Radians to Degrees Converter (rad to °)
Convert radians to degrees (rad to °). See exact degree values, π fractions, and sin/cos. Essential for interpreting programming output, physics calculations, and engineering.
ANGLE IN DEGREES
90.0002°
EXACT
π/2 = 90°
TURNS
0.2500
SIN
1.000000
COS
-0.000004
Radians to Degrees — Key Values
| Radians | Exact (π) | Degrees | sin | cos |
|---|---|---|---|---|
| 0.0000 | 0 | 0.00° | 0.0000 | 1.0000 |
| 0.5236 | π/6 | 30.00° | 0.5000 | 0.8660 |
| 0.7854 | π/4 | 45.00° | 0.7071 | 0.7071 |
| 1.0472 | π/3 | 60.00° | 0.8660 | 0.5000 |
| 1.5708 | π/2 | 90.00° | 1.0000 | -0.0000 |
| 2.0944 | 2π/3 | 120.00° | 0.8660 | -0.5000 |
| 2.3562 | 3π/4 | 135.00° | 0.7071 | -0.7071 |
| 3.1416 | π | 180.00° | -0.0000 | -1.0000 |
| 4.7124 | 3π/2 | 270.00° | -1.0000 | 0.0000 |
| 6.2832 | 2π | 360.00° | 0.0000 | 1.0000 |
How to Convert Radians to Degrees
Multiply by 180/π (approximately 57.2958):
Example: π/2 rad (right angle)
= 1.5708 × 57.2958 = 90°
Example: π/4 rad (diagonal)
= 0.7854 × 57.2958 = 45°
Example: 1 radian
= 1 × 57.2958 = 57.2958°
Why 180/π? A full circle = 2π radians = 360°. So 1 radian = 360/(2π) = 180/π ≈ 57.2958°. This is the exact inverse of the degrees-to-radians formula (×π/180).
Key Radian Values in Degrees
| Radians | Exact (π) | Degrees | sin | cos | Where You See It |
|---|---|---|---|---|---|
| 0.0000 | 0 | 0° | 0 | 1 | Starting angle |
| 0.5236 | π/6 | 30° | 0.5 | 0.866 | Special angle |
| 0.7854 | π/4 | 45° | 0.707 | 0.707 | Diagonal, atan2(1,1) |
| 1.0472 | π/3 | 60° | 0.866 | 0.5 | Hexagon angle |
| 1.5708 | π/2 | 90° | 1 | 0 | Right angle, "up" |
| 2.0944 | 2π/3 | 120° | 0.866 | −0.5 | Triangle vertex |
| 3.1416 | π | 180° | 0 | −1 | Straight line, "behind" |
| 4.7124 | 3π/2 | 270° | −1 | 0 | "Down" direction |
| 6.2832 | 2π | 360° | 0 | 1 | Full rotation |
| 1.0000 | — | 57.30° | 0.841 | 0.540 | 1 radian (radius arc) |
Common Radian Values from Programming
| Code Output | Radians | Degrees | Meaning |
|---|---|---|---|
| Math.atan2(1, 0) | 1.5708 | 90° | Pointing straight up |
| Math.atan2(0, -1) | 3.1416 | 180° | Pointing left |
| Math.atan2(-1, 0) | −1.5708 | −90° | Pointing down |
| Math.atan2(1, 1) | 0.7854 | 45° | Diagonal upper-right |
| Math.PI | 3.14159 | 180° | Half rotation |
| Math.PI * 2 | 6.28318 | 360° | Full rotation |
| Math.asin(0.5) | 0.5236 | 30° | Arc sine of 0.5 |
| Math.acos(0) | 1.5708 | 90° | Arc cosine of 0 |
Every trig function in JavaScript, Python, C++, Java, and C# returns radians. To display angles to users, you must convert to degrees: degrees = radians * 180 / Math.PI.
Interpreting Radians in Real-World contexts
| Context | Radian Value | In Degrees | What It Means |
|---|---|---|---|
| Game dev: sprite rotation | 0 to 2π | 0° to 360° | Full sprite rotation |
| Robotics: servo angle | 0 to π | 0° to 180° | Standard servo range |
| CSS transform: rotate() | 1.5708rad | 90° | Quarter turn clockwise |
| Physics: angular velocity | rad/s | °/s × π/180 | Rotation speed |
| Navigation: heading | 0 to 2π | 0° to 360° | Compass bearing |
What Is a Radian?
A radian is the angle where the arc length equals the radius. One full circle = 2π ≈ 6.2832 radians. Radians are the SI angle unit and are used by all programming languages for trig functions. The value 1 radian ≈ 57.3° — not an intuitive number, which is why developers often convert to degrees for display.
What Is a Degree?
A degree (°) is 1/360th of a full rotation. Degrees are intuitive for humans: 90° = right angle, 180° = half turn, 360° = full circle. In the US, degrees are the standard for construction, navigation, weather, and everyday use. Radians are only used in math, physics, and programming.