Degrees to Radians Converter
Convert an angle between degrees and radians, then read its quadrant, reference angle, and unit-circle coordinates (cos θ, sin θ) at a glance.
Conversion & unit-circle position
Degrees, radians, and the unit circle
Degrees split a full turn into 360 equal parts; radians measure the same turn by arc length on a unit circle, where a full turn is 2π. The conversion is a single multiplication — by π / 180 one way, and by 180 / π the other — but seeing the angle placed on the circle makes the trig values click.
This converter also normalises the angle into one turn, names its quadrant, and gives the reference angle, which together tell you the sign and size of sine, cosine, and tangent without memorising every case.
Frequently Asked Questions
How do I convert degrees to radians?
Multiply the degree measure by π / 180. A full circle is 360°, which equals 2π radians, so 180° = π radians. For example, 90° × π / 180 = π / 2 ≈ 1.5708 radians. To go the other way, multiply radians by 180 / π.
What does normalising the angle mean?
Angles that are negative or larger than a full turn point in the same direction as an angle between 0° and 360°. Normalising wraps the value into that single-turn range, which makes it easy to read off the quadrant, the reference angle, and the trig values. For instance, 450° normalises to 90°, and −90° normalises to 270°.
What is a reference angle?
The reference angle is the acute angle between the terminal side of your angle and the horizontal axis. It is always between 0° and 90°, and it lets you find the trig values of any angle from the values of a first-quadrant angle, just adjusting the sign for the quadrant.
How does this relate to the unit circle?
On a circle of radius 1 centred at the origin, the point where your angle's terminal side meets the circle has coordinates (cos θ, sin θ). This tool reports those coordinates, so you can read cosine as the x-value and sine as the y-value directly, along with the tangent where it is defined.
Educational tool only. Trig values are rounded for display; use full precision for coursework or applications that depend on it.