You have a trigonometry exam or you are coding an animation and need to turn 135° into radians, or know what angle 5π/6 is. The sine and cosine functions in almost every programming language expect radians, not degrees, and if you get it wrong the drawing rotates where it should not.
How to use Degrees to Radians step by step
1. Choose the direction
"Degrees → radians" or "Radians → degrees".
2. Type the angle
In radians it accepts decimals (1.5708) and π fractions like π/2, 3pi/4 or 2π.
3. Read and copy
You get the radians as a decimal, the exact π form when the degrees are whole, and the degrees.
The Step Count: Traditional Friction vs. KorexTools
Converting degrees to radians by hand
- Multiply the degrees by π.
- Divide by 180.
- Simplify the fraction by finding the greatest common divisor.
- Convert to a decimal if required.
With KorexTools Degrees to Radians
- Type the angle.
- Read the π form and the decimal.
- Copy the value you need.
Degrees to radians: the formula and why the answer is given in π
A full circle is 360 degrees or 2π radians, so 180° equals π. That gives the formula: radians = degrees × π / 180, and to go back, degrees = radians × 180 / π. One radian is about 57.2958°, the angle whose arc is as long as the radius.
In trigonometry and calculus the result is almost always left in terms of π (90° = π/2) because it is exact, while 1.5708 is an approximation. This tool shows both forms. And if your calculator gives odd results, check it is in the right mode, degrees or radians: it is the most frequent exam error.
What you get
- •Radians as a decimal with up to 10 significant digits.
- •Exact form in multiples of π when the degrees are a whole number (π/6, 3π/4, 2π).
- •Reverse conversion that accepts π/2, 3pi/4, 2π or decimals.
- •A table of 13 common angles, from 0° to 360°.
Most used angles
| Degrees | Radians (exact) | Radians (decimal) |
|---|---|---|
| 30° | π/6 | 0.5236 |
| 45° | π/4 | 0.7854 |
| 90° | π/2 | 1.5708 |
| 180° | π | 3.1416 |
Common Mistakes and How to Avoid Them
- ⚠️Multiplying by 180/π when you needed π/180 (or the reverse).
- ⚠️Using 3.14 as π in calculations that need precision.
Frequently Asked Questions
What is the degrees to radians formula?
Radians = degrees × π / 180. For example, 60° × π / 180 = π/3 ≈ 1.0472.
How many radians is 90 degrees?
π/2, which is about 1.5708 radians.
How do I type π in the tool?
You can copy the π symbol or type "pi". π/2, 3pi/4, 2π or even a decimal like 1.5708 all work.
Why does my calculator give a different value for sin(90)?
Because it is in radian mode: sin(90 rad) ≈ 0.894. In degree mode it gives 1. Switch the mode or convert the angle first.
What I would do if I were in your shoes
«When we code rotations we store angles in radians and convert to degrees only to display them. That way we never mix units inside the calculations.» — DataKorex Engineering Team