Radians to Degrees Converter
Enter an angle in radians and this tool returns the exact value in degrees, with a matching π fraction shown whenever the input lands on a clean value.
Radians to degrees formula
degrees = radians × (180 ÷ π)
This formula is the mirror image of the degrees-to-radians conversion, and the two are inverses of each other: apply one, then the other, and you land back on the original number. That relationship is a handy way to check a conversion by hand. Convert a result back the other direction and confirm it matches where you started.
Radians relate to degrees through the identity π radians = 180°. Multiplying a radian value by 180 ÷ π rescales it into degrees using the same ratio, just inverted from the degrees-to-radians formula. The two conversions undo each other exactly.
Radians describe an angle as the ratio of arc length to radius, which is why they show up naturally in calculus and physics. Degrees are more familiar for everyday geometry. Reference angle rules work identically in both units, π ↔ 180°, 2π ↔ 360°, so converting first, if it makes the numbers easier, never changes the answer.
Converting to degrees is often about intuition rather than necessity. Most people have a mental picture of what 45° or 120° looks like from years of working with protractors and clocks, but "1.309 radians" doesn't carry the same instant sense of direction. Converting a radian answer back to degrees is frequently the last step in a problem. The calculation itself might run entirely in radians, but the final answer gets translated into degrees so it's easier to communicate, sketch, or double-check against a mental image of the coordinate plane.
The conversion constant 180 ÷ π ≈ 57.2958 shows up so often in physics and engineering that it's worth knowing by name. It's sometimes called the "degrees per radian" factor. Multiplying any radian measurement by this constant gives degrees directly, without needing to think about π fractions at all. This is especially useful for irrational or messy radian values, like the ones that come out of solving a differential equation or measuring an angle experimentally, where the result won't land on a clean π fraction to begin with.
Whichever direction the conversion goes, the quadrant and reference angle of an angle never change. Only the number describing it changes. An angle in Quadrant III stays in Quadrant III whether it's labeled 4π/3 or 240°, and its reference angle stays π/3 or 60° either way.
A useful sanity check when converting is to keep a few landmark values in mind: π/6 is a small angle (30°), π/2 is a right angle (90°), π is a straight line (180°), and 2π is a full turn (360°). Any radian value can be roughly located by comparing it to these four landmarks before doing the exact multiplication. A value close to 1.57 should convert to something near 90°, and a result far from that after conversion is a signal to double-check the arithmetic. This kind of estimation catches most calculation mistakes before they make it into a final answer.
Step-by-step conversion
Worked example: π/3
- Start with the radian value: π/3
- Multiply by 180 ÷ π: (π/3) × (180/π) = 180/3
- Simplify: 180/3 = 60
π/3 radians = 60°
Worked example: 2.5 radians
- Start with the decimal value: 2.5
- Multiply by 180 ÷ π: 2.5 × 57.2958…
- Compute: ≈ 143.24°
2.5 radians ≈ 143.24°
Not every radian value converts to a whole number of degrees. Values like 2.5 above, or any radian measurement taken from a real-world measurement rather than a textbook problem, typically produce a decimal degree result. That's expected. The formula still applies exactly the same way, it's only the tidiness of the final answer that changes.
This matters most in applied fields: engineering tolerances, sensor readings, robotics, where angles are rarely designed to land on round numbers. A sensor might report an orientation of 1.309 radians rather than a tidy π/3, and converting that directly to roughly 75° is often more useful for a human reading a dashboard than leaving the value in radians at all.
The same logic applies to reference angles once a radian value is converted. A reported angle of 3.86 radians converts to about 221°, which falls in Quadrant III with a reference angle near 41°, numbers that are much easier to sanity-check on a mental picture of the coordinate plane than the original decimal radian value ever was.
Common radian-to-degree conversions
| 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° |
| 7π/6 | 210° |
| 5π/4 | 225° |
| 4π/3 | 240° |
| 3π/2 | 270° |
| 5π/3 | 300° |
| 7π/4 | 315° |
| 11π/6 | 330° |
| 2π | 360° |
Frequently Asked Questions
How do you convert radians to degrees?
Multiply the radian value by 180 ÷ π. For example, (π/3) × (180 ÷ π) = 60°. This formula works for any radian value, including negative angles and multiples of π larger than 2π, since it is a fixed proportional scaling factor.
What is π/2 in degrees?
π/2 radians equals 90°, since (π/2) × (180 ÷ π) = 90°. This is one of the four quadrantal angles, along with 0°, 180°, and 270°, whose terminal side lies exactly on an axis rather than inside an open quadrant.
What is π/3 in degrees?
π/3 radians equals 60°, since (π/3) × (180 ÷ π) = 60°. This is one of the special angles, along with π/6 and π/4, whose exact sine, cosine, and tangent values are worth memorizing directly in both units of measure.
What is 2π in degrees?
2π radians equals 360°, one full turn around the circle. Any radian value larger than 2π can be reduced first by subtracting multiples of 2π, the same way multiples of 360° are subtracted when working with degrees instead of radians.
What is π/6 in degrees?
π/6 radians equals 30°, since (π/6) × (180 ÷ π) = 30°. Along with π/4 and π/3, this is one of the three most common reference angles that appear repeatedly across all four quadrants in most trigonometry courses and exams.