Revolution/second² to Radian/second² (rev/s² to rad/s²) Calculator & Formula

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Live Conversion • ISO 80000-3:2019 Certified

1 Revolution/second² = 6.28318531 Radian/second²

1 rev/s² = 6.283185 rad/s² • 1 rad/s² = 0.159155 rev/s²

Decimals:

Certified Authority Value

6.28318531

rad/s²

From / Input

rev/s²

Swap to Radian/second² to Revolution/second²

To / Result

rad/s²

Quick Values:

Conversion Formula

To convert Revolution/second² to Radian/second², multiply by 6.28318531

rev/s² × 6.28318531 = rad/s²

Calculation: 1 rev/s² × 6.28318531 = 6.28318531 rad/s²

Common Revolution/second² to Radian/second² Calculations

Quick-lookup reference table showing calculated equivalents for standard increments between Revolution/second² (rev/s²) and Radian/second² (rad/s²).

Tap any row to calculate

Revolution/second² to Radian/second²: Primary Direct Table (15 Steps)

Rule: 1 Revolution/second² is equal to 6.283185 rad/s² (Radian/second²)

Revolution/second² to Radian/second² Conversion Reference Table
Conversion & Equivalent Value	Scientific Notation
0.001 rev/s² 0.00628319 rad/s²	6.283 × 10⁻³
0.01 rev/s² 0.0628319 rad/s²	6.283 × 10⁻²
0.1 rev/s² 0.628319 rad/s²	6.283 × 10⁻¹
0.5 rev/s² 3.141593 rad/s²	3.142 × 10⁰
1 rev/s² 6.283185 rad/s²	6.283 × 10⁰
2 rev/s² 12.566371 rad/s²	1.257 × 10¹
5 rev/s² 31.415927 rad/s²	3.142 × 10¹
10 rev/s² 62.831853 rad/s²	6.283 × 10¹
20 rev/s² 125.663706 rad/s²	1.257 × 10²
25 rev/s² 157.079633 rad/s²	1.571 × 10²
50 rev/s² 314.159266 rad/s²	3.142 × 10²
100 rev/s² 628.318531 rad/s²	6.283 × 10²
250 rev/s² 1570.796328 rad/s²	1.571 × 10³
500 rev/s² 3141.592655 rad/s²	3.142 × 10³
1000 rev/s² 6283.185311 rad/s²	6.283 × 10³

Radian/second² to Revolution/second²: Reciprocal Summary

Rule: 1 Radian/second² is equal to 0.159155 rev/s² (Revolution/second²)

Radian/second² to Revolution/second² Conversion Reference Table
Reciprocal & Equivalent Value	Scientific Notation
1 rad/s² 0.159155 rev/s²	1.592 × 10⁻¹
5 rad/s² 0.795775 rev/s²	7.958 × 10⁻¹
10 rad/s² 1.591549 rev/s²	1.592 × 10⁰
50 rad/s² 7.957747 rev/s²	7.958 × 10⁰
100 rad/s² 15.915494 rev/s²	1.592 × 10¹

View Complete 15-Row Radian/second² to Revolution/second² 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/second² (rev/s²) and Radian/second² (rad/s²):

Revolution/second² References:

Heavy-duty industrial electric power drill spindle acceleration 50 rev/s²
High-speed air-turbine dental drill spindle ramp-up 5000 rev/s²

Radian/second² References:

Laboratory benchtop centrifuge acceleration rate 50 rad/s²
High-performance sports car engine revving up in neutral 350 rad/s²
Computer 7200 RPM hard disk platter spin-up acceleration 1200 rad/s²

Tap any benchmark above to automatically calculate its exact equivalent in Radian/second².

ISQ Dimension: [T⁻²] Coherent SI Unit: radian per second squared (rad/s²) Classical Mechanics & Dimensional Metrology

How to Convert Revolution/second² to Radian/second²

Converting Revolution/second² (rev/s²) to Radian/second² (rad/s²) is a core calculation in Angular Acceleration, which measures the rate of change of rotational velocity over time about a rotation axis. Because Revolution/second² represents a larger magnitude than Radian/second², converting from rev/s² to rad/s² expands the numerical figure. Exactly 1 Revolution/second² encompasses 6.283185 Radian/second². To convert any quantity, multiply the value in Revolution/second² by 6.283185.

Direct Factor1 rev/s² = 6.283185 rad/s²

Inverse Ratio1 rad/s² = 0.159155 rev/s²

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 squared (rad/s²)) 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/s² = 6.283185 radian per second squared (rad/s²)

2. Target SI Bridge (k_target):1 rad/s² = 1 radian per second squared (rad/s²)

Step-by-step substitution for Revolution/second² → Radian/second²:V(rad/s²) = V(rev/s²) × ( 6.283185 / 1 ) = V(rev/s²) × 6.283185

Mathematical FormulaValue in Radian/second² = Value in Revolution/second² × 6.28318531Direct computational formula applied for standard conversion.

Worked Example

For an engineering input of 8 rev/s², applying the conversion factor yields exactly 50.265482 rad/s². At larger operational scale, 100 Revolution/second² corresponds to 628.318531 rad/s².

Inverse check: 1 rad/s² = 0.159155 rev/s².

Understanding Revolution/second² and Radian/second²

Domain Metrology & Engineering Applications

Governing Law & Equation

Rotational Dynamics Equation (α = τ / I = dω/dt)

Measurement Instrumentation

Rigorously quantified in laboratory and field settings using angular rate gyroscopes, high-speed rotary quadrature encoders, and torsional laser vibrometers.

Primary Industry Sectors

Applied across industrial robotics positioning, satellite attitude control systems, and high-performance turbine dynamics 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 Dynamics Equation (α = τ / I = dω/dt) under ISO 80000 dimensional vector [T⁻²].

Multi-Variable Engineering Bridge Rotational Dynamics & Flywheel Torque

Angular Acceleration to Dynamic Torque Bridge (Newton-Meters • Foot-Pounds • Inch-Pounds)

Calculate required rotor dynamic torque τ = I × α across industrial machinery and flywheel moments of inertia, bridging angular acceleration [T⁻²] with rotational torque [M L² T⁻²].

Input Angular Acceleration Rate (α): rev/s²

Select Rotor Moment of Inertia: 2.5 kg·m²

Governing Law: τ = I × α

Vector: [rad/s²] × [kg·m²] → [N·m]

Live Calculated Bridge Equivalent:

1 rev/s² at Industrial Electric Motor Rotor (2.5 kg·m²) = 15.708 N·m

Equals 0.01571 kN·m • 11.5856 lbf·ft • 139.0272 lbf·in

SI Torque

15.708

N·m

Newton-Meters

Heavy Drivetrain

0.01571

kN·m

Kilonewton-Meters

US Automotive

11.5856

lbf·ft

Foot-Pounds

Precision Fasteners

139.0272

lbf·in

Inch-Pounds

Metric Torque

1.6018

kgf·m

Kilogram-Force Meters

CGS Torque

1.57 × 10⁸

dyn·cm

Dyne-Centimeters

Step-by-Step Numerical Derivation Proof View Derivation

1. Normalize Input to SI Base Unit (rad/s²):
α = 1 rev/s² × 6.28318531 = 6.28318531 rad/s²
2. Apply Engineering Parameter (I):
Selected condition: Industrial Electric Motor Rotor (2.5 kg·m²) at I = 2.5 kg·m²
3. Execute Governing Physical Law in SI Units:
τ = I × α = (6.28318531 rad/s²) × (2.5 kg·m²) = 15.707963 N·m
4. Convert to Standard Engineering Units:
• N·m: 15.707963 × 1 = 15.708 N·m (Newton-Meters) • kN·m: 15.707963 × 0.001 = 0.01571 kN·m (Kilonewton-Meters) • lbf·ft: 15.707963 × 0.7376 = 11.5856 lbf·ft (Foot-Pounds) • lbf·in: 15.707963 × 8.8507 = 139.0272 lbf·in (Inch-Pounds) • kgf·m: 15.707963 × 0.102 = 1.6018 kgf·m (Kilogram-Force Meters) • dyn·cm: 15.707963 × 1 × 10⁷ = 1.57 × 10⁸ dyn·cm (Dyne-Centimeters)

Explore Full Moment of Inertia Converter →

Engineering Substance / Operating Standard	Parameter Value (kg·m²)	Reference State / Condition	Typical Industrial & Engineering Application
Bicycle Wheel (0.14 kg·m²)	`0.14`	0.14 kg·m²	Standard 700c bicycle wheel rim and tire
Automotive Engine Flywheel (0.50 kg·m²)	`0.5`	0.50 kg·m²	Internal combustion engine dual-mass flywheel
Industrial Electric Motor Rotor (2.5 kg·m²)	`2.5`	2.5 kg·m²	50 kW three-phase induction motor rotor
Industrial Ventilation Fan (25 kg·m²)	`25`	25.0 kg·m²	Mine ventilation fan impeller
Utility Wind Turbine Rotor (50,000 kg·m²)	`50000`	50,000 kg·m²	2 MW commercial wind turbine rotor blade hub

Frequently Asked Questions

There are exactly 6.28318531 radians/second² (rad/s²) in 1 revolution/second² (rev/s²). To calculate larger amounts manually, simply multiply your total number of revolutions/second² by the conversion multiplier of 6.28318531.

The mathematical formula to convert revolutions/second² to radians/second² is: [value] * 6.28318531 = radians/second². 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/second² back to revolutions/second², you must divide your starting value by 6.28318531. Our bidirectional tool automatically computes this inverse equation the moment you type into the radian/second² input field.

1 Revolution/second² is larger than 1 Radian/second². Specifically, 1 Revolution/second² equals exactly 6.28318531 radians/second², making it 6.2832 times larger (a difference of 0.80 orders of magnitude). Therefore, quantities expressed in radians/second² require a larger numerical value to represent the same physical amount.

Under standard international measurement guidelines, 1 Revolution/second² converts to 6.28318531 radians/second². Precise numerical conversion factors ensure consistency across laboratory, engineering, and field data.

There are 6.28319 rad/s² in 1 rev/s². The exact mathematical relationship is 1 rev/s² = 6.28319 rad/s².

The conversion formula is V(rad/s²) = V(rev/s²) × 6.28319. Because one complete revolution is 2π radians, multiplying by 2π (approx. 6.28319) yields the Radian/second² equivalent.

To convert in reverse, the formula is V(rev/s²) = V(rad/s²) × 0.159155. Multiply the Radian/second² measurement by 0.159155 to find the Revolution/second² value.

Revolution/second² is a critical metric in high-speed rotary dynamics, such as measuring the acceleration profile of centrifuges, electric motor shafts, and automotive turbochargers spinning up to operating speeds.