## What Is 60 Degrees to Radians Conversion?

**60 degrees to radians is **$\pi 3$**. **

Degrees and radians are the units used to measure angles.

**Degree:** A degree (denoted by °) is the amount of rotation from the initial arm to the terminal arm. A complete turn around the center of a circle is $360^{\circ}$. If it is divided into 360 equal parts, each part represents 1 degree.

**Radian:** An angle of 1 radian is defined to be the angle, in the counterclockwise direction, which spans an arc whose length is equal to the radius of the circle. Thus, if arc length $= r$, then angle is 1 radian. It holds true for all circles.

By the same logic, 2 radians is the central angle made by an arc whose length is $2 r$ (twice the length of the radius of the circle). If the arc-length equals the total circumference of the circle which is $2\pi r$, it represents an angle of $2\pi$ radians. Thus, a complete circle represents $2\pi$ radians**. **

- $360^{\circ} = 2\pi$ radians
- $180^{\circ} = \pi$ radians
- $90^{\circ} = 2$ radians
- $60^{\circ} = 3$ radians
- $45^{\circ} = 4$ radians
- $30^{\circ} = 6$ radians

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## Degrees to Radians Formula

To convert an angle from degrees to radians, we multiply it by $180^{\circ}$.

Angle in degrees $\times \frac{\pi}{180^{\circ}} =$ Angle in radians

We can use this formula to convert 60 degrees to radians.

## How to Convert 60 Degrees into Radians

We use the conversion formula to convert 60 degrees into radians.

**Angle in radians **$=$** Angle in degrees **$\times\frac{\pi}{180^{\circ}}$

Here, angle in degrees $= 60^{\circ}$

On substituting this in the formula, we get

Angle in radians $= 60^{\circ} \times \frac{\pi}{180^{\circ}} = \frac{\pi}{3}$

Thus, the value of 60 degrees to radians is 3.

**Note:**

We can also approach this problem in a different way. We know that the angle at the center of a circle is 360 degrees. It is equivalent to 2π in radians.

$360^{\circ} = 2\pi$

Dividing both sides by 6, we will get

$\frac{360^{\circ}}{6} = \frac{2\pi}{6}$

$60^{\circ} = \frac{\pi}{3}$

Thus, the value of 60 degrees to radians in terms of pi is $\frac{\pi}{3}$.

## Negative 60 Degrees to Radians

Negative angle is an angle generated in an clockwise direction from the initial arm. To convert a negative degree into a radian, we use the same method as we did for positive degrees. We will simply multiply the angle’s given value by $\frac{\pi}{180^{\circ}}$.

Let’s convert $-60^{\circ}$ into radians.

Radian $= (\frac{\pi}{180^{\circ}})$ (degrees)

Radian $= (\frac{\pi}{180^{\circ}}) \times (-60^{\circ})$

Angle in radian $= – \frac{\pi}{3}$

## Facts about 60 Degrees to Radians

- $60^{\circ} = \frac{\pi}{3}; 30^{\circ} = \frac{\pi}{6}; 120^{\circ} = \frac{2\pi}{3}$
- 60 radians is about 3437.75 degrees.
- 1 radian is about 57.3 degrees.
- 1 degree is about 0.0174533 radians.
- $2\pi$ radians $= 360$ degrees.
- To convert radians to degrees, we multiply by $\frac{180^{\circ}}{\pi}$.

Angle in radians $\times \frac{180^{\circ}}{\pi} =$ Angle in degrees - The symbol for radian given by “rad” or c is generally omitted in mathematical writing.

## Conclusion

In this article, we learned about the angle in radians equivalent to 60 degrees. We discussed the conversion formula along with some examples. Let’s solve a few more examples and practice problems for better understanding.

## Solved Examples on Degrees to Radians

**1. Convert 60 degrees to radians.**

**Solution:**

To convert $60^{\circ}$ to radians, use the formula

Angle in radians $=$ Angle in degrees $\times (\frac{\pi}{180^{\circ}})$

Therefore, $60^{\circ} \times (\frac{\pi}{180^{\circ}}) = (\frac{\pi}{3})$ radians

So, 60 degrees in radians is $(\frac{\pi}{3})$ radians.

**2**. **Convert 90 degrees to radians.**

**Solution:**

Given: 90 degrees is the angle

Angle in radian $=$ Angle in degree $\times (\frac{\pi}{180^{\circ}})$

Angle in radian $= 90^{\circ} \times (\frac{\pi}{180^{\circ}})$

Angle in radian $= \frac{\pi}{2}$

Hence, 90 degrees is equal to $\frac{\pi}{2}$ in radians.

**3. Convert ****4****9**** radians to degrees. **

**Solution: **

Angle in Degrees $=$ Angle in Radians $\times \frac{\pi}{180^{\circ}}$

Angle in Degrees $= (\frac{4\pi}{9}) \times \frac{\pi}{180^{\circ}}$

Angle in Degrees $= 4 \times 20^{\circ}$

Angle in Degrees $= 80^{\circ}$

Hence, $\frac{4\pi}{9}$ radians are 80 degrees.

**4. Convert 200 degrees into radians.**

**Solution:**

By the formula, we know

Angle in radians $=$ Angle in degree $\times \frac{\pi}{180^{\circ}}$

Thus, 200 degrees in radians $= 200 \times \frac{\pi}{180^{\circ}} = \frac{10\pi}{9}$ radians.

Hence, 200 degrees is equal to $\frac{10\pi}{9}$ in radians.

## Practice Problems on Degrees to Radians

## 60 Degrees to Radians – Definition, Formula, Examples, Facts, FAQs

### Convert $\pi$ radian to degrees.

Radians $\times(\frac{180^{\circ}}{\pi}) =$ Degrees

radians $= \times (\frac{180^{\circ}}{\pi}) = 180^{\circ}$

### Convert $30^{\circ}$ to radians.

$30^{\circ} \times (\frac{\pi}{180^{\circ}}) = \frac{\pi}{6}$

### Convert $75^{\circ}$ to radians.

Degrees $\times (\frac{\pi}{180^{\circ}}) =$ Radians

$75^{\circ} \times (\frac{\pi}{180^{\circ}}) = \frac{5 \pi}{12}$

### How many radians is 60 degrees?

60 degrees $= \frac{\pi}{3}$ radians

### If $60^{\circ} = \frac{\pi}{3}$, then $120^{\circ} =$ _____ .

$60^{\circ} = \frac{\pi}{3}$

$120^{\circ} = \frac{2\pi}{3}$

## Frequently Asked Questions about Degrees to Radians

**What is 1 radian in degrees?**

1 radian is approximately 57.2958 degrees.

**What is the connection between radians and degrees?**

Radians and degrees are connected by the relationship $360^{\circ} = 2\pi$ radians.

- If you wish to convert from degrees to radians, multiply the given degree measure by $\frac{\pi}{180}$.
- If you wish to convert from radians to degrees, multiply the given radian measure by $\frac{\pi}{180}$.

**Is 1 radian bigger than 1 degree?**

One radian is much greater than one degree. It is approximately 57.3 degrees.

**How many radians are 240 degrees?**

240 degrees is $\frac{4\pi}{3} radians.

**How many radians are 120 degrees?**

120 degrees is $\frac{2\pi}{3}$ radians.