Our radians to degrees calculator is a powerful tool that converts angular measurements from radians to degrees using degrees = radians × (180/π) formula.
- 0 radians = 0 degrees
- π/6 radians = 30 degrees
- π/4 radians = 45 degrees
- π/3 radians = 60 degrees
- π/2 radians = 90 degrees
- π radians = 180 degrees
- 2π radians = 360 degrees
Radians to Degrees Calculator
| Radians converted to | Calculation | Degrees (rounded to 2 decimal places) |
|---|---|---|
| π/6 | (π/6) × (180/π) | 30.00° |
| π/4 | (π/4) × (180/π) | 45.00° |
| π/3 | (π/3) × (180/π) | 60.00° |
| π/2 | (π/2) × (180/π) | 90.00° |
| 2π/3 | (2π/3) × (180/π) | 120.00° |
| 5π/6 | (5π/6) × (180/π) | 150.00° |
| 3π/4 | (3π/4) × (180/π) | 135.00° |
| 7π/6 | (7π/6) × (180/π) | 210.00° |
| 5π/4 | (5π/4) × (180/π) | 225.00° |
| 4π/3 | (4π/3) × (180/π) | 240.00° |
| 3π/2 | (3π/2) × (180/π) | 270.00° |
| 5π/3 | (5π/3) × (180/π) | 300.00° |
| 7π/4 | (7π/4) × (180/π) | 315.00° |
| π | π × (180/π) | 180.00° |
| 5π/2 | (5π/2) × (180/π) | 450.00° |
| 3π | 3π × (180/π) | 540.00° |
| 7π/2 | (7π/2) × (180/π) | 630.00° |
| 2π | 2π × (180/π) | 360.00° |
Radians to Degrees Conversion Formula
The formula to convert radians to degrees is:
degrees = radians × (180/π)Where:
- π (pi) is approximately 3.14159
- 180/π is approximately 57.2958
π: Approximately equal to 3.14159, this is a mathematical constant that relates the circumference of a circle to its diameter.
- Convert π/2 radians to degrees: degrees = (π/2) × (180/π) = 90°
- Convert 1 radian to degrees: degrees = 1 × (180/π) ≈ 57.2958°
How do I Convert Radians to Degrees?
By using formula : Degrees = Radians × (180 / π)
- Identify the angle in radians: Ensure you have the correct radian measurement.
- Apply the conversion formula: Multiply the radian value by (180/π).
- Simplify the expression: If the result contains π, calculate its decimal approximation.
- Round if necessary: Depending on the required precision, round the result.
Let’s convert 2π/3 radians to degrees:
- Angle in radians: 2π/3
- Apply the formula: (2π/3) × (180/π)
- Simplify: 2 × 180 / 3 = 360 / 3
- Calculate: 120°
Therefore, 2π/3 radians is equal to 120 degrees.
How do you convert 1 radian to degrees round your answer to the nearest degree?
To convert 1 radian to degrees and round to the nearest degree:
- Apply the formula: 1 × (180/π) ≈ 57.2958°
- Round to the nearest degree: 57°
One radian is defined as the angle subtended at the center of a circle by an arc equal in length to the radius. This angle is constant regardless of the circle’s size.
When we multiply 1 radian by (180/π), we’re essentially asking: “How many degrees are in the angle that an arc equal to the radius would sweep out?”
The result, 57.2958°, tells us that a little more than 57° corresponds to 1 radian. When we round to the nearest degree, we get 57°.
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