Radians to Degrees Converter
Type a decimal or π fraction in either field. The exact π form, decimal value, turns, and angle position update together.
- Radians
- Degrees
- Exact π form
- Turns
- 0°–360° position
Convert π fractions without typing a decimal first
Enter π/6, 3π/4, -π/2, or the same expressions with pi. The converter preserves a short exact π form when the angle has one, while also showing the decimal radian value.
Radians to degrees formula
Multiply radians by 180/π. The relationship comes from one half-turn: π radians equals 180 degrees. A decimal input such as 1 rad therefore becomes approximately 57.29578°.
Degrees to radians formula
Multiply degrees by π/180. For a common angle, simplify the fraction: 135° × π/180 = 3π/4 radians. The two editable fields let you run this direction without opening a separate page.
Common radians and degrees chart
| Radians | Degrees |
|---|---|
| 0 | 0° |
| π/6 | 30° |
| π/4 | 45° |
| π/3 | 60° |
| π/2 | 90° |
| 2π/3 | 120° |
| 3π/4 | 135° |
| 5π/6 | 150° |
| π | 180° |
| 3π/2 | 270° |
| 2π | 360° |
Use the circle as a position check
The dial removes complete turns only for the preview. For example, 450° and 90° end at the same positive-y-axis position, but the result keeps the original 450° value and its 1.25 turns. The quadrant label uses standard-position angles.
Frequently asked questions
How do you convert radians to degrees?
Multiply radians by 180/π. For example, π/6 × 180/π = 30°, while 1 radian is approximately 57.2958°.
How do you convert degrees to radians?
Multiply degrees by π/180. For example, 45° × π/180 simplifies to π/4 radians.
What is π radians in degrees?
π radians equals exactly 180°. A full turn is 2π radians or 360°.
Can I enter a fraction of pi?
Yes. Enter forms such as π/6, 3π/4, -π/2, 2π, or type pi instead of the π character.
Why does the converter show both an exact π form and a decimal?
Common angles can be written exactly as a fraction of π, while a decimal radian value is an approximation. Both views are useful for checking homework, code, and calculator settings.
What does the 0°–360° position mean?
It is the coterminal angle after whole turns are removed. It shows where positive, negative, or multi-turn angles end on a standard-position circle without changing the original angle value.