C# | Math.Atan2() Method

Last Updated : 11 Jul, 2025

Math.Atan2() is an inbuilt Math class method which returns the angle whose tangent is the quotient of two specified numbers. Basically, it returns an angle θ (measured in radian) whose value lies between -π and π. This is a counterclockwise angle lies between the positive x-axis, and the point (x, y). Syntax:

public static double Atan2(double value1, double value2)

Parameters:

value1: y coordinate of the point of type System.Double. value2: x coordinate of the point of type System.Double.

Return Type: Returns the angle Θ of type System.Double. Note: An angle, θ(measured in radians), such that -π ≤ θ ≤ π, and tan(θ) = value1 / value2, where (value1, value2) are the points in the cartesian plane. There are two conditions for the return values:

When the points lies in the Cartesian plane
When the points lies on the boundaries of the quadrants

Below are the programs to demonstrate the Math.Atan2() Method when the points lies in the Cartesian plane:

Program 1: If point(value1, value2) lies in the first quadrant i.e., 0 < θ < π / 2
Output:
```
45
```
Program 2: If point(value1, value2) lies in the second quadrant i.e., π / 2 < θ ≤ π
Output:
```
135
```
Program 3: If point(value1, value2) lies in the third quadrant i.e., -π < θ < -π / 2
Output:
```
-135
```
Program 4: If point(value1, value2) lies in the fourth quadrant i.e., -π / 2 < θ < 0
Output:
```
-45
```

Below are the programs to demonstrate the Math.Atan2() Method when the points lies on the boundaries of the quadrants:

Program 1: If value1 is 0 and value2 is not negative i.e. θ = 0
Output:
```
0
```
Program 2: If value1 is 0 and value2 is negative i.e. θ = π
Output:
```
180
```
Program 3: If value1 is positive and value2 is 0 i.e. θ = π / 2
Output:
```
90
```
Program 4: If value1 is negative and value2 is 0 i.e. θ = -π / 2
Output:
```
-90
```
Program 5: If value1 is 0 and value2 is 0 i.e. θ = 0
Output:
```
0
```

Important Point to Remember: If value1 or value2 is NaN, or if value1 and value1 are either PositiveInfinity or NegativeInfinity, the method returns NaN. Example:

Output: