Revolutions/minute to Radians/second Converter (rpm to rad/s)

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Live Conversion • ISO 80000-3:2019 Certified

1 Revolution/minute = 0.10471976 Radian/second

1 rpm = 0.10472 rad/s • 1 rad/s = 9.549297 rpm

Decimals:

Certified Authority Value

0.10471976

rad/s

From / Input

rpm

Swap to Radian/second to Revolution/minute

To / Result

rad/s

Quick Values:

Conversion Formula

To convert Revolution/minute to Radian/second, multiply by 0.10471976

rpm × 0.10471976 = rad/s

Calculation: 1 rpm × 0.10471976 = 0.10471976 rad/s

Common Revolution/minute to Radian/second Calculations

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

Tap any row to calculate

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

Rule: 1 Revolution/minute is equal to 0.10472 rad/s (Radian/second)

Revolution/minute to Radian/second Conversion Reference Table
Conversion & Equivalent Value	Scientific Notation
0.001 rpm 0.00010472 rad/s	1.047 × 10⁻⁴
0.01 rpm 0.0010472 rad/s	1.047 × 10⁻³
0.1 rpm 0.010472 rad/s	1.047 × 10⁻²
0.5 rpm 0.0523599 rad/s	5.236 × 10⁻²
1 rpm 0.10472 rad/s	1.047 × 10⁻¹
2 rpm 0.20944 rad/s	2.094 × 10⁻¹
5 rpm 0.523599 rad/s	5.236 × 10⁻¹
10 rpm 1.047198 rad/s	1.047 × 10⁰
20 rpm 2.094395 rad/s	2.094 × 10⁰
25 rpm 2.617994 rad/s	2.618 × 10⁰
50 rpm 5.235988 rad/s	5.236 × 10⁰
100 rpm 10.471976 rad/s	1.047 × 10¹
250 rpm 26.179939 rad/s	2.618 × 10¹
500 rpm 52.359878 rad/s	5.236 × 10¹
1000 rpm 104.719755 rad/s	1.047 × 10²

Radian/second to Revolution/minute: Reciprocal Summary

Rule: 1 Radian/second is equal to 9.549297 rpm (Revolution/minute)

Radian/second to Revolution/minute Conversion Reference Table
Reciprocal & Equivalent Value	Scientific Notation
1 rad/s 9.549297 rpm	9.549 × 10⁰
5 rad/s 47.746483 rpm	4.775 × 10¹
10 rad/s 95.492966 rpm	9.549 × 10¹
50 rad/s 477.464829 rpm	4.775 × 10²
100 rad/s 954.929659 rpm	9.549 × 10²

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

Revolution/minute References:

Standard 12-inch vinyl LP record phonograph playback turntable speed 33.3 rpm
Standard 7-inch vinyl single record phonograph playback speed 45 rpm
Passenger car gasoline engine steady idling rotation speed 750 rpm
Desktop computer high-airflow cooling fan maximum speed 2000 rpm
High-speed dental clinic air turbine drill rotation speed 350000 rpm

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/minute to Radian/second

Converting Revolution/minute (rpm) 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 Revolution/minute, converting from rpm to rad/s condenses the numerical figure. It takes 9.549297 Revolution/minute to equal a single Radian/second (1 rpm = 0.10472 rad/s). To convert any quantity, multiply by 0.10472 (or divide by 9.549297).

Direct Factor1 rpm = 0.10472 rad/s

Inverse Ratio1 rad/s = 9.549297 rpm

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 rpm = 0.10472 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/minute → Radian/second:V(rad/s) = V(rpm) × ( 0.10472 / 1 ) = V(rpm) × 0.10472

Mathematical FormulaValue in Radian/second = Value in Revolution/minute × 0.10471976Direct computational formula applied for standard conversion.

Worked Example

To convert 50 Revolution/minute (rpm) to Radian/second (rad/s): multiply 50 by 0.10472 to get 5.235988 rad/s. At an industrial engineering scale, 240 rpm converts to 25.132741 rad/s.

Inverse check: 1 rad/s = 9.549297 rpm.

Understanding Revolution/minute 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): rpm

Select Applied Shaft Torque: 250 N·m

Governing Law: P = τ × ω

Vector: [rad/s] × [N·m] → [W]

Live Calculated Bridge Equivalent:

1 rpm at Passenger Car Engine (250 N·m) = 26.1799 W

Equals 0.02618 kW • 2.617994 × 10⁻⁵ MW • 0.03511 hp

SI Power

26.1799

Watts

Grid / Utility

0.02618

Kilowatts

Power Plant

2.617994 × 10⁻⁵

Megawatts

Mechanical Rating

0.03511

Horsepower (Mechanical)

Metric Horsepower

0.03559

Metric Horsepower (PS)

HVAC Thermal Rating

89.33

BTU/h

BTU per Hour

Step-by-Step Numerical Derivation Proof View Derivation

1. Normalize Input to SI Base Unit (rad/s):
ω = 1 rpm × 0.10471976 = 0.10471976 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 = (0.10471976 rad/s) × (250 N·m) = 26.179939 W
4. Convert to Standard Engineering Units:
• W: 26.179939 × 1 = 26.1799 W (Watts) • kW: 26.179939 × 0.001 = 0.02618 kW (Kilowatts) • MW: 26.179939 × 1 × 10⁻⁶ = 2.617994 × 10⁻⁵ MW (Megawatts) • hp: 26.179939 × 0.001341 = 0.03511 hp (Horsepower (Mechanical)) • PS: 26.179939 × 0.00136 = 0.03559 PS (Metric Horsepower (PS)) • BTU/h: 26.179939 × 3.4121 = 89.33 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 0.10471976 radians/second (rad/s) in 1 revolution/minute (rpm). To calculate larger amounts manually, simply multiply your total number of revolutions/minute by the conversion multiplier of 0.10471976.

The mathematical formula to convert revolutions/minute to radians/second is: [value] * 0.10471976 = 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/minute, you must divide your starting value by 0.10471976. 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 Revolution/minute. Specifically, 1 Revolution/minute equals 0.10471976 radians/second, meaning 1 Radian/second is 9.5493 times larger than 1 Revolution/minute (a difference of 0.98 orders of magnitude). Expressing measurements in revolutions/minute requires a larger numerical value to represent the equivalent physical magnitude.

Under standard international measurement guidelines, 1 Revolution/minute converts to 0.10471976 radians/second. Precise numerical conversion factors ensure consistency across laboratory, engineering, and field data.