How to convert degrees to radians
One full turn is 360° or 2π radians, so rad = deg × π ÷ 180. For example, 180° = 180 × π ÷ 180 = π ≈ 3.1416 radians, and 90° = π ÷ 2 ≈ 1.5708 radians.
The factor π ÷ 180 is just the two descriptions of a half turn set equal to each other: 180° and π radians are the same angle, so dividing gives the conversion ratio. Because it is a simple multiplication, converting is exact in symbolic form — 45° is precisely π ÷ 4 — and only becomes approximate when written as a decimal. Radians exist precisely so that arc length is radius times angle, as the arc length calculator shows.
- 30° = π ÷ 6 ≈ 0.5236 rad
- 45° = π ÷ 4 ≈ 0.7854 rad
- 60° = π ÷ 3 ≈ 1.0472 rad
How to use this calculator
Enter the angle in degrees and read the equivalent in radians, rounded to four decimals. To convert the other way, use the radians to degrees calculator.
Negative angles work exactly the same way and simply give negative radians, indicating a clockwise turn. If your angle is written in degrees, minutes and seconds, convert it to a decimal number of degrees first — divide the minutes by 60 and the seconds by 3600 and add them on.
Why radians matter
Radians are the natural unit for calculus and trig functions like sine, where one radian is the angle that cuts an arc equal to the radius. Most programming languages expect radians, not degrees.
Feeding degrees into a function that expects radians is one of the most common silent bugs in spreadsheets and code: nothing errors out, the answer is just wrong.
Frequently asked questions
- What is 180 degrees in radians?
- 180° equals π radians, approximately 3.1416 radians.
- What is the formula to convert degrees to radians?
- Multiply the degrees by π and divide by 180: rad = deg × π ÷ 180.
- What is 90 degrees in radians?
- 90° equals π ÷ 2 radians, approximately 1.5708 radians.
- How many radians are in a full circle?
- A full circle is 360°, which equals 2π radians, about 6.2832 radians.
- Do radians have a unit?
- Radians are dimensionless — they are a ratio of arc length to radius, so the length units cancel. That is why the word radian can be dropped in formulas such as arc length = r × θ, and why spreadsheet and programming functions accept a bare number.