# Conversion of radians to degrees. Formula

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# The connection between radians and degrees. Formulas

# Conversion of radians to degrees. Formula

# π rad = 180°

# Formula for converting degrees to radians

# 1 radian in degrees

# 1 degree in radians

# 1 radian in seconds

# 1 radian in minutes

**An example of converting radians to degrees**

# Convert 2π rad to degrees.

**An example of converting degrees to radians**

# Convert 360 degrees to radians.

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Or:

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More specifically:

Let us use the first formula:

We substitute 2π for x. We find:

Therefore, the conversion of 2π rad to degrees results in 360 degrees.

Now let us use the second formula:

For α, we substitute a value to be converted to degrees, i.e. α = 2π.

We find:

So we obtain the same result: 2π equals 360 degrees.

Let us use the first formula:

For x, substitute 360. We find:

So, the conversion of 360 degrees to radians results in 2π rad.

Now let us use the second formula:

For x in the formula, we substitute a value to be converted to degrees, i.e., x = 360.

We find:

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This way we obtain the same result: 360 degrees equals 2π rad.

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