To convert radians to degrees, multiply by 180/π: a full turn is 2π radians or 360°, so 1 rad ≈ 57.2958°. For example, π/3 rad = 60° and 2 rad ≈ 114.59°.
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How to use the radians to degrees converter
- Enter the angle in radians, for example 0.5.
- Read the radians to degrees converter result: 0.5 × 180/π ≈ 28.648°.
- For multiples of π, replace π with 180°: 3π/4 rad = 135°.
What is the radians to degrees formula?
degrees = radians × 57.2958
The reverse is radians = degrees × 0.017453293 (approximately).
A full turn is 360° or 2π radians, so 1 radian = 180/π degrees exactly. The multiplier 57.2958 is rounded to six significant digits; the radians to degrees calculator uses the full-precision value.
What are radians and degrees?
An angle measures rotation between two lines. The SI-derived unit is the radian; a full turn is 2π radians or 360 degrees. Degrees, arcminutes and arcseconds dominate navigation and astronomy, gradians appear in surveying, and milliradians are used in optics and ballistics.
- Radian (rad): the base unit used here for angles.
- Degree (°): 1 ° = 0.01745329252 rad (Common unit).
Radians to degrees worked examples
- One radian: 1 × 57.2958 = 57.2958 °
- Π radians: 3.1416 × 57.2958 = 180 °
- Π/6 radians: 0.5236 × 57.2958 = 30.0001 °
Conversion chart
| rad | ° | rad | ° |
|---|---|---|---|
| 0.1 | 5.7296 | 2.0944 | 120 |
| 0.25 | 14.3239 | 3 | 171.89 |
| 0.5 | 28.6479 | 3.1416 | 180 |
| 0.7854 | 45.0001 | 4 | 229.18 |
| 1 | 57.2958 | 4.7124 | 270 |
| 1.0472 | 60.0001 | 5 | 286.48 |
| 1.5708 | 90.0002 | 6 | 343.77 |
| 2 | 114.59 | 6.2832 | 360 |
Values are rounded to four decimal places, or two for results of 100 or more.
Quick mental conversion
Multiply by 57.3 for a quick estimate; exact factor is 180/π ≈ 57.29578.
Common angles
| Radians | Degrees |
|---|---|
| π/6 | 30 |
| π/4 | 45 |
| π/3 | 60 |
| π/2 | 90 |
| π | 180 |
| 3π/2 | 270 |
| 2π | 360 |
Radians from degrees: reverse chart
Going the other way, radians = degrees × 0.017453293. Common values:
| degrees | radians |
|---|---|
| 1 | 0.01745329 |
| 2 | 0.03490659 |
| 5 | 0.08726647 |
| 10 | 0.1745329 |
| 20 | 0.3490659 |
| 50 | 0.8726647 |
| 100 | 1.745329 |
| 500 | 8.726647 |
| 1,000 | 17.45329 |
Degrees, minutes and seconds
Surveying and navigation split the decimal part of a degree into minutes (1/60°) and seconds (1/3,600°):
| Radians | Decimal degrees | Degrees, minutes, seconds |
|---|---|---|
| 0.01 | 0.573 | 0° 34′ 22.65″ |
| 0.1 | 5.7296 | 5° 43′ 46.48″ |
| 0.25 | 14.3239 | 14° 19′ 26.20″ |
| 0.5 | 28.6479 | 28° 38′ 52.40″ |
| 1 | 57.2958 | 57° 17′ 44.81″ |
| 2 | 114.5916 | 114° 35′ 29.61″ |
One radian is 57° 17′ 44.81″.
Angle conversion in Excel and code
Most software works in radians. In Excel or Google Sheets, =DEGREES(A1) converts radians to degrees and =RADIANS(A1) goes back. In Python, math.degrees(x) and math.radians(x) do the same, and in JavaScript multiply by 180 / Math.PI. Trigonometric functions such as SIN() expect radians, so =SIN(30) does not give 0.5; use =SIN(RADIANS(30)) instead. Calculators have a DEG/RAD mode switch for the same reason, and a wrong mode is one of the most common sources of trigonometry errors in homework and engineering spreadsheets. Use the degrees to radians converter for the reverse and the angle converter for gradians and turns.
Angular speed
Rotation rates come in radians per second, degrees per second and rpm. One radian per second is about 57.3 degrees per second, or about 9.55 rpm. A motor turning at 3,000 rpm spins at about 314 rad/s. Physics formulas for kinetic energy and torque need rad/s, while data sheets usually list rpm.
Small angles and arc length
For small angles, sin θ is almost equal to θ when θ is in radians. At 0.1 rad, which is about 5.73°, sin θ is 0.0998, within 0.2%. The same shortcut fails if θ is in degrees, which is one reason scientists prefer radians.
Arc length is also simple in radians: s = r × θ. A wheel of radius 0.3 m turning through 2 rad rolls 0.6 m. With degrees you would need an extra π ÷ 180. A radians to degrees converter helps when you need to show the angle to someone who thinks in degrees.
Calculators and spreadsheets default to radians for trig functions. If SIN(30) returns −0.988, the input was read as 30 radians; use SIN(RADIANS(30)) instead.
Navigation and surveying often use degrees, minutes and seconds instead of decimals. After converting radians to decimal degrees, multiply the fractional part by 60 for minutes and the fractional minutes by 60 again for seconds. An angle of 0.5 rad is 28.6479°, or 28° 38′ 52″. Programs such as GIS tools usually accept decimal degrees, so you only need that step for printed maps.
Related converters and calculators
Related conversions:
- Degrees to radians: deg to rad
- Angle converter: deg, rad, grad
- Scientific calculator: trig functions
- Frequency to wavelength converter: waves
- Scientific notation calculator: powers of ten
Sources
BIPM: SI Brochure; Microsoft Support: DEGREES function.
Questions about this calculator
How many degrees is one radian?
About 57.2958°, exactly 180/π.
How do I convert radians to degrees?
Multiply by 180/π. For example, 1.5 rad ≈ 85.94°.
What is π/3 in degrees?
60°.
How do I convert radians to degrees in Excel?
Use =DEGREES(value).
What is 1 radian in degrees, minutes and seconds?
57° 17′ 44.81″.
Check the assumptions and units before relying on a result. Financial, tax and health estimates do not replace advice for your individual circumstances.
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