Radians/second² to Degrees/second² Converter (rad/s² to °/s²)

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Live Conversion • ISO 80000-3:2019 Certified

1 Radian/second² = 57.2957795 Degree/second²

1 rad/s² = 57.29578 °/s² • 1 °/s² = 0.0174533 rad/s²

Decimals:

Certified Authority Value

57.29577950

°/s²

From / Input

rad/s²

Swap to Degree/second² to Radian/second²

To / Result

°/s²

Quick Values:

Conversion Formula

To convert Radian/second² to Degree/second², multiply by 57.2957795

rad/s² × 57.2957795 = °/s²

Calculation: 1 rad/s² × 57.2957795 = 57.2957795 °/s²

Common Radian/second² to Degree/second² Calculations

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

Tap any row to calculate

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

Rule: 1 Radian/second² is equal to 57.29578 °/s² (Degree/second²)

Radian/second² to Degree/second² Conversion Reference Table
Conversion & Equivalent Value	Scientific Notation
0.001 rad/s² 0.0572958 °/s²	5.73 × 10⁻²
0.01 rad/s² 0.572958 °/s²	5.73 × 10⁻¹
0.1 rad/s² 5.729578 °/s²	5.73 × 10⁰
0.5 rad/s² 28.64789 °/s²	2.865 × 10¹
1 rad/s² 57.29578 °/s²	5.73 × 10¹
2 rad/s² 114.591559 °/s²	1.146 × 10²
5 rad/s² 286.478898 °/s²	2.865 × 10²
10 rad/s² 572.957795 °/s²	5.73 × 10²
20 rad/s² 1145.91559 °/s²	1.146 × 10³
25 rad/s² 1432.394488 °/s²	1.432 × 10³
50 rad/s² 2864.788975 °/s²	2.865 × 10³
100 rad/s² 5729.57795 °/s²	5.73 × 10³
250 rad/s² 14323.944875 °/s²	1.432 × 10⁴
500 rad/s² 28647.88975 °/s²	2.865 × 10⁴
1000 rad/s² 57295.7795 °/s²	5.73 × 10⁴

Degree/second² to Radian/second²: Reciprocal Summary

Rule: 1 Degree/second² is equal to 0.0174533 rad/s² (Radian/second²)

Degree/second² to Radian/second² Conversion Reference Table
Reciprocal & Equivalent Value	Scientific Notation
1 °/s² 0.0174533 rad/s²	1.745 × 10⁻²
5 °/s² 0.0872665 rad/s²	8.727 × 10⁻²
10 °/s² 0.174533 rad/s²	1.745 × 10⁻¹
50 °/s² 0.872665 rad/s²	8.727 × 10⁻¹
100 °/s² 1.745329 rad/s²	1.745 × 10⁰

View Complete 15-Row Degree/second² to Radian/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 Radian/second² (rad/s²) and Degree/second² (°/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

Degree/second² References:

Industrial robotic arm wrist rapid pivot joint acceleration 1200 °/s²
High-speed military gimbal turret rapid slew acceleration 3000 °/s²

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

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

How to Convert Radian/second² to Degree/second²

Converting Radian/second² (rad/s²) to Degree/second² (°/s²) is a core calculation in Angular Acceleration, which measures the rate of change of rotational velocity over time about a rotation axis. Because Radian/second² represents a larger magnitude than Degree/second², converting from rad/s² to °/s² expands the numerical figure. Exactly 1 Radian/second² encompasses 57.29578 Degree/second². To convert any quantity, multiply the value in Radian/second² by 57.29578.

Direct Factor1 rad/s² = 57.29578 °/s²

Inverse Ratio1 °/s² = 0.0174533 rad/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 rad/s² = 1 radian per second squared (rad/s²)

2. Target SI Bridge (k_target):1 °/s² = 0.0174533 radian per second squared (rad/s²)

Step-by-step substitution for Radian/second² → Degree/second²:V(°/s²) = V(rad/s²) × ( 1 / 0.0174533 ) = V(rad/s²) × 57.29578

Mathematical FormulaValue in Degree/second² = Value in Radian/second² × 57.2957795Direct computational formula applied for standard conversion.

Worked Example

To convert 2.5 Radian/second² (rad/s²) to Degree/second² (°/s²): multiply 2.5 by 57.29578 to get 143.239449 °/s². At an industrial engineering scale, 1000 rad/s² converts to 57295.7795 °/s².

Inverse check: 1 °/s² = 0.0174533 rad/s².

Understanding Radian/second² and Degree/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): rad/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 rad/s² at Industrial Electric Motor Rotor (2.5 kg·m²) = 2.5 N·m

Equals 0.0025 kN·m • 1.8439 lbf·ft • 22.1269 lbf·in

SI Torque

2.5

N·m

Newton-Meters

Heavy Drivetrain

0.0025

kN·m

Kilonewton-Meters

US Automotive

1.8439

lbf·ft

Foot-Pounds

Precision Fasteners

22.1269

lbf·in

Inch-Pounds

Metric Torque

0.2549

kgf·m

Kilogram-Force Meters

CGS Torque

2.5 × 10⁷

dyn·cm

Dyne-Centimeters

Step-by-Step Numerical Derivation Proof View Derivation

1. Normalize Input to SI Base Unit (rad/s²):
α = 1 rad/s² × 1 = 1 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 = (1 rad/s²) × (2.5 kg·m²) = 2.5 N·m
4. Convert to Standard Engineering Units:
• N·m: 2.5 × 1 = 2.5 N·m (Newton-Meters) • kN·m: 2.5 × 0.001 = 0.0025 kN·m (Kilonewton-Meters) • lbf·ft: 2.5 × 0.7376 = 1.8439 lbf·ft (Foot-Pounds) • lbf·in: 2.5 × 8.8507 = 22.1269 lbf·in (Inch-Pounds) • kgf·m: 2.5 × 0.102 = 0.2549 kgf·m (Kilogram-Force Meters) • dyn·cm: 2.5 × 1 × 10⁷ = 2.5 × 10⁷ 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 57.2957795 degrees/second² (°/s²) in 1 radian/second² (rad/s²). To calculate larger amounts manually, simply multiply your total number of radians/second² by the conversion multiplier of 57.2957795.

The mathematical formula to convert radians/second² to degrees/second² is: [value] * 57.2957795 = degrees/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 degrees/second² back to radians/second², you must divide your starting value by 57.2957795. Our bidirectional tool automatically computes this inverse equation the moment you type into the degree/second² input field.

1 Radian/second² is larger than 1 Degree/second². Specifically, 1 Radian/second² equals exactly 57.2957795 degrees/second², making it 57.2958 times larger (a difference of 1.76 orders of magnitude). Therefore, quantities expressed in degrees/second² require a larger numerical value to represent the same physical amount.

Under standard international measurement guidelines, 1 Radian/second² converts to 57.2957795 degrees/second². Precise numerical conversion factors ensure consistency across laboratory, engineering, and field data.