Convert degrees to radians and vice versa. Includes unit circle visual, trig values, and a 16-row reference table of common angles.
The degrees to radians calculator converts angle measurements between the two most common angular units. Enter an angle in degrees to get its radian equivalent (or reverse direction) along with turns, gradians, arcminutes, and trigonometric values.
Radians are the SI unit of angle — one radian is the angle subtended at the center of a circle by an arc equal in length to the radius. There are 2π radians in a full circle (360°), making 1 radian ≈ 57.2958°.
The interactive unit circle shows the angle's position, and the reference table lists all 16 standard angles (every 30° and 45° increment) with their exact trig values. Preset buttons cover the most commonly needed degree and radian values. This helps students and developers verify both numeric outputs and geometric intuition before applying angles in code or equations. It is also useful for checking homework steps, CAD geometry inputs, and graphics transformations that require strict unit consistency.
Programming languages, physics equations, and calculus all use radians. If you work with degrees and need to feed a value to sin() or cos(), you must convert first. This calculator also gives trig values and a visual confirmation so you can catch errors before they propagate into larger computations and project deliverables.
Radians = Degrees × π/180. Degrees = Radians × 180/π. Turns = Degrees/360. Gradians = Degrees × 10/9.
Result: 180° = π radians = 0.5 turns
180 × π/180 = π ≈ 3.141593. This is a half turn, where sin = 0 and cos = −1.
The most important conversions for trigonometry are multiples of 30° and 45°: 30° = π/6, 45° = π/4, 60° = π/3, 90° = π/2, 180° = π, 270° = 3π/2, 360° = 2π. These correspond to the "special angles" whose sine and cosine have exact algebraic values.
Every major language — C, Python, JavaScript, Java — uses radians for trigonometric functions. Convert before calling sin/cos/tan: `angle_rad = angle_deg * Math.PI / 180`. Forgetting this is one of the most common bugs in geometry code.
Gradians divide a right angle into 100 parts; used in surveying. Turns (revolutions) measure full rotations (1 turn = 360°). Milliradians (mrad) are used in military aiming — 1 mrad subtends ~1 m at 1 km.
Radians = Degrees × (π/180). Multiply the degree value by approximately 0.01745329. This keeps trigonometric function inputs consistent with most scientific libraries. It is the same conversion used in calculators and programming APIs. You can also write this as degrees times pi divided by 180.
1 radian = 180/π ≈ 57.2958°. It is the angle where the arc length equals the radius. This value is often rounded to 57.3° for quick estimates.
Radians simplify calculus and physics: d/dx sin(x) = cos(x) only works in radians. Programming functions like Math.sin() expect radians.
Degrees split a full rotation into 360 equal parts (historical from Babylonians). Radians are based on the ratio of arc length to radius — there are 2π radians in a full circle.
The formula works identically for negative values: −45° × π/180 = −π/4 radians. The negative sign simply indicates clockwise rotation in the standard convention.
Gradians (gon) divide a right angle into 100 units. Used in surveying and some European countries. 400 gradians = 360°.