### π **Part 1: Introduce**

#### π **Definition**

The **ATAN2 function** in Microsoft Excel calculates the arctangent, or inverse tangent, of given x- and y-coordinates.

#### π― **Purpose**

This function determines the angle between the x-axis and a line that connects the origin (0, 0) to a point with coordinates (x_num, y_num). The resulting angle is provided in radians, ranging between -Ο and Ο, but not including -Ο.

#### π **Syntax & Arguments**

The function’s structure is:

`ATAN2(x_num, y_num)`

Where:

**x_num**is the x-coordinate.**y_num**is the y-coordinate.

#### π **Return Value**

The function returns the arctangent of the input coordinates in radians.

#### π‘ **Remarks**

- Positive outcomes denote counterclockwise angles, while negative ones are clockwise.
**ATAN2(a,b)**is equivalent to**ATAN(b/a)**, but in ATAN2, ‘a’ can be 0.- If both x_num and y_num are 0, the function returns a #DIV/0! Error.
- To get the result in degrees, use
**DEGREES**or multiply by**180/PI()**.

### π **Part 2: Examples**

π **Example 1**

**Purpose**: To determine angles in business graphs.**Data & Formulas**:

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

1 | X | Y | Formula | Result |

2 | 1 | 1 | =ATAN2(A2, B2) | 0.785398163 |

3 | -1 | -1 | =ATAN2(A3, B3) | -2.35619449 |

4 | 1 | 1 | =DEGREES(ATAN2(A4, B4)) | -135 |

**Explanation**: This demonstrates how to compute the angle between two points using ATAN2 and convert it to degrees.

π **Example 2**

**Purpose**: Analyzing wind direction for a business’s outdoor event planning.**Data & Formulas**:

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

1 | East | North | Formula | Result |

2 | 5 | 3 | =ATAN2(A2, B2) | 0.5404195 |

3 | -5 | -3 | =ATAN2(A3, B3) | -2.60117315 |

4 | 5 | 3 | =DEGREES(ATAN2(A4, B4)) | -149 |

**Explanation**: This example helps determine the wind direction based on the east and north components. The ATAN2 function calculates the angle in radians, which can then be converted to degrees using the DEGREES function. Such data can be crucial for businesses planning outdoor events, ensuring they account for wind direction when setting up stalls, stages, or other structures.

π **Example 3**

**Purpose**: Determining a construction company’s slope angle between two geographical points.**Data & Formulas**:

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

1 | X | Y | Formula | Result |

2 | 10 | 5 | =ATAN2(A2, B2) | 1.1071487 |

3 | -10 | -5 | =ATAN2(A3, B3) | -2.0344439 |

4 | 10 | 5 | =DEGREES(ATAN2(A4, B4)) | -116 |

**Explanation**: This example calculates the slope angle between two geographical points, which can be essential for construction companies when planning infrastructure or building projects on hilly terrains. The ATAN2 function increases radians, and the DEGREES function converts it to degrees.

π **Example 4**

**Purpose**: Analyzing the slope of a trend line in a financial chart for stock market analysis.**Data & Formulas**:

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

1 | X | Y | Formula | Result |

2 | 50 | 30 | =ATAN2(A2, B2) | 1.0303768 |

3 | -50 | -30 | =ATAN2(A3, B3) | -2.1112156 |

4 | 50 | 30 | =DEGREES(ATAN2(A4, B4)) | -121 |

**Explanation**: In this example, the ATAN2 function is used to determine the angle of a trend line in a financial chart. This can be crucial for stock market analysts when predicting market trends. The tip is initially in radians but can be converted to degrees for better understanding.

π **Example 5**

**Purpose**: Calculating the angle between two vectors in physics for product design in the automobile industry.**Data & Formulas**:

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

1 | X | Y | Formula | Result |

2 | 7 | 4 | =ATAN2(A2, B2) | 1.0516502 |

3 | -7 | -4 | =ATAN2(A3, B3) | -2.0907701 |

4 | 7 | 4 | =DEGREES(ATAN2(A4, B4)) | -120 |

**Explanation**: This example is crucial for product designers in the automobile industry. By calculating the angle between two vectors using the ATAN2 function, designers can make informed decisions about vehicle dynamics and design. The result is initially in radians but can be converted to degrees for a more intuitive understanding.

π **Example 6: Using ATAN2 with IF**

**Purpose**: Determine if the angle between two points is positive or negative.**Data & Formulas**:

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

1 | X | Y | Formula | Result |

2 | 3 | 2 | =IF(ATAN2(A2, B2)>0, “Positive”, “Negative”) | Positive |

3 | -3 | -2 | =IF(ATAN2(A3, B3)>0, “Positive”, “Negative”) | Negative |

4 | 3 | -2 | =IF(ATAN2(A4, B4)>0, “Positive”, “Negative”) | Negative |

**Explanation**: This example checks if the angle between two points is positive or negative. It’s helpful in navigation or robotics, where the direction of the angle matters.

π **Example 7: Using ATAN2 with SUM**

**Purpose**: Sum the angles of multiple point pairs.**Data & Formulas**:

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

1 | X | Y | Formula | Result |

2 | 4 | 3 | =ATAN2(A2, B2) | 0.643501109 |

3 | 5 | 4 | =ATAN2(A3, B3) | 0.674740942 |

4 | =SUM(C2:C3) | 1.318242051 |

**Explanation**: This example aggregates the angles of multiple point pairs. Useful in engineering or astrophysics where cumulative angular measurements are needed.

π **Example 8: Using ATAN2 with VLOOKUP**

**Purpose**: Find the angle of a specific point pair from a table.**Data & Formulas**:

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

1 | ID | X | Y | Formula | Result |

2 | 101 | 6 | 5 | ||

3 | 102 | -6 | -5 | ||

4 | 103 | 6 | -5 | ||

5 | 102 | =ATAN2(VLOOKUP(B5, A2:C4, 2, FALSE), VLOOKUP(B5, A2:C4, 3, FALSE)) | -2.0344439 |

**Explanation**: This example retrieves and computes the angle for a specific entry from a large dataset. Useful in data analytics.

π **Example 9: Using ATAN2 with AVERAGE**

**Purpose**: Calculate the average angle from multiple point pairs.**Data & Formulas**:

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

1 | X | Y | Formula | Result |

2 | 7 | 5 | =ATAN2(A2, B2) | 0.9505468 |

3 | 8 | 6 | =ATAN2(A3, B3) | 0.9272952 |

4 | 9 | 7 | =ATAN2(A4, B4) | 0.9097532 |

5 | =AVERAGE(C2:C4) | 0.9291984 |

**Explanation**: This example calculates the average angle from multiple point pairs. It’s helpful in scenarios requiring an average directional measurement, such as meteorological studies.

π **Example 10: Using ATAN2 with MAX**

**Purpose**: Determine the maximum angle from a set of point pairs.**Data & Formulas**:

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

1 | X | Y | Formula | Result |

2 | 2 | 1 | =ATAN2(A2, B2) | 1.1071487 |

3 | 3 | 2 | =ATAN2(A3, B3) | 0.9827937 |

4 | 4 | 3 | =ATAN2(A4, B4) | 0.9272952 |

5 | =MAX(C2:C4) | 1.1071487 |

**Explanation**: Using the ATAN2 function with the MAX function, this example determines the maximum angle from a set of point pairs. This can be beneficial in engineering when analyzing maximum stress or tension angles.

π **Example 11: Using ATAN2 with MIN**

**Purpose**: Determine the minimum angle from a set of point pairs.**Data & Formulas**:

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

1 | X | Y | Formula | Result |

2 | 5 | 4 | =ATAN2(A2, B2) | 0.6747409 |

3 | 6 | 5 | =ATAN2(A3, B3) | 0.6435011 |

4 | 7 | 6 | =ATAN2(A4, B4) | 0.6202495 |

5 | =MIN(C2:C4) | 0.6202495 |

**Explanation**: This example determines the minimum angle from a set of point pairs using the ATAN2 function nested with the MIN function. It’s helpful in scenarios where the slightest angle of deviation or deflection is required, such as optics or signal processing.

π **Example 12: Using ATAN2 with ROUND**

**Purpose**: Round the result of the ATAN2 function to a specified number of decimal places.**Data & Formulas**:

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

1 | X | Y | Formula | Result |

2 | 8 | 7 | =ROUND(ATAN2(A2, B2), 2) | 0.85 |

3 | 9 | 8 | =ROUND(ATAN2(A3, B3), 2) | 0.79 |

4 | 10 | 9 | =ROUND(ATAN2(A4, B4), 2) | 0.79 |

**Explanation**: This example rounds the result of the ATAN2 function to two decimal places using the ROUND function. It’s beneficial in financial or statistical analyses where precision is essential, but too many decimal places can be cumbersome.

### π **Part 3: Tips and Tricks**

- π
**Degrees Over Radians**: The ATAN2 function returns values in radians. Convert to degrees using**DEGREES**or**180/PI()**. - β
**Avoid Errors**: Be cautious of the #DIV/0! error when both x_num and y_num are 0. - π§
**Angle Orientation**: Positive results from ATAN2 indicate counterclockwise angles, while negative ones are clockwise.