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Radian to Degree - Degree to Radians Converter

Convert Radians to Degrees (rad to deg) or Convert 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 to convert Degree to Radians. How Many Degrees In Radians?

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Degrees to Radians Formula

  • To convert 1 degree to radians, use the equation below

  • 1 ° = 0.01745329252 rad

  • For example, to convert 90 degrees to radians, you would use the following formula:

    • radians = 90° * π / 180°

    radians = π / 2

    Therefore,

    90 degrees is equal to π / 2 radians.

  • Radian symbol is 'rad'.
  • There are 6.28 (2 * 3.14) radians in a circle (radian unit circle).
  • There are 3.14 radians in half circle.

    • Radians to Degrees Formula

    • To Convert 1 radian to degrees use the equation below

    • 1 rad = 57.295779513 ° (1 radian is 57.29 degrees)

    • Radians × 180 / π
    • For example, to convert 0.5 radians to degrees, you would use the following formula:
    • degrees = 0.5 * 180 / π
    • This would give you a result of 0.5 radians = 28.65 degrees.

    Introduction to Radians and Degrees

    radian degree relation

    • Radians and Degrees are units of measurement of an angle.

    • 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 central angle of 1 radian subtends an arc length that is equal to the radius of the circle.

      This means that 1 radian is equal to 57.2958 degrees.

    • 1 radian is equal to 180/π, or about 57.29578°.

      In other words, a radian angle measure is 57 degrees
    • Angles are measured in degrees. One revolution is divided into 360 equal parts and each part is known as a degree.

    • Multiply the degree value with π / 180 ° to convert to radians and multiply radian value with 180 / π to convert to 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.

    Degrees vs Radians

    radian degree

    • The radian is the natural unit of angle measurement

      . This is because it is based on the circumference of a circle, which is a fundamental geometric concept. Degrees, on the other hand, are an arbitrary unit of angle measurement that is based on the number of days in a year.

    • Degrees are the more common unit of measurement,

      and are used in everyday life and in many industries, such as construction and engineering.
    • Degrees are often used in measuring angles on a compass or when setting the time on a clock.
    • Degrees are not as precise as radians and can lead to errors when performing calculations but they are easier to visualize, more common and intuitive.
    • Radians are difficult to visualize but more precise and therefore more convenient to use in mathematics and physics and in computer graphic applications. Many trigonometric functions, such as sine and cosine, are defined in terms of radians.
    • The radian is named after the French mathematician François Viète. Viète was a pioneer in the use of trigonometric functions in mathematics.
    • The degree is named after the Greek astronomer Hipparchus. Hipparchus was the first person to divide the circle into 360 degrees.
    • The radian is the preferred unit of angle measurement in the International System of Units (SI).
    • The degree is still widely used in many fields, such as engineering, surveying, and navigation.
      • Which unit of measurement is better depends on the specific application. For everyday use, degrees are generally the better choice. For mathematical and physical calculations, radians are generally the better choice.
      Here are some examples of when to use degrees and radians:
    • Degrees:
      • Measuring the angle of a turn on a steering wheel.
      • Measuring the angle of a roof pitch.
      • Measuring the angle of a mountain slope.
    • Radians:
      • Calculating the circumference of a circle.
      • Calculating the area of a sector.
      • Calculating the velocity of an object moving in a circular path.

      Note: This content has inputs from both the AI language model developed by OpenAI and by Bard, the Google AI model.

    Degrees to Radians calculator table (Angle to Radians)

    Conversion Table icon

    Angle in Degree (deg)

    In Radians (rad)

    1 degrees in radians

    0.017 rad

    2 degrees in radians

    0.034 rad

    5 degrees in radians

    0.087 rad

    10 degrees in radians

    0.174 rad

    30 degrees in radians

    0.523 rad

    45 degrees in radians

    0.785 rad

    57.3 degrees in radians

    1 rad

    60 degrees in radians

    1.047 rad

    90 degrees in radians

    1.57 rad

    135 degrees in radians

    2.3561 rad

    180 degrees in radians

    3.14 rad

    240 degrees in radians

    4.2 rad

    270 degrees in radians

    4.71 rad

    360 degrees in radians

    6.28 rad

    450 degrees in radians

    7.85 rad

    540 degrees in radians

    9.42 rad

    630 degrees in radians

    10.99 rad

    720 degrees in radians

    12.56 rad

    810 degrees in radians

    14.13 rad

    900 degrees in radians

    15.7 rad

    990 degrees in radians

    17.27 rad

    1080 degrees in radians

    18.84 rad

    1170 degrees in radians

    20.42 rad

    1260 degrees in radians

    21.99 rad

    1350 degrees in radians

    23.56 rad

    1440 degrees in radians

    25.13 rad

    1530 degrees in radians

    26.7 rad

    1620 degrees in radians

    28.27 rad

    1710 degrees in radians

    29.84 rad

    1800 degrees in radians

    31.41 rad

    1890 degrees in radians

    32.98 rad

    1980 degrees in radians

    34.55 rad

    2070 degrees in radians

    36.12 rad

    2160 degrees in radians

    37.69 rad

    2250 degrees in radians

    39.26 rad

    2340 degrees in radians

    40.84 rad

    2430 degrees in radians

    42.41 rad

    2520 degrees in radians

    43.98 rad

    2610 degrees in radians

    45.55 rad

    2700 degrees in radians

    47.12 rad

    2790 degrees in radians

    48.69 rad

    2880 degrees in radians

    50.26 rad

    2970 degrees in radians

    51.83 rad

    3060 degrees in radians

    53.4 rad

    3150 degrees in radians

    54.977 rad

    3240 degrees in radians

    56.54 rad

    3330 degrees in radians

    58.11 rad

    3420 degrees in radians

    59.69 rad

    3510 degrees in radians

    54.97 rad

    3600 degrees in radians

    62.83 rad

    Pi Radians to Degrees (Rad to Degrees Conversion) Table

    Conversion Table icon

    Pi Radians (rad)

    In Degrees (deg)

    0.25 Pi / Quarter Pi rad

    45 degrees

    0.5 Pi / Half Pi / 0.5 rad

    90 degrees (Quarter Circle)

    1 Pi Radian / 1 rad

    180 degrees (Half Circle)

    2 Pi Radians / 2 rad

    360 degrees (One Circle)

    3 Pi Radians / 3 rad

    540 degrees (One and Half Circle)

    4 Pi Radians / 4 rad

    720 degrees (Two Circle)

    5 Pi Radians / 5 rad

    900 degrees (Two and Half Circle)

    6 Pi Radians / 6 rad

    1080 degrees (Three Circle)

    7 Pi Radians / 7 rad

    1260 degrees (Three and Half Circle)

    8 Pi Radians / 8 rad

    1440 degrees (Four Circle)

    9 Pi Radians / 9 rad

    1620 degrees (Four and Half Circle)

    10 Pi Radians / 10 rad

    1800 degrees (Five Circle)

    FAQ on Degree to Radian and Radian to Degree conversion

    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

    • 2.3561 rad

    • 10313.24 degrees

    • Since Unit circle is a circle of radius = 1 unit. It is 2 Pi or 6.28 radians

    • 171.88 degrees

    • 20626.48 degrees

    • 6875.49 degrees

    • 0.6108 rad

    • 1.0471 rad

    • 57.29 degrees

    • 2578.31 degrees

    • 1718.87 degrees

    • 229.18 degrees

    • 5156.62 degrees

    • 3437.74 degrees

    • 0 rad

    • 7.8539 rad

    • 0.0349 rad

    • 3.8397 rad

    • 6875.49 degrees

    • 5156.62 degrees

    • 458.36 degrees