# How to use the RADIANS function

**What is the RADIANS function?**

The RADIANS function converts degrees to radians.

**What is radian?**

Radians measure angles by the length of the arc they make in a circle rather than degrees. The full circumference of any circle is 2Ï€ multiplied by the circle's radius (2Ï€r).

Since the circumference goes all the way around a circle, that means the full circle measures 2Ï€ radians. Half a circle would be Ï€ radians (half of 2Ï€). A quarter circle is 2Ï€/4 = Ï€/2 radians. An eighth of a circle is 2Ï€/8 = Ï€/4 radians.

Excel has a function that returns the number pi:Â PI function

**What is the number pi?**

Pi is a irrational number meaning it cannot be expressed as a ratio of two integers. In other words, it has an infinite number of decimal places with no repeating pattern.

It is calculated by the ratio of the circumference of a circle to its diameter.

circumference = diameter * Ï€

or

circumference = 2 * Ï€ * radius

this means that the diameter = 2 x radius.

**What is the circumference of a circle?**

The circumference is the linear distance enclosing the circle.

**What is the diameter of a circle?**

The diameter of a circle is the straight line distance that passes through the center of the circle connecting one point on the circumference to another, going all the way across the circle.

**What is the radius of a circle?**

The radius of a circle is the distance from the center point to any point on the circle's edge or circumference.

**Why is the PI function useful?**

The trigonometric functions in Excel accept radians as the angular measurement. The basic trigonometry ratios like sine, cosine and tangent come from the ratios of sides in a right triangle. Sine, cosine and tangent ratios relate the lengths of sides to angles in a right triangle. If you know one side and angle, you can use these ratios to find the other sides. The ratios link geometry and angles together.

**What is the relationship between the number pi and radians?**

Radians measure angles by the length of the arc they make in a circle rather than degrees. The full circumference of any circle is 2Ï€ multiplied by the circle's radius (2Ï€r).

Since the circumference goes all the way around a circle, that means the full circle measures 2Ï€ radians. Half a circle would be Ï€ radians (half of 2Ï€). A quarter circle is 2Ï€/4 = Ï€/2 radians. An eighth of a circle is 2Ï€/8 = Ï€/4 radians.

**What is an arc in a circle?**

The arc in a circle is a segment of the circle's circumference. Arcs are an angle measured in degrees or radians.

**What is a segment in a circle?**

A segment (also called chord) connects two points on a circle's edge by a straight line, and can be used to analyze geometric aspects of the circle like angles, area, and tangents.

**What is a sector?**

A sector of a circle is the section enclosed by two radii and an arc.

**What is radii?**

The plural form of the word "radius".

**What is the connection between a circle and trigonometry?**

The geometry of the circle underlies the theory, definitions, models, identities, and applications of trigonometry. The circle and trigonometry are deeply mathematically connected.

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

The circumference of a circle is 360 degrees or 2Ï€ radians.

360 degrees = 2Ï€ radians

which is

degrees = radians x (180 / Ï€)

### RADIAN Function Syntax

RADIANS(*angle*)

### Arguments

angle |
Required. The degree you want to convert. |

### Comments

This is what the RADIANS function does:

Radians = Degrees * PI() / 180

### RADIAN Function example

Formula in cell C3:

### 'RADIANS' function examples

The following article has a formula that contains the RADIANS function.

### Functions in 'Math and trigonometry' category

The RADIANS function function is one of 73 functions in the 'Math and trigonometry' category.

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