Radians to Degrees – Formulas and Examples

Radians and degrees are types of units for measuring angles. There are other types of units, but radians and degrees are the most used. Each of these units has its respective application. Radians are mainly used in differential and integral calculus. On the other hand, degrees are used in geometry and allow expressing directionality and angle size. We can convert radians to degrees by multiplying by 180° and dividing by π.

Here, we will look at some problems where we will learn the process used to convert from radians to degrees.

TRIGONOMETRY
formula to transform from radians to degrees

Relevant for

Learning to transform from radians to degrees with examples.

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TRIGONOMETRY
formula to transform from radians to degrees

Relevant for

Learning to transform from radians to degrees with examples.

See examples

How to convert from radians to degrees?

To convert from radians to degrees, we need to multiply the radians by 180° and divide by π. Therefore, we have the formula:

x\cdot \frac{180^{\circ}}{\pi}=y^{\circ}

where x is the angle in radians and y is the angle in degrees.

relationship radians degrees

This formula is derived from the fact that we have 360° in a circle. When we express the angle in radians, we know that we have 2π radians in a circle. This means that 2π = 360°. We can divide this expression by two to obtain π = 180°.

Therefore, this is the relationship we use to convert from radians to degrees.


Transformation from radians to degrees – Examples with answers

The following examples are solved using the radians to degrees transformation formula seen above. Each example has its respective solution, but it is recommended that you try to solve the problems yourself before looking at the answer.

EXAMPLE 1

Transform \frac{4 \pi}{5} radians to degrees.

We simply use the radians given in the conversion formula to get the degrees:

x\cdot \frac{180^{\circ}}{\pi}=y^{\circ}

\frac{4\pi}{5}\cdot \frac{180^{\circ}}{\pi}=144^{\circ}

Therefore, \frac{4\pi}{5} radians is equivalent to 144°.

EXAMPLE 2

How many degrees is equal to \frac{2 \pi}{9} radians?

We substitute the given value in the conversion formula. Therefore, we have:

x\cdot \frac{180^{\circ}}{\pi}=y^{\circ}

\frac{2\pi}{9}\cdot \frac{180^{\circ}}{\pi}=40^{\circ}

Thus, \frac{2\pi}{9} radians is equivalent to 40°.

EXAMPLE 3

How many degrees is equal to \frac{12 \pi}{7} radians?

We use the radians to degrees conversion formula along with the given value to get the degrees:

x\cdot \frac{180^{\circ}}{\pi}=y^{\circ}

\frac{12\pi}{7}\cdot \frac{180^{\circ}}{\pi}=308.6^{\circ}

Therefore, 308.6° is equal to \frac{12\pi}{7} radians.

EXAMPLE 4

Convert 2.5 radians to degrees.

In this case, we simply have x=2.5. Therefore, we have:

x\cdot \frac{180^{\circ}}{\pi}=y^{\circ}

2.5\cdot \frac{180^{\circ}}{\pi}=143.2^{\circ}

Thus, 2.5 radians is equivalent to 143.2°.

EXAMPLE 5

What is 3.2 radians in degrees?

We have the value x=3.2. Using this value in the formula, we have:

x\cdot \frac{180^{\circ}}{\pi}=y^{\circ}

3.2\cdot \frac{180^{\circ}}{\pi}=183.3^{\circ}

Thus, 3.2 radians is equivalent to 183.3°.


Radians to degrees – Practice problems

Use what you have learned about transforming radians to degrees and the derived formula to solve the following practice problems. Select an answer and click “Check” to check your answer.

If we have \frac{\pi}{3} radians, what is its equivalent in degrees?

Choose an answer






How many degrees is equal to \frac{5\pi}{6} radians?

Choose an answer






If we have \frac{9\pi}{10} radians, what is its equivalent in degrees?

Choose an answer






How many degrees is equal to 4.5 radians?

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