Radians to Degrees Conversion Calculator
Convert Radians to Degrees (rad to deg) or Degrees to Radians (deg to rad)
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Enter either radian or degree and calculate the equivalent
Formula to convert between Radians and Degrees
How many Radians to Degrees?
rad = π/180 * degree = 0.0174 * degrees, where π = 3.14
For example, to convert 90 degrees to radians, multiply degrees by π/180
radians = π/180 * 90 = 0.0174 * 90 = 1.57 radians
How many Degrees in a Radian?
- To convert radian to degrees, multiple radian value with 180 / π
- Therefore, 0.5 radians = 28.65 degrees.
degree = 180 / π * radians = 57.32 * radians, where π = 3.14
For example, to convert 0.5 radians to degrees:
degrees = 180 / π * 0.5 = 57.32 * 0.5 = 28.65 degrees
What are Radians and Degrees?
- Radians and Degrees are units of measurement of an angle. The SI Unit of an angle is 'Radians'.
- A radian is defined as the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle.
- A degree is defined as the angle subtended at the center of a circle by an arc whose length is equal to 1/360th of the circumference of the circle. The full circle is 360 degrees
- A radian is a bigger unit than a degree. 1 radian is equal to 57.2958 degrees.
- Symbol of a degree is 'θ'. Symbol of a Radian is 'rad'
- Degrees are simpler and easy to visualize with a circle of 360 degrees. Degrees are used in any exterior activities such as surveying, construction work, drawing arcs and circles on paper using protractor and in maps and clocks
- Radians are more precise than degrees and used in calculations such as in trignometry, physics angular and rotational motion.
How is Pi related to Radians and Degrees?
- The ratio of Circumference of a Circle to the Diameter (C/D) is a fixed value and it is always equal to 22/7 which is 3.14159. This fixed value for C/D = 3.141 holds good for any type of circle
- This ratio is defined as Pi represented by the symbol π which represents the value 3.14.
- We know that the diameter of any circle is twice of the radius.
Therefore, Circumference/Diameter = Circumference/(2 * Radius) = π - Circumference = 2* π * Radius = 2πR
- As we know a Radian is defined as the angle formed by the arc of a circle with the radius.
A circumference is a full arc of 360 degrees. Therefore, radian of a full circle = circumference/radius = 2*π = 2 * 3.14 = 6.14 radians - The angle formed by the full circle is 360 degrees. Therefore 360 degrees = 2π radians. which forms the basis for the conversion between the 2 units
Degrees to Radians Table
| Angle in Degree (deg) | In Radians (rad) |
|---|---|
| 1 degree | 0.017 rad |
| 2 degrees | 0.034 rad |
| 5 degrees | 0.087 rad |
| 10 degrees | 0.174 rad |
| 30 degrees | 0.523 rad |
| 45 degrees | 0.785 rad |
| 57.3 degrees | 1 rad |
| 60 degrees | 1.047 rad |
| 90 degrees | 1.57 rad |
| 135 degrees | 2.3561 rad |
| 180 degrees | 3.14 rad |
| 240 degrees | 4.2 rad |
| 270 degrees | 4.71 rad |
| 360 degrees | 6.28 rad |
| 450 degrees | 7.85 rad |
| 540 degrees | 9.42 rad |
| 630 degrees | 10.99 rad |
| 720 degrees | 12.56 rad |
| 810 degrees | 14.13 rad |
| 900 degrees | 15.7 rad |
| 990 degrees | 17.27 rad |
| 1080 degrees | 18.84 rad |
| 1170 degrees | 20.42 rad |
| 1260 degrees | 21.99 rad |
| 1350 degrees | 23.56 rad |
| 1440 degrees | 25.13 rad |
| 1530 degrees | 26.7 rad |
| 1620 degrees | 28.27 rad |
| 1710 degrees | 29.84 rad |
| 1800 degrees | 31.41 rad |
| 1890 degrees | 32.98 rad |
| 1980 degrees | 34.55 rad |
| 2070 degrees | 36.12 rad |
| 2160 degrees | 37.69 rad |
| 2250 degrees | 39.26 rad |
| 2340 degrees | 40.84 rad |
| 2430 degrees | 42.41 rad |
| 2520 degrees | 43.98 rad |
| 2610 degrees | 45.55 rad |
| 2700 degrees | 47.12 rad |
| 2790 degrees | 48.69 rad |
| 2880 degrees | 50.26 rad |
| 2970 degrees | 51.83 rad |
| 3060 degrees | 53.4 rad |
| 3150 degrees | 54.977 rad |
| 3240 degrees | 56.54 rad |
| 3330 degrees | 58.11 rad |
| 3420 degrees | 59.69 rad |
| 3510 degrees | 54.97 rad |
| 3600 degrees | 62.83 rad |
Radians to Degrees Table
| Pi Radians (rad) | In Degrees (deg) |
|---|---|
| Quarter Pi / 0.25 rad | 45 degrees |
| Half Pi / 0.5 rad | 90 degrees (Quarter Circle) |
| 1 rad | 180 degrees (Half Circle) |
| 2 rad | 360 degrees (One Circle) |
| 3 rad | 540 degrees (One and Half Circle) |
| 4 rad | 720 degrees (Two Circle) |
| 5 rad | 900 degrees (Two and Half Circle) |
| 6 rad | 1080 degrees (Three Circle) |
| 7 rad | 1260 degrees (Three and Half Circle) |
| 8 rad | 1440 degrees (Four Circle) |
| 9 rad | 1620 degrees (Four and Half Circle) |
| 10 rad | 1800 degrees (Five Circle) |
FAQ on Rad-Degree conversions
1 circle = 360 degrees.
A circle multiplied by 360 gives the angle in degrees.
2 circle = 720 degrees.
10 circle = 3600 degrees.
6.28 radians
pi radians is 180 degrees
2 pi radians is 360 degrees
The unit circle is a circle with a radius of 1 unit.
An angle of 1 radian subtends an arc length of 1 unit on the unit circle.
This makes the unit circle a convenient tool for visualizing angles in radians.
Since Unit circle is a circle of radius = 1 unit.
It is 2 Pi or 6.28 radians.
A degree is a unit of measurement of an angle.
One rotation around a circle is equal to 360 degrees.
Theta (θ) is simply a variable to indicate an angle and is typically used in mathematical equations.
. It can be represented in radians or in degrees.
It is 1.0471 rad which means 60 degrees
