About this degrees to radians converter
Degrees split a full turn into 360 parts, while radians measure an angle by the length of the arc it cuts on a circle of radius 1, so a full turn is 2π radians. Maths, physics, and programming functions such as Math.sin expect radians, which is why converting is so common. The rule is simple: multiply by π and divide by 180. This converter also keeps exact answers exact, writing 135° as 3π/4 instead of only 2.356194, and shows the angle on a unit circle with its quadrant and its sine and cosine values.
How to convert degrees to radians
- Enter the angle. Type an angle in degrees, including negatives and decimals, or press a common angle.
- Choose precision and format. Pick the number of Decimal places and whether to show a decimal, a fraction of π, or both.
- Press Convert to radians. Read the result, the unit circle, the quadrant, and the sine and cosine.
Frequently asked questions
How do I convert degrees to radians by hand?
Multiply the degrees by π and divide by 180. For 60°, 60 × π ÷ 180 = π/3, which is about 1.047198 radians. To go the other way, multiply radians by 180 and divide by π.
When is the answer shown as an exact fraction of π?
Whenever the angle divided by 180 reduces to a fraction with a denominator of 1000 or less, such as 22.5° = π/8. Otherwise the decimal multiple of π is shown with a ≈ sign.
How big is one radian?
One radian is about 57.2958°. It is the angle at which the arc length equals the radius, which is why a full circle of 360° equals 2π, about 6.283 radians.
Which quadrant is my angle in?
Angles are measured counter-clockwise from the positive x-axis. 0° to 90° is quadrant I, 90° to 180° is II, 180° to 270° is III, and 270° to 360° is IV. Angles of exactly 0°, 90°, 180°, or 270° lie on an axis.
What about angles above 360° or below 0°?
The radian value is converted exactly as entered, so 400° is 20π/9. For the circle and quadrant the angle is wrapped to between 0° and 360°, so 400° is drawn like 40°.