Conversion result
Calculation steps
Angle converter
Formula used
Radians = Degrees × π ÷ 180
Radians measure an angle using the radius of a circle. Degrees divide one full turn into 360 equal parts. Multiplying by 180 divided by π completes conversion accurately.
How to use this calculator
- Enter a decimal value or a safe π expression.
- Select the required conversion mode and decimal precision.
- Choose Calculate to view results and detailed steps.
- Copy, print, share, or download the completed result.
Common radians and degrees
| Radians | Degrees | Revolutions |
|---|---|---|
| 0 | 0° | 0 |
| π/6 | 30° | 1/12 |
| π/4 | 45° | 1/8 |
| π/3 | 60° | 1/6 |
| π/2 | 90° | 1/4 |
| π | 180° | 1/2 |
| 3π/2 | 270° | 3/4 |
| 2π | 360° | 1 |
Recent calculation history
| Input | Mode | Result | Time |
|---|---|---|---|
| No saved calculations yet. | |||
Radians and degrees explained
Degrees are familiar in navigation, construction, and everyday geometry. Radians connect angles directly to circle radius and arc length. Calculus and physics often use radians for simpler formulas.
One complete revolution equals 360 degrees or 2π radians. A straight angle equals 180 degrees or π radians. These identities make reliable conversion possible across many disciplines.
Frequently asked questions
How do I convert radians to degrees?
Multiply the radian value by 180, then divide by π. The calculator performs this operation while preserving your selected precision. It also displays supporting units and calculation steps clearly.
Why is π radians equal to 180 degrees?
A full circle measures 2π radians and 360 degrees. Dividing both values by two gives their half-turn relationship. Therefore π radians always equals exactly 180 degrees.
How many degrees are in one radian?
One radian equals approximately 57.295779513 degrees. The decimal continues because π is an irrational number. Choose higher precision when detailed scientific work requires accuracy.
How do I enter π?
Enter pi, π, pi/2, or expressions like 3pi/4. Multiplication signs may be included or omitted near pi. The parser rejects unsafe characters and unsupported expression syntax.
Can radians be negative?
Yes, negative radians represent rotation in the opposite direction. The resulting degree value also remains negative before normalization. Coterminal outputs show useful equivalent angles within standard ranges.
What is 2π in degrees?
Two π radians equals exactly 360 degrees. This value represents one complete rotation around a circle. It also equals one revolution or 400 gradians.
How are decimal radians converted?
Decimal radians use the same conversion formula as π expressions. For example, one radian becomes about 57.2958 degrees. Precision controls determine how many decimal places appear.
What is the difference between radians and degrees?
Degrees split a circle into 360 equal angular units. Radians measure angles through the ratio of arc length. Both describe identical angles using different numerical scales.
Why are radians used in mathematics?
Radians simplify derivatives, integrals, wave equations, and circular motion. Many important formulas assume angles are measured in radians. This convention removes unnecessary conversion factors from calculations.
How are coterminal angles calculated?
Coterminal angles differ by whole multiples of 360 degrees. Normalization repeatedly adds or subtracts one complete revolution. The calculator provides two commonly used normalized ranges.
Can degrees convert back to radians?
Yes, select Degrees to radians from the conversion menu. The calculator multiplies degrees by π divided by 180. Related angular units remain visible for convenient comparison.