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.
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📐 Formula
💡 Practical Example
A right angle of $\frac{\pi}{2}$ radians ($1.5708\text{ rad}$) converts to exactly $90.000^\circ$ on a protractor (or $100.0\text{ gradians}$).
📖 About 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 Radian (rad): (180) / (π)^ ≈ 57.2957795^ = 57^ 17' 44.81'' = 63.662 grad = 0.159155 rev
- 1^ (Degree): (π) / (180) rad ≈ 0.01745329 rad = 1.111 grad = (1) / (360) rev
Primary Unit Circle Angle Equivalents
- (π) / (6) rad: 30.0^ = 33.33 grad = (1) / (12) rev
- (π) / (4) rad: 45.0^ = 50.00 grad = (1) / (8) rev
- (π) / (3) rad: 60.0^ = 66.67 grad = (1) / (6) rev
- (π) / (2) rad: 90.0^ = 100.00 grad = (1) / (4) rev
- π rad: 180.0^ = 200.00 grad = (1) / (2) rev
- (3π) / (2) rad: 270.0^ = 300.00 grad = (3) / (4) rev
- 2π rad: 360.0^ = 400.00 grad = 1.00 rev
Equations
- Degrees = Radians × (180) / (π)
- Radians = Degrees × (π) / (180)
How to Use This Calculator
Enter your Angle Value to Convert (e.g. 3.14159), Unit Circle & Trigonometric Benchmark — choose from Custom Angle Value, 1.000 rad (57.296° / 1 Radian Exact), π/6 rad (0.524 rad / 30.0° / 1/12 Turn), and Conversion Direction — choose from Radians to Degrees (rad → deg / multiply by 180/π), Degrees to Radians (deg → rad / multiply by π/180). Results update instantly as you type — adjust any value to compare scenarios.
The Formula
Conversion factors (to SI base unit or reference unit):
rad: 1.0
deg: 30.0
Worked Example
A right angle of (π) / (2) radians (1.5708 rad) converts to exactly 90.000^ on a protractor (or 100.0 gradians).
Understanding Your Result
Unit conversion precision: round to the same number of significant figures as your original measurement. Converting 6 feet to meters gives 1.8288 m — but if your measurement was approximate (±1 inch), expressing more than 2 decimal places is false precision. For international trade and technical specifications, SI units (meters, kilograms, liters) are the standard. US customary units (feet, pounds, gallons) differ from Imperial UK units: 1 US gallon = 3.785 L vs. 1 UK gallon = 4.546 L.
💡 Methodological Standards & Calculation Accuracy
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- Ensure input values are entered in consistent units matching the selector options to guarantee accurate outputs.
- Periodic recalibration is recommended whenever baseline assumptions, operating parameters, or external conditions change.
Results are for informational and educational purposes only. Always verify critical decisions with a qualified professional.