How to Convert Between Radians and Degrees (with a Formula and Some Real-World Applications)

Knowing the definition and formula for converting radians to degrees, as well as accessing a handy conversion chart and set of solutions, is essential for anyone working with angles.

Changing the measurement of an angle from radians to degrees is a common task for geometry students. There are two common methods of measuring angles. Both radians and degrees can be used to express angular distances. The concept of trigonometry makes extensive use of the radian unit. There exists a formula for changing the angular measurement system from radians to degrees. The formula and the degree-to-radian conversion will make much more sense once we've established what each angle measurement unit actually means. The article also includes a table showing the conversion between radians and degrees.

A Degree Is Equal to How Many Radians?

An angle can be measured in either radians or degrees. This is why knowing how to convert between radians and degrees, and degrees to radians, is essential. By rotating the circle's radius, we can create an angle with a degree or radian measure. Let's take a look at the different angular units and how they're measured.


In one revolution, the radius travels the full circumference of the circle. After one full rotation, the radius subtends an angle of 2 radians at the circle's center. The subtended radian angle at the circle's center is equal to the arc length divided by the radius. When the arc's length is equal to the radius's length, the angle subtended at the center is 1 radian. Rad is the symbol for the radian, which is the SI unit of angular measurement. The radian is the international standard angle measure.


In order to measure angles, degrees are used. There are 360 "degrees" in a full rotation. It takes a full rotation of the radius, or 360 degrees, for the angle subtended at the circle's center to change by 90 degrees. The degree sign is written as a degree sign ('°'). Angles are commonly measured in degrees, which is not an SI unit but is still widely used. Therefore, converting radians to degrees is preferred when solving problems for clarity. A protractor is used to determine the degree value of an angle.

By contrasting the various measures of a full rotation's angle, we find,

  • The equation for 360 degrees is 2 Radians.

Method for Converting Angular Radicals to Degrees

To convert between radians and degrees, one must use a specific formula. Multiply the radians by 180°/ radians to get the degrees equivalent. We use degrees and radians to express angle measurements, with 1 degree being represented by the symbol "°" The notation for one radian is 1 (or 1c i). e For angles, if no unit is specified after the number, then it is assumed to be in radians. A degree is a unit of measurement that is used to describe a fraction of a circle's circumference. Two radians, or 360 degrees, constitute a full rotation in the anticlockwise direction. As a result, the relationship between degrees and radians can be seen. The formula for converting radians to degrees is:

180/ = Degrees from a Radical Measurement

Radians to Degrees is shown in a figure.

The Formula for Converting between Radians and Degrees

Exactly 360 degrees, or 2 radians, correspond to one revolution around a circle. Therefore, 2 radians equals 360 degrees. Now we can simplify this equation to obtain the formula for converting radians to degrees.

Two radians are equal to three hundred and sixty degrees.

Radians equal 360 degrees plus two-thirds of a circle.

180 degrees is equal to radians.

Simply put, 180 degrees equals 1 radian.

Thus, the angle in degrees is calculated by multiplying the angle in radians by 180°/. i e ,

Angle in Degrees = Radian Angle - 180 /

As a result, we have the formula to convert radians to degrees.

Radian to Degrees Formula

Therefore, here is the formula to use for converting radians to degrees: = Radian measure (180°/). The final degree will be the unit of measurement. The relationship between 1 rad and 57 296°

Radicals to Degrees Conversion

There are two ways to express angle measurement: in radians or degrees. One full rotation of a circle, measured in radians, is equal to 360 degrees. The formula "Angle in Radians 180°/ = Angle in Degrees" can be used to perform the radian-to-degree conversion. The following steps will help you convert any angle from radians to degrees.

  • Take note of the radian value of the angle.
  • 1 radian is equal to 180 degrees or. Multiplying the radian angle by 180 degrees per radian yields the corresponding degree value.
    Degrees = 180 minus the radian equivalent of the angle.
  • Reduce the numbers to degrees (°), please.

Let's take a look at a sample to see what I mean.

Take an angle of / 6 radians, for example. The radians of this angle must be converted to degrees using the appropriate formula.

The angle in degrees is equal to ( / 6) (180° / ).

180 degrees minus 6 degrees is 30 degrees.

Therefore, 30 degrees is equal to / 6 radians.

A Table for Converting Radians to Degrees

First, let's make a list of the most commonly used angles in problem solving and the corresponding radian to degree conversions. See the table below for the radian equivalents of the angle measurements given in degrees.

Radians to Degrees Conversion Table

Conversion of Radicals to Degrees

This radians to degrees chart will show you the relationship between the radian and degree measures of any angle. The below diagram illustrates how we know the circumference of a unit circle will always be 2, just like when we turn 360 degrees.

Radians to Degrees Chart

Important Remarks Concerning the Conversion from Radians to Degrees

If you need to convert radians to degrees, here are a few things to keep in mind:

  • There are two standard methods for expressing angles: degrees and radians.
  • In radians, 2 rad is equal to one complete rotation anticlockwise.
  • A degree is equal to zero degrees With 1 radian equaling 57 degrees, the value of 017453 radians is as follows: 2958°
  • Multiplying a radian angle by 180 degrees per radian yields a degree value.
  • We multiply a degree angle by /180 to get its radian equivalent.

Related Subjects

Learn more about radians and degrees by exploring some related topics.

  1. Use the radians to degrees formula to convert the first example, an angle of 5 radians, to degrees.

    The formula to use when converting radians to degrees is:

    Angle in Degrees = Radian Angle - 180 /

    Mathematically, the angle in degrees is equal to (/5) (180°/).

    Degrees of an Angle = 180 minus 5

    The degree angle is 36 degrees.

    The conversion formula for radians into degrees yields 36 for /5 rad.

    36 degrees is the correct solution to the problem (/5 rad).

  2. Points A and B are on the circle that has its center at (O), as shown in (B) in the second example. The angle of arc of bending (AOB) is /4 rad. Find the degree equivalent of the angle given in radians by AOB.

    For this problem, we know that AOB = /4 rad, so we can solve it as follows:

    Using the radians to degrees formula, we can convert /4 rad to degrees.

    To convert a radian measure of an angle into a degree measure, the formula is:

    (Angle in degrees) = (/4 rad) (180°/).

    Calculating an Angle: 180° 4

    Angle equal to 45 degrees

    Consequently, 45 degrees represents a value for AOB.

    To recap: AOB = 45°

  3. Third, Amy's mom gave her a quarter of a cake and asked her to determine the angle formed by the slice taken from the center of the cake. Could you please assist Amy in calculating the radian and degree angle of the slice?

    Amy's slice of cake = 15 of the whole cake, so this is the answer. Since the cake is circular and a full circle has an angle of 360 degrees, we can deduce that:

    To get the overall cake angle, multiply 2 rad by 0.

    The (1/5)th section has an angle equal to 2/5 rad.

    We know,

    This angle's degree value is equal to the inverse of the radian value: (180°/).

    = (2π/5) × (180°/π) = 72°

    With this information, we can calculate that Amy's slice has an angle of 2/5 rad, which is equal to 72° when expressed in degrees.

    Amy's slice is 72 degrees, or 2.5 radians, in radians.

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Radicals to Degrees: Frequently Asked Questions

In geometry, we use radians and degrees to measure angles. Angles are measured in radians, which is a standard SI unit. 360 degrees are equal to 2 radians, or one complete revolution of a circle. Since 2 radians equals 360 degrees, we can calculate that 1 radian is equal to (180 degrees minus degrees). Therefore, the process of applying the formula to change the unit of angles from radians to degrees is known as the "conversion from radians to degrees."

Learn How to Change Radians Into Degrees

The formula for converting an angle measured in radians to degrees is: Angle in Radians 180°/ = Angle in Degrees. Here's an example: take the angle /9 rad as a starting point. To convert from radians to degrees, we use the following formula: (Angle in Degrees) = (Radians) (Significant Digit) (Significant Digit) (Significant 180 degrees minus 9 degrees is 20 degrees.

For this reason, we know that 20 degrees corresponds to a sine angle of /9 rad.

How Do You Find the Angle Between Two Radians?

Two radians are equivalent to one full circle, or 360 degrees. The formula for converting radians to degrees can be obtained by simplifying this equation. 1 radian = 180 degrees divided by 2 pi radians = 360 degrees

This necessitates the formula Angle in Radians 180°/ = Angle in Degrees.

Can You Explain the Variation Between Radians and Degrees?

It's possible to express angles in either radians or degrees. While degrees are not an SI unit, radians are commonly used to measure angles. The radian system measures angles based on distance traveled, while the angular system uses tilt.

Why and When Would You Need a Radians to Degrees Calculator?

The Radians to Degrees Calculator is a web-based utility that can be used to convert a given radian value into degrees. It's a quick and easy way to convert radians to degrees. Multiplying an angle in radians by 180 degrees / is all that's needed to get the corresponding value in degrees.

How Many Radians Are There in One Degree?

Since 2 radians are equal to 360°, the equation for a degree in radians is: 1° = 2/360 rad 1° = /180 rad

That's why 1 degree is equal to /180 radians.

In what expression do we find the degree equivalent of pi/4 radians?

Degrees = Radians 180 / Y° = (180/) /4 is the formula used to convert radians to degrees.

For a Y-angle, 45 degrees is the equivalent.

Exactly what are the formulas for transforming radians into degrees, minutes, and seconds?

The formula for converting radians to degrees is: () / (180) Minutes can be calculated from degrees by multiplying the fraction by 60. Similarly, the number of seconds remaining is calculated by multiplying the remaining fraction of minutes by 60.

Do we have a way to use the Radian to Degree Formula to convert a Negative Radian to a Degree?

Using the radian to degree formula, we can indeed convert a negative radian to a degree. This formula, Degrees = Radians 180 /, works for both positive and negative numbers.

What is the Expression to Convert 8 Radians to Degrees?

Degrees = Radians 180 / Z° = (180/) 8 is the formula for converting radians to degrees.

Z Degrees = 1440 Degrees

Using the Radian Degree Formula to Convert 6 Rad

Degrees = Radians 180 / X° = (180 / ) 6 X°= 180 6 is the formula for converting radians to degrees.

X°= 1080°

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