# Excel ATAN2 Function

## What is ATAN2 function in Excel?

The ATAN2 function is one of the math functions of Excel.

It Returns the arctangent of the specified x- and y- coordinates, in radians between -Pi and Pi, excluding -Pi.

We can find this function in Math & trig category of insert function Tab.

## How to use ATAN2 function in excel

1. Click on an empty cell (like F5).

2. Click on the fx icon (or press shift+F3).

3. In the insert function tab you will see all functions.

4. Select math and trig category.

5. Select ATAN2 function.

6. Then select ok.

7. In the function arguments Tab you will see ATAN2 function.

8. X section num is the x-coordinate of the point.

9. Y section num is the y-coordinate of the point.

10. You will see results in the formula result section.

## Examples of ATAN2 function in Excel

1. If you have two values representing the x and y coordinates of a point, you can use ATAN2 to calculate the angle between that point and the origin:

`=ATAN2(B2,A2)`

1. You can use ATAN2 with trigonometry functions like SIN and COS to solve for missing angles or sides in right triangles:

`=ATAN2(B2,A2)-SIN(B2/A2)`

1. ATAN2 can help you calculate the bearing (or direction) between two points on a map based on their coordinates. For example:

`=DEGREES(ATAN2(C2-E2,D2-F2))`

1. You can use ATAN2 to convert rectangular coordinates to polar coordinates:

`=SQRT(A2^2+B2^2), ATAN2(B2,A2)`

1. In 3D graphics programming, ATAN2 is often used to calculate the rotation angle needed to orient an object towards a specific position.

`=ATAN2(Y1-Y2,X1-X2)`

1. If you have a dataset with two columns representing pairs of x and y data, you can use ATAN2 to create a scatterplot and calculate the correlation between the two variables:

`=ATAN2(CORREL(A2:A100,B2:B100),1)`

1. ATAN2 can be used to calculate the distance and bearing between two GPS coordinates:

`=ACOS(SIN(Lat1)*SIN(Lat2)+COS(Lat1)*COS(Lat2)*COS(Long2-Long1)), ATAN2(COS(Lat2)*SIN(Long2-Long1),COS(Lat1)*SIN(Lat2)-SIN(Lat1)*COS(Lat2)*COS(Long2-Long1))`

1. In robotics, ATAN2 is used to calculate the angle between a robot’s sensor and a target object:

`=ATAN2(TargetY-RobotY,TargetX-RobotX)-RobotAngle`

1. ATAN2 can be used to determine the angle of incidence for a ray of light hitting a surface:

`=ATAN2(COS(IncidentAngle),SIN(IncidentAngle)/n)`

1. You can use ATAN2 in combination with other Excel functions to create advanced financial models, such as calculating the optimal hedging strategy for a portfolio of investments.

Example 1:

### How to use ATAN2 function in excel

You can see examples of ATAN2 function below:

``````atan2(A2,B2) ----->>>>answer is  0.785

## Mastering the Syntax of the ATAN2 Function in Excel

The syntax for the ATAN2 function in Excel is as follows: =ATAN2(x_num, y_num) where x_num is the numeric value of the x-coordinate and y_num is the numeric value of the y-coordinate. The function returns the arctangent of the specified coordinates, expressed in radians.

Example: Let’s say we have a right triangle with sides A = 3 and B = 4. To find the angle θ opposite side A, we can use the ATAN2 function as follows: =ATAN2(3,4) The result will be approximately 0.93 radians, which is equivalent to 53.13 degrees.

## Understanding the Arguments of the ATAN2 Function in Excel

As mentioned earlier, the ATAN2 function takes two arguments: x_num and y_num. These arguments correspond to the x-coordinate and y-coordinate of the point, respectively. The atan2 function is particularly useful in geometry, where it is used to calculate the angle between the x-axis and a line from the origin to a point (x,y).

Example: Let’s say we have a point P with coordinates (6,8). To find the angle between the x-axis and the line segment connecting the origin and P, we can use the ATAN2 function as follows: =ATAN2(8,6) The result will be approximately 0.93 radians, which is equivalent to 53.13 degrees.

## ATAN vs ATAN2 Functions in Excel: What’s the Difference?

The main difference between the ATAN and ATAN2 functions in Excel is that the former only takes one argument (the tangent of an angle), while the latter takes two arguments (the x-coordinate and y-coordinate of a point). The ATAN2 function is therefore more versatile than the ATAN function.

Example: Let’s say we have a right triangle with sides A = 3 and B = 4. To find the angle θ opposite side A, we can use either the ATAN or ATAN2 function as follows: =ATAN(3/4) or =ATAN2(3,4) Both functions will return approximately 0.93 radians, which is equivalent to 53.13 degrees.

## Using ATAN2 Function in Excel to Calculate Angles in Degrees

By default, the ATAN2 function returns the angle in radians. To convert the result to degrees, you can use the DEGREES function in Excel.

Example: Let’s say we have a point P with coordinates (6,8). To find the angle between the x-axis and the line segment connecting the origin and P in degrees, we can use the ATAN2 and DEGREES functions as follows: =DEGREES(ATAN2(8,6)) The result will be approximately 53.13 degrees.

## Using ATAN2 Function in Excel to Calculate Angles in Radians

The ATAN2 function in Excel is used to calculate the arctangent of two numbers (x and y). The syntax of the ATAN2 function is as follows:

``````=ATAN2(x,y)
``````

where x is the horizontal coordinate and y is the vertical coordinate. The result of the function is an angle in radians between -π and π.

Example: Let’s say you have a right triangle with sides A = 3 and B = 4. To find the angle θ opposite side A, we can use the ATAN2 function as follows:

``````=ATAN2(3,4)
``````

This will give you the angle in radians, which is approximately 0.93 radians.

## Negative Angles with ATAN2 Function in Excel: Is It Possible?

Yes, the ATAN2 function in Excel can also return negative angles. Negative angles represent angles that are measured clockwise from the positive x-axis, rather than counterclockwise.

Example: Let’s say you have a point P with coordinates (-1,-1). To find the angle between the x-axis and the line segment connecting the origin and P, you can use the ATAN2 function as follows:

``````=ATAN2(-1,-1)
``````

This will give you the angle in radians, which is approximately -2.35 radians.

## Incorporating the ATAN2 Function into Formulas in Excel

The ATAN2 function in Excel can be incorporated into formulas to perform more complex calculations involving trigonometry and geometry. For example, you can use the ATAN2 function to find the direction of a vector in two-dimensional space.

Example: Let’s say you have two points, A and B, with coordinates (2,3) and (5,7), respectively. To find the direction of the vector pointing from A to B, you can use the ATAN2 function as follows:

``````=ATAN2(7-3,5-2)
``````

This will give you the angle in radians between the positive x-axis and the vector pointing from A to B.

## Implementing the ATAN2 Function in VBA Code in Excel

You can also use the ATAN2 function in VBA code in Excel to perform more advanced calculations. To do so, simply call the ATAN2 function within your VBA code, using the same syntax as you would in a regular Excel formula.

Example: Let’s say you have a user-defined function in VBA that takes two arguments, x and y, and returns the arctangent of the ratio y/x. You can implement this function using ATAN2 as follows:

``````Function MyArctan(x As Double, y As Double) As Double
MyArctan = Application.WorksheetFunction.Atan2(y, x)
End Function
``````

This code will return the arctangent in radians of the ratio y/x, using the ATAN2 function in Excel.

## The Output Range of the ATAN2 Function in Excel: What You Need to Know

The ATAN2 function in Excel returns an output range of values between -π and π radians (-180 and 180 degrees). This is because the function calculates the angle of the line connecting two points with respect to the positive x-axis, which can be negative or positive.

Example: Let’s say you have two points, A and B, with coordinates (2,3) and (5,7), respectively. To find the direction of the vector pointing from A to B, you can use the ATAN2 function as follows:

``````=ATAN2(7-3,5-2)
``````

This will give you the angle in radians between the positive x-axis and the vector pointing from A to B, which will fall within the range of -π to π.

## Tips for Ensuring Accurate Results with the ATAN2 Function in Excel

To ensure accurate results when using the ATAN2 function in Excel, it is important to remember that the function requires two arguments: the horizontal coordinate (x_num) and the vertical coordinate (y_num). Here are some tips to keep in mind when using the function:

1. Make sure that you specify the correct order for the x_num and y_num arguments. The first argument should always be the horizontal coordinate, and the second argument should be the vertical coordinate.
2. Ensure that the signs of the x_num and y_num arguments are correct. The sign of the x_num argument determines the quadrant in which the point lies (positive x and y for the first quadrant, negative x and positive y for the second quadrant, etc.).
3. Use the DEGREES function to convert the output of the ATAN2 function from radians to degrees, if necessary.

## Common Errors to Avoid When Using the ATAN2 Function in Excel

Here are some common errors to avoid when using the ATAN2 function in Excel:

1. Specifying the wrong order for the x_num and y_num arguments. This can result in incorrect output values, since the ATAN2 function treats the two arguments differently.
2. Forgetting to convert the output of the ATAN2 function from radians to degrees (or vice versa), if necessary. This can lead to incorrect angle measurements.
3. Using incorrect or inconsistent units of measure for the x_num and y_num arguments. Make sure that both arguments use the same units of measure (e.g. inches, meters, etc.).

## Handling Complex Numbers with the ATAN2 Function in Excel

The ATAN2 function in Excel is designed to handle real numbers only. However, you can use the IMAGINARY and REAL functions in Excel to separate complex numbers into their real and imaginary parts, and then use the ATAN2 function to calculate the angle between the real and imaginary components.

Example: Let’s say you have a complex number z = 3 + 4i. To find the angle between the real and imaginary components of z, you can use the following formula:

``````=ATAN2(IMAGINARY(z), REAL(z))
``````

This will give you the angle in radians between the positive x-axis and the vector pointing from the origin to the point represented by the complex number z.

## Inverse of the ATAN2 Function in Excel: What Does It Do?

The inverse of the ATAN2 function in Excel is the TAN function. The TAN function takes an angle in radians as its argument and returns the tangent of that angle. In other words, if you know the angle between a line and the positive x-axis (calculated using the ATAN2 function), you can use the TAN function to find the slope of the line.

Example: Let’s say you have a line with an angle of 0.93 radians (or 53.13 degrees) relative to the positive x-axis. To find the slope of the line, you can use the TAN function as follows:

``````=TAN(0.93)
``````

This will give you the slope of the line.

## Trigonometric Calculations with the ATAN2 Function in Excel

In addition to finding the direction between two points, the ATAN2 function in Excel can also be used for other trigonometric calculations, such as finding the distance between two points or the angle between two lines.

Example: Let’s say you have two points, A and B, with coordinates (2,3) and (5,7), respectively. To find the distance between the two points, you can use the following formula:

``````=SQRT((5-2)^2+(7-3)^2)
``````

To find the angle between the line passing through A and B and the positive x-axis, you can use the ATAN2 function as follows:

``````=ATAN2(7-3,5-2)
``````

## Finding Direction Between Two Points with the ATAN2 Function in Excel

One common use of the ATAN2 function in Excel is to find the direction between two points. By calculating the angle between the line connecting two points and the positive x-axis, you can determine the direction of the line relative to due east.

Example: Let’s say you have two points, A and B, with coordinates (2,3) and (5,7), respectively. To find the direction of the line pointing from A to B, you can use the ATAN2 function as follows:

``````=ATAN2(7-3,5-2)
``````

This will give you the angle in radians between the positive x-axis and the vector pointing from A to B. To convert this angle to degrees and determine the direction, you can use the following formula:

``````=ROUND(DEGREES(ATAN2(7-3,5-2))/22.5,0)*22.5
``````

This will give you the direction of the line rounded to the nearest 22.5 degrees.

## Working with Non-Numeric Values and the ATAN2 Function in Excel

The ATAN2 function in Excel is designed to handle numeric values only. If you try to use the function with non-numeric values, such as text or Boolean values, you will get a #VALUE error. To avoid this error, make sure that both arguments for the ATAN2 function are numeric.

Example: Let’s say you have a table with coordinates for several points, but some of the cells contain text instead of numbers. To find the direction between two points, you can use the following formula to ensure that only numeric values are used:

``````=IF(ISNUMBER(A2),IF(ISNUMBER(B2),ATAN2(B2-A2,D2-C2),""),"")
``````

## Practical Applications of the ATAN2 Function in Excel

The ATAN2 function in Excel has a wide range of practical applications, particularly in the fields of engineering, physics, and mathematics. Some examples of its applications include:

1. Navigation: The ATAN2 function can be used to determine the direction between two points on a map, which is useful for navigation purposes.
2. Robotics: The ATAN2 function can be used to calculate the angle between a robot arm and its base, which is important for controlling the movement of the arm.
3. Statistics: The ATAN2 function can be used to calculate the direction of a trend line in a scatter plot, which is useful for analyzing data trends.
4. Physics: The ATAN2 function can be used to determine the direction of a vector in three-dimensional space, which is important for calculating forces and velocities.

## Comparing the ATAN2 Function to Other Trigonometric Functions in Excel

The ATAN2 function in Excel is similar to other trigonometric functions, such as SIN, COS, and TAN. However, there are some key differences between these functions.

• The SIN and COS functions take an angle as their argument, whereas the ATAN2 function takes two coordinates (x and y) as its arguments.
• The TAN function returns the tangent of an angle, while the ATAN2 function returns the angle itself.
• The ATAN function in Excel is similar to the ATAN2 function, but it only takes one argument (the ratio of the opposite and adjacent sides of a right triangle).
• The COT function in Excel is the reciprocal of the TAN function, while the ACOT function is the inverse of the ATAN function.

## Limitations and Restrictions When Using the ATAN2 Function in Excel

While the ATAN2 function in Excel is a powerful tool for trigonometric calculations, there are some limitations and restrictions to keep in mind:

1. The ATAN2 function is limited to two-dimensional space. It cannot be used for calculations involving three-dimensional space.
2. The ATAN2 function can return undefined values (i.e. #DIV/0! errors) if the denominator of the slope calculation is zero.
3. The ATAN2 function may produce inaccurate results if the input coordinates are very large or very small. In such cases, it may be necessary to use specialized software or algorithms to achieve greater precision.