Find The Angle of Degrees Calculator

How to Use This Calculator

Using the Find the Angle of Degrees Calculator is straightforward. Follow these steps:

1. Enter the coordinates of the first point (x₁, y₁).
2. Enter the coordinates of the second point (x₂, y₂).
3. Click the "Calculate" button to find the angle in degrees.
4. Review the result and the visualization of the angle.

The calculator will display the angle between the two points in degrees, along with a graphical representation of the angle.

Formula Explained

The angle θ between two points (x₁, y₁) and (x₂, y₂) can be calculated using the following formula:

This formula uses the arctangent function (atan2) to calculate the angle in radians, which is then converted to degrees by multiplying by (180/π).

The atan2 function is particularly useful because it correctly determines the quadrant of the angle based on the signs of the x and y differences.

Worked Examples

Example 1: Basic Angle Calculation

Let's find the angle between the points (1, 2) and (4, 6).

1. Calculate the differences: Δx = 4 - 1 = 3, Δy = 6 - 2 = 4.
2. Use the formula: θ = atan2(4, 3) × (180/π) ≈ 53.13°.

The angle between the points (1, 2) and (4, 6) is approximately 53.13 degrees.

Example 2: Angle in Different Quadrant

Find the angle between the points (3, 4) and (-2, 5).

1. Calculate the differences: Δx = -2 - 3 = -5, Δy = 5 - 4 = 1.
2. Use the formula: θ = atan2(1, -5) × (180/π) ≈ 163.69°.

The angle between the points (3, 4) and (-2, 5) is approximately 163.69 degrees, which places it in the second quadrant.