## Part 1: Introduction

### Definition

The ATAN function in Microsoft Excel is a mathematical function that returns the arctangent, or inverse tangent, of a number.

### Purpose

The purpose of the ATAN function is to calculate the angle whose tangent is the provided number. This can be useful in various mathematical and engineering calculations.

### Syntax & Arguments

The syntax for the ATAN function is as follows:

`ATAN(number) `

The ATAN function has the following argument:

**Number**: This is a required argument. It represents the tangent of the angle you want.

### Return Value

The ATAN function returns the arctangent of the provided number. The returned angle is given in radians from pi/2 to pi/2.

### Remarks

To express the arctangent in degrees, multiply the result by 180/PI( ) or use the DEGREES function.

## Part 2: Examples

### Example 1

**Purpose of Example:** To calculate the arctangent of a number in radians.

**Data Tables and Formulas:**

A | B | C | |
---|---|---|---|

1 | Number | Formula | Result |

2 | 0.5 | =ATAN(A2) | 0.463647609 |

3 | 1.0 | =ATAN(A3) | 0.785398163 |

4 | 1.5 | =ATAN(A4) | 0.982793723 |

**Explanation:** In this example, the numbers represent the tangent of the angles we want to find. The ATAN function calculates the arctangent of these numbers in radians.

### Example 2

**Purpose of Example:** To calculate the arctangent of a number in degrees.

**Data Tables and Formulas:**

A | B | C | |
---|---|---|---|

1 | Number | Formula | Result |

2 | 0.5 | =DEGREES(ATAN(A2)) | 26.56505118 |

3 | 1.0 | =DEGREES(ATAN(A3)) | 45.00000000 |

4 | 1.5 | =DEGREES(ATAN(A4)) | 56.30993247 |

**Explanation:** In this example, the numbers represent the tangent of the angles we want to find. The ATAN function calculates the arctangent of these numbers in radians, and then the DEGREES function is used to convert the result to degrees.

### Example 3

**Purpose of Example:** To calculate the arctangent of a number and check if it is within a specific range.

**Data Tables and Formulas:**

A | B | C | D | |
---|---|---|---|---|

1 | Number | Formula | Result | Within Range? |

2 | 0.5 | =ATAN(A2) | 0.463647609 | =IF(C2>0.5, “Yes”, “No”) |

3 | 1.5 | =ATAN(A3) | 0.982793723 | =IF(C3>0.5, “Yes”, “No”) |

4 | 2.5 | =ATAN(A4) | 1.190289949 | =IF(C4>0.5, “Yes”, “No”) |

**Explanation:** In this example, the numbers represent values in a mathematical model. The ATAN function is used to calculate the arctangent of these numbers. The IF function then checks if the calculated value is within a certain range.

### Example 4

**Purpose of Example:** To calculate the arctangent of a number and sum them up.

**Data Tables and Formulas:**

A | B | C | D | |
---|---|---|---|---|

1 | Number | Formula | Result | Total |

2 | 0.5 | =ATAN(A2) | 0.463647609 | =SUM(C2:C4) |

3 | 1.5 | =ATAN(A3) | 0.982793723 | |

4 | 2.5 | =ATAN(A4) | 1.190289949 |

**Explanation:** In this example, the numbers represent values in a mathematical model. The ATAN function is used to calculate the arctangent of these numbers. The SUM function is then used to calculate the total of these values.

### Example 5

**Purpose of Example:** To calculate the arctangent of a number and find the maximum value.

**Data Tables and Formulas:**

A | B | C | D | |
---|---|---|---|---|

1 | Number | Formula | Result | Max Value |

2 | 0.5 | =ATAN(A2) | 0.463647609 | =MAX(C2:C4) |

3 | 1.5 | =ATAN(A3) | 0.982793723 | |

4 | 2.5 | =ATAN(A4) | 1.190289949 |

**Explanation:** In this example, the numbers represent values in a mathematical model. The ATAN function is used to calculate the arctangent of these numbers. The MAX function is then used to find the maximum of these values.

### Example 6

**Purpose of Example:** To calculate the arctangent of a number and check if it is within a specific range using the IF function.

**Data Tables and Formulas:**

A | B | C | D | |
---|---|---|---|---|

1 | Number | Formula | Result | Within Range? |

2 | 0.5 | =ATAN(A2) | 0.463647609 | =IF(C2>0.5, “Yes”, “No”) |

3 | 1.5 | =ATAN(A3) | 0.982793723 | =IF(C3>0.5, “Yes”, “No”) |

4 | 2.5 | =ATAN(A4) | 1.190289949 | =IF(C4>0.5, “Yes”, “No”) |

**Explanation:** In this example, the numbers represent values in a mathematical model. The ATAN function is used to calculate the arctangent of these numbers. The IF function then checks if the calculated value is within a certain range.

### Example 7

**Purpose of Example:** To calculate the arctangent of a number and sum them up using the SUM function.

**Data Tables and Formulas:**

A | B | C | D | |
---|---|---|---|---|

1 | Number | Formula | Result | Total |

2 | 0.5 | =ATAN(A2) | 0.463647609 | =SUM(C2:C4) |

3 | 1.5 | =ATAN(A3) | 0.982793723 | |

4 | 2.5 | =ATAN(A4) | 1.190289949 |

**Explanation:** In this example, the numbers represent values in a mathematical model. The ATAN function is used to calculate the arctangent of these numbers. The SUM function is then used to calculate the total of these values.

### Example 8

**Purpose of Example:** To calculate the arctangent of a number and find the maximum value using the MAX function.

**Data Tables and Formulas:**

A | B | C | D | |
---|---|---|---|---|

1 | Number | Formula | Result | Max Value |

2 | 0.5 | =ATAN(A2) | 0.463647609 | =MAX(C2:C4) |

3 | 1.5 | =ATAN(A3) | 0.982793723 | |

4 | 2.5 | =ATAN(A4) | 1.190289949 |

**Explanation:** In this example, the numbers represent values in a mathematical model. The ATAN function is used to calculate the arctangent of these numbers. The MAX function is then used to find the maximum of these values.

### Example 9

**Purpose of Example:** To calculate the arctangent of a number and find the minimum value using the MIN function.

**Data Tables and Formulas:**

A | B | C | D | |
---|---|---|---|---|

1 | Number | Formula | Result | Min Value |

2 | 0.5 | =ATAN(A2) | 0.463647609 | =MIN(C2:C4) |

3 | 1.5 | =ATAN(A3) | 0.982793723 | |

4 | 2.5 | =ATAN(A4) | 1.190289949 |

**Explanation:** In this example, the numbers represent values in a mathematical model. The ATAN function is used to calculate the arctangent of these numbers. The MIN function is then used to find the minimum of these values.

### Example 10

**Purpose of Example:** To calculate the arctangent of a number and round it to the nearest whole number using the ROUND function.

**Data Tables and Formulas:**

A | B | C | D | |
---|---|---|---|---|

1 | Number | Formula | Result | Rounded |

2 | 0.5 | =ATAN(A2) | 0.463647609 | =ROUND(C2, 0) |

3 | 1.5 | =ATAN(A3) | 0.982793723 | =ROUND(C3, 0) |

4 | 2.5 | =ATAN(A4) | 1.190289949 | =ROUND(C4, 0) |

**Explanation:** In this example, the numbers represent values in a mathematical model. The ATAN function is used to calculate the arctangent of these numbers. The ROUND function then rounds the calculated value to the nearest whole number.

### Example 11

**Purpose of Example:** To calculate the arctangent of a number and find the average value using the AVERAGE function.

**Data Tables and Formulas:**

A | B | C | D | |
---|---|---|---|---|

1 | Number | Formula | Result | Average |

2 | 0.5 | =ATAN(A2) | 0.463647609 | =AVERAGE(C2:C4) |

3 | 1.5 | =ATAN(A3) | 0.982793723 | |

4 | 2.5 | =ATAN(A4) | 1.190289949 |

**Explanation:** In this example, the numbers represent values in a mathematical model. The ATAN function is used to calculate the arctangent of these numbers. The AVERAGE function is then used to calculate the average of these values.

### Example 12

**Purpose of Example:** To calculate the arctangent of a number and find the median value using the MEDIAN function.

**Data Tables and Formulas:**

A | B | C | D | |
---|---|---|---|---|

1 | Number | Formula | Result | Median |

2 | 0.5 | =ATAN(A2) | 0.463647609 | =MEDIAN(C2:C4) |

3 | 1.5 | =ATAN(A3) | 0.982793723 | |

4 | 2.5 | =ATAN(A4) | 1.190289949 |

**Explanation:** In this example, the numbers represent values in a mathematical model. The ATAN function is used to calculate the arctangent of these numbers. The MEDIAN function is then used to find the median of these values.

## Part 3: Tips and Tricks

Remember that the ATAN function returns the result in radians. If you need the result in degrees, use the DEGREES function or multiply the result by 180/PI( ).

The ATAN function can handle both positive and negative values.

If the number argument is not numeric, the ATAN function will return a #VALUE! Error.

The ATAN function can be combined with other Excel functions for more complex calculations.

The ATAN function is part of a suite of Excel functions that can perform trigonometric calculations. Other functions in this suite include SIN, COS, TAN, ASIN, ACOS, and others.