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 2π multiplied by the circle's radius (2πr).

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

Excel has a function that returns the number pi: 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 * π

or

circumference = 2 * π * 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 2π multiplied by the circle's radius (2πr).

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

360 degrees = 2π radians

which is

degrees = radians x (180 / π)

RADIAN Function Syntax

RADIANS(angle)

Arguments

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.

How to convert radians to fractions of pi
The formula in cell D3 converts the radian decimal value to fractions of pi. Formula in cell D3: =TEXT(C3/PI(),"?/?")&"*"&CHAR(182) Explaining […]

Functions in 'Math and trigonometry' category

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

Excel categories

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