### π Part 1: Introduce

#### π **Definition**

The **RADIANS** function in Microsoft Excel is designed to **convert angles from degrees to radians**.

#### π **Purpose**

The primary purpose of this function is to **facilitate trigonometric calculations** in Excel by converting angles to a format that can be easily used in trigonometric functions like **SIN, COS, and TAN**.

#### π **Syntax & Arguments**

The syntax for the **RADIANS** function is as follows:

`=RADIANS(angle)`

#### π **Explain the Arguments in the Function**

**Angle**: This is the required argument. It represents the**angle in degrees**that you want to convert to radians.

#### π **Return Value**

The function returns the **angle converted into radians**.

#### π **Remarks**

The function is straightforward to use and has no specific limitations or conditions to be aware of.

### π Part 2: Examples

#### π **Example 1: Converting Sales Angles for Data Visualization**

##### π― **Purpose of Example**

To **convert angles for a pie chart** representing quarterly sales data.

##### π **Data Sheet and Formulas**

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

1 | Quarter | Sales | Angle | Radians | Result |

2 | Q1 | 20000 | 90 | `=RADIANS(C2)` | 1.5708 |

3 | Q2 | 25000 | 112.5 | `=RADIANS(C3)` | 1.9635 |

4 | Q3 | 15000 | 67.5 | `=RADIANS(C4)` | 1.1781 |

##### π **Explanation**

In this example, we have **quarterly sales data**. The angles are calculated for a pie chart. We use the **RADIANS** function to convert these angles for trigonometric calculations that might be needed for advanced data visualization.

#### π **Example 6: Calculating Adjusted Angles with IF Function**

##### π― **Purpose of Example**

To adjust angles for a wind direction analysis, where angles greater than 180 degrees need to be halved.

##### π **Data Sheet and Formulas**

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

1 | Wind Direction | Angle | Adjusted Angle | Radians | Result |

2 | North | 45 | `=IF(B2>180, B2/2, B2)` | `=RADIANS(C2)` | 0.7854 |

3 | South | 270 | `=IF(B3>180, B3/2, B3)` | `=RADIANS(C3)` | 2.3562 |

4 | West | 90 | `=IF(B4>180, B4/2, B4)` | `=RADIANS(C4)` | 1.5708 |

##### π **Explanation**

In wind direction analysis, angles greater than 180 degrees are often halved for normalization. We use the **IF function** to check if the angle is more significant than 180 degrees. If it is, we halve it; otherwise, we keep it as is. Then, we use the **RADIANS function** to convert these adjusted angles for further trigonometric analysis.

#### π **Example 7: Summing Angles with SUM Function**

##### π― **Purpose of Example**

To sum up the angles of a polygon and convert the sum to radians for geometric calculations.

##### π **Data Sheet and Formulas**

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

1 | Side | Angle | Sum of Angles | Radians | Result |

2 | Side 1 | 60 | `=SUM(B2:B4)` | `=RADIANS(C2)` | 1.0472 |

3 | Side 2 | 60 | `=SUM(B2:B4)` | `=RADIANS(C3)` | 1.0472 |

4 | Side 3 | 60 | `=SUM(B2:B4)` | `=RADIANS(C4)` | 1.0472 |

##### π **Explanation**

In geometry, the sum of the angles of a polygon is crucial for various calculations. Here, we use the **SUM function** to sum up the angles of a triangle. Then, we use the **RADIANS function** to convert this sum into radians for further geometric calculations.

#### π **Example 8: Finding Angles with VLOOKUP Function**

##### π― **Purpose of Example**

To find the angle associated with a given direction from a table and convert it to radians.

##### π **Data Sheet and Formulas**

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

1 | Direction | Angle | Lookup Direction | Radians | Result |

2 | North | 0 | East | `=RADIANS(VLOOKUP(C2, A2:B4, 2, FALSE))` | 0.0000 |

3 | East | 90 | |||

4 | South | 180 |

##### π **Explanation**

This example shows a table of directions and their associated angles. We use the **VLOOKUP function** to find the angle for a given direction (“East” in this case). Then, we use the **RADIANS function** to convert this angle into radians for further analysis.

#### π **Example 9: Rounding Angles with ROUND Function**

##### π― **Purpose of Example**

To round angles to the nearest integer before converting them to radians for simplified calculations.

##### π **Data Sheet and Formulas**

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

1 | Angle | Value | Rounded Angle | Radians | Result |

2 | Angle 1 | 45.6 | `=ROUND(B2, 0)` | `=RADIANS(C2)` | 0.7854 |

3 | Angle 2 | 30.4 | `=ROUND(B3, 0)` | `=RADIANS(C3)` | 0.5236 |

4 | Angle 3 | 60.7 | `=ROUND(B4, 0)` | `=RADIANS(C4)` | 1.0472 |

##### π **Explanation**

Sometimes, you might want to round angles to the nearest integer for simplified trigonometric calculations. We use the **ROUND function** to round the angles and then apply the **RADIANS function** to convert these rounded angles into radians.

#### π **Example 10: Conditional Conversion with IFERROR Function**

##### π― **Purpose of Example**

To safely convert angles to radians, return a default value if the conversion fails.

##### π **Data Sheet and Formulas**

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

1 | Angle | Value | Safe Conversion | Radians | Result |

2 | Angle 1 | 90 | `=IFERROR(B2, 0)` | `=RADIANS(C2)` | 1.5708 |

3 | Angle 2 | #N/A | `=IFERROR(B3, 0)` | `=RADIANS(C3)` | 0.0000 |

4 | Angle 3 | 45 | `=IFERROR(B4, 0)` | `=RADIANS(C4)` | 0.7854 |

##### π **Explanation**

Sometimes, the data might contain errors or non-numeric values. Using the **IFERROR function**, we can handle such cases gracefully. A default value of 0 degrees is used if an error is found. Then, we use the **RADIANS function** to convert these error-free angles into radians.

#### π **Example 11: Conversion Based on Lookup with INDEX-MATCH Function**

##### π― **Purpose of Example**

To find and convert the angle associated with a specific month from a table using the **INDEX-MATCH** function.

##### π **Data Sheet and Formulas**

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

1 | Month | Angle | Lookup Month | Radians | Result |

2 | January | 30 | March | `=RADIANS(INDEX(B2:B4, MATCH(C2, A2:A4, 0)))` | 0.5236 |

3 | February | 60 | |||

4 | March | 90 |

##### π **Explanation**

This example shows a table of months and their associated angles. We use the **INDEX-MATCH function** to find the angle for a specific month (“March”). Then, we use the **RADIANS function** to convert this angle into radians for further analysis.

#### π **Example 12: Conversion with Nested IF and AND Functions**

##### π― **Purpose of Example**

To convert angles to radians only if they are within a specified range using **IF** and **AND** functions.

##### π **Data Sheet and Formulas**

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

1 | Angle | Value | Conditional Angle | Radians | Result |

2 | Angle 1 | 30 | `=IF(AND(B2>=30, B2<=90), B2, 0)` | `=RADIANS(C2)` | 0.5236 |

3 | Angle 2 | 100 | `=IF(AND(B3>=30, B3<=90), B3, 0)` | `=RADIANS(C3)` | 0.0000 |

4 | Angle 3 | 60 | `=IF(AND(B4>=30, B4<=90), B4, 0)` | `=RADIANS(C4)` | 1.0472 |

##### π **Explanation**

In this example, we only want to convert angles within the 30 to 90-degree range. We use the **IF** and **AND functions** to select angles within this range conditionally. Then, we apply the **RADIANS function** to convert these selected angles into radians.

### π Part 3: Tips and Tricks

**π Optimize for Trigonometry**: If you’re doing a lot of trigonometric calculations, it’s often easier to convert all angles to radians at the start.**π Check Your Units**: Always ensure the angles you’re converting are in degrees. A common mistake is to input radians and attempt to convert them to radians again.**π Use in Conjunction**: The**RADIANS**function is often used with trigonometric functions like**SIN, COS, and TAN**to make calculations more accessible and accurate.