Radians to Degrees Converter
Convert angles between radians and degrees instantly.
Convert between degrees and radians
What Is the Radians to Degrees Converter?
This converter converts angles between degrees and radians — the two most common units for measuring angles. Degrees divide a full rotation into 360 equal parts; radians measure angles by the arc length on a unit circle. Radians are the natural unit for calculus and most scientific formulas.
Formula
How to Use
Enter an angle in degrees to convert it to radians, or enter an angle in radians to convert it to degrees. Both fields are independent — type in either one and click the corresponding Convert button.
Example Calculation
Convert 270° to radians: 270 × (π/180) = 270π/180 = 3π/2 ≈ 4.71239 rad Convert 2 radians to degrees: 2 × (180/π) = 360/π ≈ 114.5916° Convert π/3 radians (≈1.0472) to degrees: (π/3) × (180/π) = 60°
Understanding Radians to Degrees Converter
Radians and degrees both measure rotation, but radians have a deep connection to the unit circle that makes them indispensable in mathematics. The arc length formula s = rθ and the area of a sector formula A = ½r²θ are elegantly simple only in radians.
In calculus, the chain rule for trigonometric derivatives requires radians: d/dx[sin(x)] = cos(x) works only when x is measured in radians. If x were in degrees, there would be an extra π/180 factor.
Programming languages like JavaScript, Python, and C++ use radians in their trigonometric functions. Forgetting to convert from degrees to radians is a very common programming bug.
Frequently Asked Questions
Why do we have two ways to measure angles?
Degrees (360° per revolution) come from ancient Babylonian astronomy and are intuitive for everyday use. Radians arise naturally in calculus — the derivative of sin(x) is cos(x) only when x is in radians.
What is a radian?
One radian is the angle subtended at the center of a circle by an arc equal in length to the radius. A full circle is 2π radians ≈ 6.2832 radians.
Which unit should I use?
Use degrees for navigation, construction, and everyday geometry. Use radians in calculus, physics formulas, complex numbers, and programming (JavaScript's Math.sin, Math.cos take radians).
How do I convert mentally?
A quick approximation: 1 radian ≈ 57.3°. For common angles, memorize: 30°=π/6, 45°=π/4, 60°=π/3, 90°=π/2, 180°=π, 360°=2π.
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