Radians to Degrees Converter
Convert radians to degrees instantly. Essential for mathematics, physics, engineering, and programming.
Last updated: May 2026
Enter a value to see the conversion instantly.
How to convert
Enter a radian value in the "From" field to instantly see the equivalent in degrees. The conversion uses the formula: degrees = radians × (180 / π). You can use the preset buttons (0, π/4, π/2, π, 2π) to quickly test common angles, or swap the units to convert degrees back to radians.
Common reference values
| Radians | Degrees | Context |
|---|---|---|
| 0 | 0° | Starting angle |
| π/6 ≈ 0.5236 | 30° | One-twelfth of a full circle |
| π/4 ≈ 0.7854 | 45° | One-eighth of a full circle |
| π/3 ≈ 1.0472 | 60° | Equilateral triangle angle |
| π/2 ≈ 1.5708 | 90° | Right angle (quarter circle) |
| π ≈ 3.1416 | 180° | Straight angle (half circle) |
| 2π ≈ 6.2832 | 360° | Full circle (complete rotation) |
Understanding Radians and Degrees
Radians and degrees are two different ways to measure angles. Degrees divide a full circle into 360 equal parts. Radians relate the angle to the arc length on a unit circle—a full circle is 2π radians. The conversion relationship is: 360° = 2π radians, or equivalently, 180° = π radians.
When to Use Each System
Radians are used in: Calculus and higher mathematics, physics (circular motion, oscillation), engineering (rotational systems), and programming (trigonometric functions use radians by default in most languages).
Degrees are preferred for: Navigation and surveying (compass bearings), everyday angle descriptions, architecture and construction, astronomy, and any context where whole or simple fractional angles make sense.
Practical Context
- 0.785 rad / 45°: Optimal angle for projectile range, typical camera tilt
- 1.571 rad / 90°: Right angle, perpendicular lines, quarter turn
- 3.142 rad / 180°: Straight angle, complete reversal, π radians
- 6.283 rad / 360°: Full rotation, one complete circle, 2π radians
Frequently Asked Questions
Why do I need to convert radians to degrees?
You need to convert radians to degrees when you want a human-readable angle (like compass bearings or architectural plans) from a mathematical or programming calculation. Most programming languages and scientific functions use radians internally, so converting to degrees makes results easier to understand in everyday contexts.
What does π (pi) mean in radians?
π (pi) is approximately 3.14159 and represents the ratio of a circle's circumference to its diameter. One radian is defined as the angle subtended by an arc equal to the radius of the circle. Since a circle's circumference is 2πr, a full circle is 2π radians. Therefore, π radians equals exactly 180°.
Can I convert decimal radians?
Yes. The converter handles any decimal value. For example, 0.5 radians ≈ 28.65°, and 2.5 radians ≈ 143.24°. Decimal radians are common in physics, engineering, and programming calculations.
Why does my programming language use radians?
Most programming languages use radians for trigonometric functions (sin, cos, tan) because radians have elegant mathematical properties. The derivatives of sine and cosine are simpler in radians, and many algorithms are derived using radian-based math. For practical use, it's often necessary to convert to degrees for display or user interface purposes.
What's the relationship between arc length and radians?
In a unit circle (radius = 1), the radian measure of an angle equals the arc length of the angle. For example, an angle of 1 radian subtends an arc of length 1 unit. For a circle with radius r, the arc length equals the radian angle multiplied by r. This direct geometric relationship is why radians are preferred in mathematics and physics.