Angle Converter
Convert between degrees, radians, gradians, and turns instantly — type once, see every unit update live.
Instant & live
Every unit updates as you type — no "Convert" button, no waiting.
4 units supported
Degrees, radians, gradians, and turns.
Private by design
Runs entirely in your browser. Nothing is ever uploaded or logged.
Convert Angles Online
CurePDF's angle converter instantly converts between degrees, radians, gradians, and turns — the four units most commonly used in math, physics, engineering, and computer graphics. Type a value once and every unit updates immediately, with no page reload.
How Angle Conversion Works
Every angle unit is a fixed ratio of a full circle, so converting between them is a straightforward multiplication:
Worked example: 180° × (π / 180) = π radians, approximately 3.14159 radians.
Popular Angle Conversions
- Degrees to radians — multiply by π/180. 90° = 1.5708 rad.
- Radians to degrees — multiply by 180/π. 1 rad ≈ 57.2958°.
- Degrees to turns — divide by 360. 90° = 0.25 turn.
- Radians to gradians — multiply by 200/π. π rad = 200 gradians.
Who Uses an Angle Converter?
Trigonometry students
Check work between degree-based textbook problems and radian-based answers.
Programmers
Most languages' math libraries (Math.sin, Math.cos, etc.) expect radians, not degrees.
Engineers & architects
Convert between CAD software units and design specifications.
Game developers
Rotation and physics math is almost always done in radians internally.
Surveyors
Gradians (also called gons) are still used in some land-surveying traditions.
Robotics & CNC
Turns are a convenient way to express full-rotation counts for motors and spindles.
Common Mistakes When Converting Angles
- Mixing degree and radian mode. Most programming languages' trig functions expect radians by default — passing a degree value directly is one of the most common angle-related bugs.
- Assuming a "turn" always means 360°. That's correct by definition, but it's easy to forget when a tool or API instead expects a fractional turn (e.g. 0.5 for a half turn).
- Confusing gradians with degrees. Both start near similar small numbers for small angles, but a gradian is only 0.9 of a degree (400 gradians per circle, not 360).
Frequently Asked Questions
How do I convert degrees to radians?
Multiply the degree value by pi / 180. For example, 90 degrees x (pi / 180) = 1.5708 radians.
How many radians are in a full circle?
A full circle is 2 x pi radians (about 6.2832 radians), equal to 360 degrees or 1 full turn.
What is a gradian?
A gradian (also called a gon) divides a right angle into 100 units instead of 90, so a full circle is 400 gradians.
Is this angle converter accurate?
Yes -- every conversion uses the exact mathematical relationship between degrees, radians, gradians, and turns, with no rounding until the final displayed result.