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

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Live Conversion • ISO 80000-3:2019 Certified

1 Revolution/second = 6.28318531 Radian/second

1 rev/s = 6.283185 rad/s • 1 rad/s = 0.159155 rev/s

Decimals:

Certified Authority Value

6.28318531

rad/s

From / Input

rev/s

Swap to Radian/second to Revolution/second

To / Result

rad/s

Quick Values:

Conversion Formula

To convert Revolution/second to Radian/second, multiply by 6.28318531

rev/s × 6.28318531 = rad/s

Calculation: 1 rev/s × 6.28318531 = 6.28318531 rad/s

Common Revolution/second to Radian/second Calculations

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

Tap any row to calculate

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

Rule: 1 Revolution/second is equal to 6.283185 rad/s (Radian/second)

Revolution/second to Radian/second Conversion Reference Table
Conversion & Equivalent Value	Scientific Notation
0.001 rev/s 0.00628319 rad/s	6.283 × 10⁻³
0.01 rev/s 0.0628319 rad/s	6.283 × 10⁻²
0.1 rev/s 0.628319 rad/s	6.283 × 10⁻¹
0.5 rev/s 3.141593 rad/s	3.142 × 10⁰
1 rev/s 6.283185 rad/s	6.283 × 10⁰
2 rev/s 12.566371 rad/s	1.257 × 10¹
5 rev/s 31.415927 rad/s	3.142 × 10¹
10 rev/s 62.831853 rad/s	6.283 × 10¹
20 rev/s 125.663706 rad/s	1.257 × 10²
25 rev/s 157.079633 rad/s	1.571 × 10²
50 rev/s 314.159265 rad/s	3.142 × 10²
100 rev/s 628.318531 rad/s	6.283 × 10²
250 rev/s 1570.796327 rad/s	1.571 × 10³
500 rev/s 3141.592654 rad/s	3.142 × 10³
1000 rev/s 6283.185307 rad/s	6.283 × 10³

Radian/second to Revolution/second: Reciprocal Summary

Rule: 1 Radian/second is equal to 0.159155 rev/s (Revolution/second)

Radian/second to Revolution/second Conversion Reference Table
Reciprocal & Equivalent Value	Scientific Notation
1 rad/s 0.159155 rev/s	1.592 × 10⁻¹
5 rad/s 0.795775 rev/s	7.958 × 10⁻¹
10 rad/s 1.591549 rev/s	1.592 × 10⁰
50 rad/s 7.957747 rev/s	7.958 × 10⁰
100 rad/s 15.915494 rev/s	1.592 × 10¹

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

Revolution/second References:

Passenger car alternator rotor shaft speed at engine idle 30 rev/s
Commercial high-speed blender blade rotational speed 350 rev/s
High-speed air-bearing dental drill turbine maximum velocity 6500 rev/s

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 Revolution/second to Radian/second

Converting Revolution/second (rev/s) 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 Revolution/second represents a larger magnitude than Radian/second, converting from rev/s to rad/s expands the numerical figure. Exactly 1 Revolution/second encompasses 6.283185 Radian/second. To convert any quantity, multiply the value in Revolution/second by 6.283185.

Direct Factor1 rev/s = 6.283185 rad/s

Inverse Ratio1 rad/s = 0.159155 rev/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 rev/s = 6.283185 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 Revolution/second → Radian/second:V(rad/s) = V(rev/s) × ( 6.283185 / 1 ) = V(rev/s) × 6.283185

Mathematical FormulaValue in Radian/second = Value in Revolution/second × 6.28318531Direct computational formula applied for standard conversion.

Worked Example

For an engineering input of 15 rev/s, applying the conversion factor yields exactly 94.24778 rad/s. At larger operational scale, 240 Revolution/second corresponds to 1507.964474 rad/s.

Inverse check: 1 rad/s = 0.159155 rev/s.

Understanding Revolution/second 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): rev/s

Select Applied Shaft Torque: 250 N·m

Governing Law: P = τ × ω

Vector: [rad/s] × [N·m] → [W]

Live Calculated Bridge Equivalent:

1 rev/s at Passenger Car Engine (250 N·m) = 1570.7963 W

Equals 1.5708 kW • 0.0015708 MW • 2.1065 hp

SI Power

1570.7963

Watts

Grid / Utility

1.5708

Kilowatts

Power Plant

0.0015708

Megawatts

Mechanical Rating

2.1065

Horsepower (Mechanical)

Metric Horsepower

2.1357

Metric Horsepower (PS)

HVAC Thermal Rating

5359.78

BTU/h

BTU per Hour

Step-by-Step Numerical Derivation Proof View Derivation

1. Normalize Input to SI Base Unit (rad/s):
ω = 1 rev/s × 6.28318531 = 6.28318531 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 = (6.28318531 rad/s) × (250 N·m) = 1570.796327 W
4. Convert to Standard Engineering Units:
• W: 1570.796327 × 1 = 1570.7963 W (Watts) • kW: 1570.796327 × 0.001 = 1.5708 kW (Kilowatts) • MW: 1570.796327 × 1 × 10⁻⁶ = 0.0015708 MW (Megawatts) • hp: 1570.796327 × 0.001341 = 2.1065 hp (Horsepower (Mechanical)) • PS: 1570.796327 × 0.00136 = 2.1357 PS (Metric Horsepower (PS)) • BTU/h: 1570.796327 × 3.4121 = 5359.78 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 6.28318531 radians/second (rad/s) in 1 revolution/second (rev/s). To calculate larger amounts manually, simply multiply your total number of revolutions/second by the conversion multiplier of 6.28318531.

The mathematical formula to convert revolutions/second to radians/second is: [value] * 6.28318531 = 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 revolutions/second, you must divide your starting value by 6.28318531. Our bidirectional tool automatically computes this inverse equation the moment you type into the radian/second input field.

1 Revolution/second is larger than 1 Radian/second. Specifically, 1 Revolution/second equals exactly 6.28318531 radians/second, making it 6.2832 times larger (a difference of 0.80 orders of magnitude). Therefore, quantities expressed in radians/second require a larger numerical value to represent the same physical amount.

Under standard international measurement guidelines, 1 Revolution/second converts to 6.28318531 radians/second. Precise numerical conversion factors ensure consistency across laboratory, engineering, and field data.