (rad/s) to Revolution/day (rev/d) 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 Revolution/day, converting from rad/s to rev/d expands the numerical figure. Exactly 1 Radian/second encompasses 13750.987083 Revolution/day. To convert any quantity, multiply the value in Radian/second by 13750.987083.

Direct Factor1 rad/s = 13750.987083 rev/d

Inverse Ratio1 rev/d = 7.272205 × 10⁻⁵ 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 rev/d = 7.272205 × 10⁻⁵ radian per second (rad/s)

Step-by-step substitution for Radian/second → Revolution/day:V(rev/d) = V(rad/s) × ( 1 / 7.272205 × 10⁻⁵ ) = V(rad/s) × 13750.987083

Mathematical FormulaValue in Revolution/day = Value in Radian/second × 13750.98708314Direct computational formula applied for standard conversion.

Worked Example

For an engineering input of 8 rad/s, applying the conversion factor yields exactly 110007.896665 rev/d. At larger operational scale, 240 Radian/second corresponds to 3300236.899954 rev/d.

Inverse check: 1 rev/d = 7.272205 × 10⁻⁵ rad/s.

Understanding Radian/second and Revolution/day

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 13750.98708314 revolutions/day (rev/d) in 1 radian/second (rad/s). To calculate larger amounts manually, simply multiply your total number of radians/second by the conversion multiplier of 13750.98708314.

The mathematical formula to convert radians/second to revolutions/day is: [value] * 13750.98708314 = revolutions/day. 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 revolutions/day back to radians/second, you must divide your starting value by 13750.98708314. Our bidirectional tool automatically computes this inverse equation the moment you type into the revolution/day input field.

1 Radian/second is larger than 1 Revolution/day. Specifically, 1 Radian/second equals exactly 13750.98708314 revolutions/day, making it 13750.9871 times larger (a difference of 4.14 orders of magnitude). Therefore, quantities expressed in revolutions/day require a larger numerical value to represent the same physical amount.

Under standard international measurement guidelines, 1 Radian/second converts to 13750.98708314 revolutions/day. Precise numerical conversion factors ensure consistency across laboratory, engineering, and field data.