Radians to Degrees

Angular Metrology & ISO 80000-2 Standards

The radian is the SI derived unit of plane angle, defined as the angle subtended at the center of a circle by an arc equal in length to the radius of the circle:

• $1\text{ Radian (rad)}$: $\equiv \frac{180}{\pi}^\circ \approx 57.2957795^\circ = 57^\circ 17' 44.81'' = 63.662\text{ grad} = 0.159155\text{ rev}$

• $1^\circ\text{ (Degree)}$: $\equiv \frac{\pi}{180}\text{ rad} \approx 0.01745329\text{ rad} = 1.111\text{ grad} = \frac{1}{360}\text{ rev}$

Primary Unit Circle Angle Equivalents

• $\frac{\pi}{6}\text{ rad}$: $\equiv 30.0^\circ = 33.33\text{ grad} = \frac{1}{12}\text{ rev} \quad$

• $\frac{\pi}{4}\text{ rad}$: $\equiv 45.0^\circ = 50.00\text{ grad} = \frac{1}{8}\text{ rev} \quad$

• $\frac{\pi}{3}\text{ rad}$: $\equiv 60.0^\circ = 66.67\text{ grad} = \frac{1}{6}\text{ rev} \quad$

• $\frac{\pi}{2}\text{ rad}$: $\equiv 90.0^\circ = 100.00\text{ grad} = \frac{1}{4}\text{ rev} \quad$

• $\pi\text{ rad}$: $\equiv 180.0^\circ = 200.00\text{ grad} = \frac{1}{2}\text{ rev} \quad$

• $\frac{3\pi}{2}\text{ rad}$: $\equiv 270.0^\circ = 300.00\text{ grad} = \frac{3}{4}\text{ rev}$

• $2\pi\text{ rad}$: $\equiv 360.0^\circ = 400.00\text{ grad} = 1.00\text{ rev}$

Equations

• $\text{Degrees} = \text{Radians} \times \frac{180}{\pi}$

• $\text{Radians} = \text{Degrees} \times \frac{\pi}{180}$

How to Use This Calculator

Enter Angle Value to Convert, Conversion Direction into the input fields and the calculator will instantly compute Converted Angle, Decimal Degrees (°). All calculations happen in real time — no submission or page reload required. You can adjust any input value and see the result update immediately.

Understanding Your Result

The Radians to Degrees result gives you a precise, calculated value based on the inputs you provide. Compare your result against published benchmarks from NIST, BIPM, and ISO 80000 to assess where you stand. A single calculation is a useful starting point, but tracking this metric over time — as inputs change — gives you a much more complete picture.

Practical Application

The Radians to Degrees is most useful when you have specific, real-world data to enter. For example: enter your actual Angle Value to Convert to calculate your converted angle. The result helps engineers, scientists, students, and international traders make informed decisions about converting between measurement units for science, engineering, and commerce. This calculator is trusted by professionals and individuals alike because it follows the exact formulas validated by NIST, BIPM, and ISO

80000.

Accuracy Notes and Limitations

For legal or trade filings, verify conversions against official government or standards body references. The accuracy of any calculator is limited by the quality of the inputs provided. Double-check your units before entering values — unit errors are the most common source of incorrect results. For critical decisions, cross-reference with at least one additional source or professional consultation.

Frequently Used With

This calculator is often used alongside other conversion tools to build a complete analytical picture. Combining multiple related calculations provides stronger evidence for decisions than relying on any single metric. Browse the Conversion category to find complementary calculators for your specific use case.