Degrees to Radians Converter
Convert degrees to radians instantly — radians = degrees × π/180. Shows the π form too: 90° = π/2 ≈ 1.5708 rad. Works both ways.
About the Degrees to Radians Converter
This free degrees to radians converter multiplies by π/180, showing both the decimal value and the answer as a multiple of π — so 90° displays as 1.570796 rad and π/2. Edit either field to convert in both directions.
Radians are the natural angle unit in mathematics: trigonometric functions in calculus, and in every major programming language (Math.sin in JavaScript, math.sin in Python, sine functions in C and Excel's SIN), expect radians, not degrees. Passing 90 instead of π/2 is one of the most common trigonometry bugs. Students converting for calculus homework, and developers working with rotation, game physics and GPS math, use this conversion daily.
The reference table lists the standard angles — 30°, 45°, 60°, 90°, 180°, 360° — with their radian values.
How to Use the Degrees to Radians Converter
- 1Enter an angle in degrees — radians appear instantly, with the π form below.
- 2Or type radians to convert back to degrees.
- 3Copy the result, or use the table of standard angles.
Frequently Asked Questions
How do I convert degrees to radians?
Multiply degrees by π/180 (approximately 0.0174533). So 45° × π/180 = π/4 ≈ 0.7854 rad, 90° = π/2 ≈ 1.5708 rad, and 180° = π ≈ 3.14159 rad.
What is 90 degrees in radians?
90° equals π/2 radians, approximately 1.570796. Other quarter-circle values: 180° = π ≈ 3.141593, 270° = 3π/2 ≈ 4.712389, and a full 360° = 2π ≈ 6.283185 radians.
What is 30, 45 and 60 degrees in radians?
30° = π/6 ≈ 0.5236 rad, 45° = π/4 ≈ 0.7854 rad, and 60° = π/3 ≈ 1.0472 rad. These three angles plus 90° cover most trigonometry problems and unit-circle exercises.
Why do programming languages use radians?
Because calculus identities like d/dx sin(x) = cos(x) only hold when x is in radians, making them the mathematically natural unit. JavaScript, Python, C, Java and Excel all expect radians — convert with degrees × π/180 first, or your sin(90) will return 0.894 instead of 1.
How many degrees is 1 radian?
1 radian equals 180/π ≈ 57.2958 degrees. A radian is the angle subtended when the arc length equals the radius, and a full circle contains exactly 2π ≈ 6.2832 radians.