Degrees/second to Revolutions/minute Converter (°/s to rpm)

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Live Conversion • ISO 80000-3:2019 Certified

1 Degree/second = 0.16666667 Revolution/minute

1 °/s = 0.166667 rpm • 1 rpm = 6 °/s

Decimals:

Certified Authority Value

0.16666667

rpm

From / Input

°/s

Swap to Revolution/minute to Degree/second

To / Result

rpm

Quick Values:

Conversion Formula

To convert Degree/second to Revolution/minute, multiply by 0.16666667

°/s × 0.16666667 = rpm

Calculation: 1 °/s × 0.16666667 = 0.16666667 rpm

Common Degree/second to Revolution/minute Calculations

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

Tap any row to calculate

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

Rule: 1 Degree/second is equal to 0.166667 rpm (Revolution/minute)

Degree/second to Revolution/minute Conversion Reference Table
Conversion & Equivalent Value	Scientific Notation
0.001 °/s 0.000166667 rpm	1.667 × 10⁻⁴
0.01 °/s 0.00166667 rpm	1.667 × 10⁻³
0.1 °/s 0.0166667 rpm	1.667 × 10⁻²
0.5 °/s 0.0833333 rpm	8.333 × 10⁻²
1 °/s 0.166667 rpm	1.667 × 10⁻¹
2 °/s 0.333333 rpm	3.333 × 10⁻¹
5 °/s 0.833333 rpm	8.333 × 10⁻¹
10 °/s 1.666667 rpm	1.667 × 10⁰
20 °/s 3.333333 rpm	3.333 × 10⁰
25 °/s 4.166667 rpm	4.167 × 10⁰
50 °/s 8.333333 rpm	8.333 × 10⁰
100 °/s 16.666667 rpm	1.667 × 10¹
250 °/s 41.666667 rpm	4.167 × 10¹
500 °/s 83.333333 rpm	8.333 × 10¹
1000 °/s 166.666667 rpm	1.667 × 10²

Revolution/minute to Degree/second: Reciprocal Summary

Rule: 1 Revolution/minute is equal to 6 °/s (Degree/second)

Revolution/minute to Degree/second Conversion Reference Table
Reciprocal & Equivalent Value	Scientific Notation
1 rpm 6 °/s	6 × 10⁰
5 rpm 30 °/s	3 × 10¹
10 rpm 60 °/s	6 × 10¹
50 rpm 300 °/s	3 × 10²
100 rpm 600 °/s	6 × 10²

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

Degree/second References:

Second hand movement rate on standard analog clock 6 °/s
Human smooth pursuit eye tracking maximum visual velocity 30 °/s
Aerobatic competition stunt airplane maximum roll rate 360 °/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

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

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

How to Convert Degree/second to Revolution/minute

Converting Degree/second (°/s) to Revolution/minute (rpm) is a core calculation in Angular Velocity, which measures the rotational speed and rate of angular displacement per unit of time. Because Revolution/minute is a broader physical scale than Degree/second, converting from °/s to rpm condenses the numerical figure. It takes 6 Degree/second to equal a single Revolution/minute (1 °/s = 0.166667 rpm). To convert any quantity, multiply by 0.166667 (or divide by 6).

Direct Factor1 °/s = 0.166667 rpm

Inverse Ratio1 rpm = 6 °/s

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 °/s = 0.0174533 radian per second (rad/s)

2. Target SI Bridge (k_target):1 rpm = 0.10472 radian per second (rad/s)

Step-by-step substitution for Degree/second → Revolution/minute:V(rpm) = V(°/s) × ( 0.0174533 / 0.10472 ) = V(°/s) × 0.166667

Mathematical FormulaValue in Revolution/minute = Value in Degree/second × 0.16666667Direct computational formula applied for standard conversion.

Worked Example

Evaluating an input of 120 Degree/second (°/s) produces 20 Revolution/minute (rpm). In heavy-duty utility and industrial workloads, 10000 °/s equals 1666.666667 rpm.

Inverse check: 1 rpm = 6 °/s.

Understanding Degree/second and Revolution/minute

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): °/s

Select Applied Shaft Torque: 250 N·m

Governing Law: P = τ × ω

Vector: [rad/s] × [N·m] → [W]

Live Calculated Bridge Equivalent:

1 °/s at Passenger Car Engine (250 N·m) = 4.3633 W

Equals 0.004363 kW • 4.363323 × 10⁻⁶ MW • 0.005851 hp

SI Power

4.3633

Watts

Grid / Utility

0.004363

Kilowatts

Power Plant

4.363323 × 10⁻⁶

Megawatts

Mechanical Rating

0.005851

Horsepower (Mechanical)

Metric Horsepower

0.005932

Metric Horsepower (PS)

HVAC Thermal Rating

14.89

BTU/h

BTU per Hour

Step-by-Step Numerical Derivation Proof View Derivation

1. Normalize Input to SI Base Unit (rad/s):
ω = 1 °/s × 0.01745329 = 0.01745329 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 = (0.01745329 rad/s) × (250 N·m) = 4.363323 W
4. Convert to Standard Engineering Units:
• W: 4.363323 × 1 = 4.3633 W (Watts) • kW: 4.363323 × 0.001 = 0.004363 kW (Kilowatts) • MW: 4.363323 × 1 × 10⁻⁶ = 4.363323 × 10⁻⁶ MW (Megawatts) • hp: 4.363323 × 0.001341 = 0.005851 hp (Horsepower (Mechanical)) • PS: 4.363323 × 0.00136 = 0.005932 PS (Metric Horsepower (PS)) • BTU/h: 4.363323 × 3.4121 = 14.89 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 0.16666667 revolutions/minute (rpm) in 1 degree/second (°/s). To calculate larger amounts manually, simply multiply your total number of degrees/second by the conversion multiplier of 0.16666667.

The mathematical formula to convert degrees/second to revolutions/minute is: [value] * 0.16666667 = revolutions/minute. 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/minute back to degrees/second, you must divide your starting value by 0.16666667. Our bidirectional tool automatically computes this inverse equation the moment you type into the revolution/minute input field.

1 Revolution/minute is larger than 1 Degree/second. Specifically, 1 Degree/second equals 0.16666667 revolutions/minute, meaning 1 Revolution/minute is 6 times larger than 1 Degree/second (a difference of 0.78 orders of magnitude). Expressing measurements in degrees/second requires a larger numerical value to represent the equivalent physical magnitude.

Under standard international measurement guidelines, 1 Degree/second converts to 0.16666667 revolutions/minute. Precise numerical conversion factors ensure consistency across laboratory, engineering, and field data.