**In this tutorial, you’ll learn how to use Python to convert degrees to radians and radians to degrees.** You’ll learn what the relationship between degrees and radians is. Then you’ll learn how to use `math`

library and the `numpy`

library to use Python to convert degrees to radians and radians to degrees.

**The Quick Answer: Use math.radians() and math.degrees()**

Table of Contents

## What are degrees and radians?

Degrees and radians are commonly used metrics that are used to represent angles. Because of their utility, its helpful to know how to convert between them.

The formula used to calculate a degree, with a known radian is:

`degrees = r * (180° / pi)`

The formula used to calculate a radian, with a known number of degrees:

`radians = degrees * (pi / 180°)`

Now that you know the relationship between degrees and radians, let’s explore how to convert between them using the `math`

library.

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## Use Math to Convert Degrees to Radians

The `math`

library comes with a helpful function, `radians()`

, that allows us to convert between degrees and radians. The `math.radians()`

function takes a single input, a value that represents a degree, and returns a value that represents a radian.

Let’s try a few practical examples. We know, based on the formula, that if we were to pass in the value of `pi`

, that we should be able to return the value of `180`

.

Let’s give this a shot by using the `math`

library’s `pi`

constant, which can be accessed by `math.pi`

:

# Use math to convert degrees to radians import math print(math.degrees(math.pi)) # Returns: 180.0

We can see here that the correct value is returned. Now let’s try passing in another value:

# Use math to convert degrees to radians import math print(math.degrees(3)) # Returns: 171.88733853924697

In the next section, you’ll learn how to use the `math`

library to convert from radians to degrees.

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## Use Math to Convert Radians to Degrees

Similar to how the `math`

library has a function to convert radians into degrees, we can use the `radians`

function to convert degrees into radians.

We know, based on the formula, that if we pass in the value of `180`

degrees, that the value of `pi`

should be returned.

Let’s try doing this using Python:

# Use math to convert radians to degrees import math print(math.radians(180)) # Returns: 3.141592653589793

Now that we have confirmed this, let’s try passing in another value:

# Use math to convert radians to degrees import math print(math.radians(90)) # Returns: 1.5707963267948966

In the next section, you’ll learn how to convert degrees to radians using Python and numpy.

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## Use Numpy to Convert Radians to Degrees

Similar to how the `math`

library comes with built-in functions to convert between radians and degrees, the popular numerical library `numpy`

comes with similar functions.

In order to use `numpy`

to convert from degrees to radians, we can use the `radians()`

function.

Let’s try again to convert the value of `pi`

to see if it returns the value of 180:

# Use numpy to convert radians to degrees import numpy as np import math print(np.degrees(math.pi)) # Returns: 180.0

Now let’s try another numpy to see its result:

# Use numpy to convert radians to degrees import numpy as np print(np.degrees(3)) # Returns: 171.88733853924697

In the next section, you’ll use numpy to convert radians to degrees.

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## Use Numpy to Convert Degrees to Radians

Similar to using numpy to convert degrees to radians, we can also use numpy to convert radians to degrees. For this, we’ll use the `np.radians()`

function. This function takes a single input, a value that represents radians, and returns a single output, a value that represents degrees.

Let’s pass in the value of 180 again and see if it returns the value of `pi`

:

# Use numpy to convert degrees to radians import numpy as np print(np.radians(180)) # Returns: 3.141592653589793

Now that that’s confirmed, let’s check another value:

# Use numpy to convert degrees to radians import numpy as np print(np.radians(90)) # Returns: 1.5707963267948966

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## Conclusion

In this tutorial, you learned how to use Python to convert radians to degrees and degrees to radians. You also learned how to use both the `math`

and `numpy`

libraries to convert radians to degrees.

To learn more about the `math`

library, check out the official documentation here.