# How to use the DEGREES function

**What is the DEGREES function?**

The DEGREES function calculates degrees based on radians.

**What is degree?**

Degrees are a unit used to measure angles. It is based on dividing a full circle into 360 equal parts. Degrees are divided into fractional parts like minutes and seconds for more precision.

**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.

**When is the DEGREES function useful?**

The trigonometric arc functions return a value in radians. If you need the value in degrees you need to convert it to degrees using the DEGREES function.

Excel Function | Right Triangle Relationship |
---|---|

ASIN | sin(Î¸) = opposite/hypotenuse |

ACOS | cos(Î¸) = adjacent/hypotenuse |

ATAN | tan(Î¸) = opposite/adjacent |

ACOT | tan(Î¸) = opposite/adjacent |

The trigonometric functions relate an angle expressed in radians or degrees to two out of three sides in a right triangle.

**What is the angle Î¸?**

The Greek letter theta (Î¸) is commonly used to represent an unknown angle in a right triangle.

**What is a right triangle?**

A right triangle is a type of triangle that contains one internal angle measuring 90 degrees or Ï€/2 radians (a right angle).

**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€)

The following table shows degrees from 0 to 360 in 15 degree increments along with the corresponding radian values as fractions of pi:

Degrees |
Radians |

15 | Â 1/12Ï€ |

30 | Â 1/6 Ï€ |

45 | Â 1/4 Ï€ |

60 | Â 1/3 Ï€ |

75 | Â 5/12Ï€ |

90 | Â 1/2 Ï€ |

105 | Â 7/12Ï€ |

120 | Â 2/3 Ï€ |

135 | Â 3/4 Ï€ |

150 | Â 5/6 Ï€ |

165 | 11/12Ï€ |

180 | Â 1/1 Ï€ |

195 | 13/12Ï€ |

210 | Â 7/6 Ï€ |

225 | Â 5/4 Ï€ |

240 | Â 4/3 Ï€ |

255 | 17/12Ï€ |

270 | Â 3/2 Ï€ |

285 | 19/12Ï€ |

300 | Â 5/3 Ï€ |

315 | Â 7/4 Ï€ |

330 | 11/6 Ï€ |

345 | 23/12Ï€ |

360 | Â 2/1 Ï€ |

**How is a circle related to trigonometry?**

The geometry and periodicity of circles interconnect deeply with the definitions, identities, and applications of trigonometry. The unit circle bridges the geometry of the circle with the behavior of trig functions.

Right angle is 90 degrees, straight angle is 180 degrees, and a full circle is 360 degrees.

**What is the unit circle?**

The unit circle is a circle with a radius of 1 unit that is centered at the origin (0, 0) on the Cartesian coordinate plane.

**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.

### Excel Function Syntax

DEGREES(*angle*)

### Arguments

angle |
Required. The radian you want to convert into degrees. |

Formula in cell C3:

### 'DEGREES' function examples

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

### Functions in 'Math and trigonometry' category

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

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