Degree to Radian Converter

What Are Degrees and Radians?

Degrees divide a full circle into 360 equal parts, while radians measure angles based on the relationship between arc length and radius. A radian is the angle subtended by an arc equal in length to the radius of the circle. One full circle equals 2π radians (approximately 6.28318 rad).

Conversion Formula

The fundamental relationship between degrees and radians is:

Example: 90° to Radians

radians = 90 × π/180 = π/2 ≈ 1.5708 rad

Common Angle Conversions

• 30° = π/6 ≈ 0.5236 rad
• 45° = π/4 ≈ 0.7854 rad
• 60° = π/3 ≈ 1.0472 rad
• 90° = π/2 ≈ 1.5708 rad
• 180° = π ≈ 3.1416 rad
• 270° = 3π/2 ≈ 4.7124 rad
• 360° = 2π ≈ 6.2832 rad

Why Use Radians?

• Calculus: The derivative of sin(x) equals cos(x) only when x is in radians.
• Arc Length: s = rθ works directly with radians.
• Angular Velocity: ω = θ/t works naturally with radian measure.
• Computer Graphics: Most programming languages and graphics libraries use radians for rotation functions.

How to Use This Converter

1. Enter an angle in degrees, or click a common angle button for quick access.
2. Select decimal precision (2-8 decimal places).
3. Choose output format: Decimal, Pi Fraction, or Both.
4. View the converted radian value and step-by-step calculation.

Also check: Radian to Degree Converter, Trigonometric Functions Calculator, Unit Converter.