Radians to Degrees Converter
Convert radians to degrees (rad to °), including π fractions
1 radian = 180/π degrees ≈ 57.29578°. To convert radians to degrees, multiply by 180/π, so π/4 rad = 45° and 2 rad = 114.59°.
How to convert radians to degrees
Because a full circle is both 2π radians and 360°, half a circle gives the key identity π rad = 180°. Divide both sides by π and one radian is 180/π degrees, about 57.29578°. So to turn any radian value into degrees, multiply it by 180 and divide by π. The degrees to radians converter runs the reverse with π/180, and the angle converter adds gradians, turns and arcminutes.
How you apply it depends on how the angle is written. If it contains π, such as 5π/6, simply replace π with 180 and do the arithmetic: 5 × 180 ÷ 6 = 150°. No calculator needed. If it is a plain decimal, such as 0.8 rad, multiply by 57.29578 to get 45.8366°. The common slip is typing 5π/6 into a calculator as 5 × 3.14 ÷ 6 and then forgetting that the result, 2.617…, is still in radians.
Step by step
- Take the angle in radians.
- Multiply it by 180 and divide by π (or multiply by 57.29578).
- If the angle is written with π, just replace π with 180 and simplify.
See it on a scale
Worked examples
Radian values that often come out of formulas and code: half a radian, exactly one radian and 4 rad, which is more than half a turn.
0.5 rad × 57.29577951 = 28.64789 °
= 28.64789 °
1 rad × 57.29577951 = 57.29578 °
= 57.29578 °
4 rad × 57.29577951 = 229.18312 °
= 229.18312 °
Is π equal to 180 degrees?
π radians equals exactly 180°, but π on its own is just the number 3.14159…; the equality holds only when π is read as an angle in radians.
The link comes from the circle. Half a circle's circumference is π times the radius, so a half turn sweeps an arc of π radii, which is π radians, and a half turn is also 180°. Writing “π = 180°” is common shorthand in trigonometry classes, but what it really means is “π rad = 180°”.
The difference matters as soon as π appears outside an angle. In sin(π) the π is an angle, so the answer is 0, the sine of 180°. In the circle area formula A = πr², π is a pure number, and swapping in 180 would be nonsense. The reverse trap exists too: an angle of π degrees is only 3.14159°, which is 0.054831 rad.
Because the radian is defined by arc length (s = rθ), the arc comes out in whatever unit the radius uses, from millimeters to miles, and the length converter can translate it from there.
How do I convert radians to degrees on a calculator?
Multiply the radian value by 180 and divide by π using the π key, which works in any mode: 1.2 rad × 180 ÷ π = 68.7549°.
Two other routes save keystrokes:
- Let the calculator convert. In DEG mode, enter the value with a radian marker and the display shows degrees. On a TI-84 the marker (ʳ) sits in the ANGLE menu, so (π/4)ʳ returns 45; many Casio models put the same marker in a DRG menu.
- Redo inverse functions in DEG mode. If the radians came from sin⁻¹, cos⁻¹ or tan⁻¹, switch to DEG and repeat the calculation, and the answer arrives in degrees directly.
Check the mode indicator afterwards. A calculator left in RAD mode treats the next degree value you type as radians, a slip that quietly spoils every answer after it.
Radians to degrees conversion chart
Decimal radian values converted to degrees and rounded to four decimal places. For radian angles written with π, use the π chart below.
| Radians (rad) | Degrees (°) |
|---|---|
| 0.01 rad | 0.573 ° |
| 0.05 rad | 2.8648 ° |
| 0.1 rad | 5.7296 ° |
| 0.2 rad | 11.4592 ° |
| 0.25 rad | 14.3239 ° |
| 0.3 rad | 17.1887 ° |
| 0.4 rad | 22.9183 ° |
| 0.5 rad | 28.6479 ° |
| 0.6 rad | 34.3775 ° |
| 0.7 rad | 40.107 ° |
| 0.75 rad | 42.9718 ° |
| 0.8 rad | 45.8366 ° |
| 0.9 rad | 51.5662 ° |
| 1 rad | 57.2958 ° |
| 1.2 rad | 68.7549 ° |
| 1.25 rad | 71.6197 ° |
| 1.5 rad | 85.9437 ° |
| 1.75 rad | 100.2676 ° |
| 2 rad | 114.5916 ° |
| 2.5 rad | 143.2394 ° |
| 3 rad | 171.8873 ° |
| 3.5 rad | 200.5352 ° |
| 4 rad | 229.1831 ° |
| 4.5 rad | 257.831 ° |
| 5 rad | 286.4789 ° |
| 5.5 rad | 315.1268 ° |
| 6 rad | 343.7747 ° |
| 7 rad | 401.0705 ° |
| 8 rad | 458.3662 ° |
| 10 rad | 572.9578 ° |
Radians vs degrees: how do they compare?
A radian is a large angle, about 57.3°, while a degree is 1/360 of a turn. Which one you meet depends on whether the angle came from geometry and code or from a map, compass or protractor.
| Attribute | Radians | Degrees |
|---|---|---|
| Symbol | rad | ° |
| System | SI derived unit | Common |
| Defined as | 180/π ° (≈ 57.29578°) | 1/360 of a turn |
| One unit equals | 57.29578 ° | 0.017453293 rad |
| Calculator mode | RAD, shown as R or RAD | DEG, shown as D or DEG |
| Typical source | Inverse trig functions, physics formulas and code libraries | Protractors, compasses, maps and CAD input |
| Common angles as decimals | Irrational: π/6 = 0.5235988… | Whole numbers: 30° |
| Defined in | BIPM SI Brochure; ISO 80000-3 | BIPM SI Brochure, as a unit accepted for use with the SI |
4 key differences
- Common angles are whole numbers in degrees but irrational in radians, so a decimal radian value is almost always a rounded one.
- A radian cuts an arc as long as the radius, and just over 6.28 of them fill a circle, compared with 360 degrees.
- Inverse trigonometric functions in Excel, Python, Java and JavaScript return radians, so their output usually needs converting before it is shown to people.
- One degree is 17.4533 milliradians, while one milliradian is 0.0573°.
π radians to degrees chart
Angles written as fractions of π, as they appear in textbooks, with their decimal radian value and the exact angle in degrees.
| Radians (π form) | Radians (decimal) | Degrees |
|---|---|---|
| π/12 | 0.261799 | 15° |
| π/10 | 0.314159 | 18° |
| π/8 | 0.392699 | 22.5° |
| π/6 | 0.523599 | 30° |
| π/5 | 0.628319 | 36° |
| π/4 | 0.785398 | 45° |
| π/3 | 1.047198 | 60° |
| 2π/5 | 1.256637 | 72° |
| π/2 | 1.570796 | 90° |
| 2π/3 | 2.094395 | 120° |
| 3π/4 | 2.356194 | 135° |
| 5π/6 | 2.617994 | 150° |
| π | 3.141593 | 180° |
| 7π/6 | 3.665191 | 210° |
| 5π/4 | 3.926991 | 225° |
| 4π/3 | 4.18879 | 240° |
| 3π/2 | 4.712389 | 270° |
| 5π/3 | 5.235988 | 300° |
| 7π/4 | 5.497787 | 315° |
| 11π/6 | 5.759587 | 330° |
| 2π | 6.283185 | 360° |
| 4π | 12.566371 | 720° |
Reading angles from inverse trig functions and code
Inverse trigonometric functions return radians in nearly every programming language and spreadsheet, and on a calculator in RAD mode. That is where most people meet radians they need to turn into degrees.
- acos(0.5) returns 1.047198 rad, which is 60°.
- atan(1) returns 0.785398 rad, which is 45°.
- atan2(1, −1) returns 2.356194 rad, which is 135°.
- atan2(−1, −1) returns −2.356194 rad, which is −135°.
atan2 returns angles between −π and π, so results in degrees run from −180° to 180°. For a compass-style bearing between 0° and 360°, add 360 to any negative result: −135° becomes 225°. To convert, use DEGREES(x) in Excel or Google Sheets, math.degrees(x) in Python, Math.toDegrees(x) in Java, or x * 180 / Math.PI in JavaScript.
How big is one radian?
One radian is about 57.3°, or 57° 17′ 44.8″ in degrees, minutes and seconds. Picture a slice of a circle whose curved edge is exactly as long as the radius; that slice is one radian. Just over six of them (6.2832) make a full turn, which is why 2π appears whenever something goes all the way round.
Milliradians in optics and shooting
A milliradian (mrad or mil) is a thousandth of a radian, 0.0573°. Its appeal is simple geometry: at 100 m, 1 mrad covers 10 cm, and at 1,000 yards it covers 1 yard. Many riflescopes adjust in 0.1 mrad clicks. One mrad is about 3.438 minutes of angle (MOA), so do not mix the two scales. The NATO mil used for artillery is a different, rounded unit of 1/6,400 of a circle.
Angular speed: rad/s to degrees per second and rpm
Motors, wheels and gyroscopes are often specified in radians per second. Multiply by 180/π for degrees per second, or by 60/(2π) for revolutions per minute. For rpm and hertz, see the rpm to Hz converter.
| Angular speed (rad/s) | Degrees per second | Revolutions per minute |
|---|---|---|
| 0.1 rad/s | 5.73 °/s | 0.95 rpm |
| 0.5 rad/s | 28.65 °/s | 4.77 rpm |
| 1 rad/s | 57.30 °/s | 9.55 rpm |
| 2 rad/s | 114.59 °/s | 19.10 rpm |
| 5 rad/s | 286.48 °/s | 47.75 rpm |
| 10 rad/s | 572.96 °/s | 95.49 rpm |
| 50 rad/s | 2,864.79 °/s | 477.46 rpm |
| 100 rad/s | 5,729.58 °/s | 954.93 rpm |
| 377 rad/s | 21,600.51 °/s | 3,600.08 rpm |
| 1000 rad/s | 57,295.78 °/s | 9,549.30 rpm |
What are the most common radian conversion mistakes?
Most wrong answers come from a calculator left in the wrong angle mode, or from rounding π too early.
- Leaving the calculator in RAD mode. If sin⁻¹(0.5) shows 0.5236 instead of 30, the calculator is answering in radians. Convert, or switch to DEG mode.
- Rounding π to 3.14 too early. 180 ÷ 3.14 = 57.3248, not 57.2958. Over large angles the error grows: 100 rad comes out 2.91° too high.
- Forgetting to normalize. 7 rad is 401.07°, more than a full turn. Subtract 360° to get the equivalent direction, 41.07°.
- Mixing up rad and gradians. Some calculators label GRAD mode with a G that is easy to misread. The degrees to gradians converter explains that third unit.
Sources and further reading
The standards and references behind the numbers on this page. Links open in a new tab.
Standards and official sources
Radians to degrees FAQs
Short, exact answers to what people ask most.
What is 1 radian in degrees?
One radian is 180/π degrees, about 57.29578°. It is the angle at which the arc along a circle equals the circle's radius.
What is π/3 radians in degrees?
π/3 radians is exactly 60°. Replace π with 180 and divide by 3: 180 ÷ 3 = 60.
How many degrees is 2 radians?
2 radians is about 114.5916°. Multiply 2 by 180/π, which is roughly 57.2958.
How do I convert radians to degrees without a calculator?
If the angle is written with π, replace π with 180 and simplify, so 3π/4 becomes 3 × 180 ÷ 4 = 135°. For a decimal, multiply by about 57.3.
How many degrees is 2π radians?
2π radians is exactly 360°, one full turn. π radians is 180° and π/2 radians is 90°.
What is 0.5 radians in degrees?
0.5 radians is about 28.6479°. Multiply 0.5 by 180/π to get it.
How many degrees is 3 radians?
3 radians is about 171.8873°, a little less than a half turn.
What is π/6 radians in degrees?
π/6 radians is exactly 30°. Replace π with 180 and divide by 6.
What is 3π/2 radians in degrees?
3π/2 radians is exactly 270°, three quarters of a full turn.
How many degrees is 1.5 radians?
1.5 radians is about 85.9437°, just short of a right angle.
What is 0.1 radian in degrees?
0.1 radian is about 5.7296°.
Related conversions
Radian definition from the BIPM SI Brochure (9th edition) and ISO 80000-3; function behavior from the Python, Java, JavaScript (ECMAScript) and Microsoft Excel documentation; calculator menus from the Texas Instruments TI-84 Plus and Casio scientific calculator guides. Last updated . How we verify our numbers.