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Radian to Degree - Degree to Radians Converter

Convert Radians to Degrees (rad to deg) or Degrees to Radians (deg to rad)

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Radian - Degree Converter


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Enter either radian or degree and calculate the equivalent

How many Degrees in a Radian? How many Radians to Degrees?

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Degrees to Radians Formula

  • To convert degree to radians, multiply the degrees with π/180
  • rad = π/180 * degree = 0.0174 * degrees, where π = 3.14
    For example, to convert 90 degrees to radians, you would use the following formula:
    radians = π/180 * 90 = 0.0174 * 90 = 1.57 radians
  • This would give you a result of 90 degrees = 1.57 radians

  • Radians to Degrees Formula

    • To convert radian to degrees, multiple radian value with 180 / π
    • degree = 180 / π * radians = 57.32 * radians, where π = 3.14
      For example, to convert 0.5 radians to degrees, you would use the following formula:
      degrees = 180 / π * 0.5 = 57.32 * 0.5 = 28.65 degrees
    • This would give you a result of 0.5 radians = 28.65 degrees.

    Definition of Radians and Degrees

    radian degree relation
    • 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
    • 1 radian is equal to 57.2958 degrees.
    • Symbol of a degree is 'θ'. Symbol of a Radian is 'rad'

    How is Pi related to Radians and Degrees?

    radian degree relation
    • 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

    Why do we need to convert between Degrees and Radians?

    • Degrees are easier to understand and better for visualization.
    • Degrees are used in surveying, construction, housework, art and craft, carpentry, navigation guide and it is also part of gadgets such as compass, clocks, maps and protractor. ,
    • Radians are more precise and derived based on ratio of arc on circumference to radius. It is most suitable for calculations though not easy to visualize
    • Radians are used in mathematics such as in trignometry and calculus, physics such as in rotational movement/angular motion and in programming.
    • While using any trignometric and calculus equations, we need to convert degrees to radians as all these equations are in radians
    • If we have a radian value but we need to use that to visualize or apply it physically in practice for any visual activity, we have to convert rad to degrees.

    Degrees to Radians Table

    Conversion Table icon
    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

    Conversion Table icon
    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

    FAQ icon

    • Both Radian and Degree are units of measurement of an angle.
      Radian is the SI unit for angle.
      Radian is defined as the distance travelled in an arc divided by the radius angle in radians
      (theta)= (distance travelled / radius )
      Θ = s/r.
      Degree measures the angle of displacement from original to new position

    • Radian is a bigger unit than Degree.
      1 Radian = 57.3 degrees
      3.14 Radian (1 Pi) = 180 degrees
      6.28 Radian (2 Pi) = 360 degrees

    • Angle of full circle = 360 degrees. Radian of full circle = (distance covered by arc/ Radius) = Perimeter of the circle / Radius = 2 Pi * R / R = 2 * Pi . This implies, 2 * Pi Radians = 360 Degrees Therefore, 1 Radian = 57.3 Degrees 1 Degree = 0.017 Radians

    • It is 1.0471 rad which means 60 degrees