The Coordinate Angle Calculator helps determine the angle between a line connecting two points on a Cartesian coordinate system and the positive x-axis. This tool is widely used in navigation, physics, engineering, and computer graphics. By entering the coordinates of two points, it calculates the angle in degrees or radians, simplifying complex geometric problems.
This calculator ensures precision, saves time, and is ideal for professionals and students working with coordinate-based systems.
Formula of Coordinate Angle Calculator
The formula to calculate the coordinate angle is:
Coordinate Angle (theta) = arctan((y2 – y1) / (x2 – x1))
Detailed Formula Components:
- x1, y1: The coordinates of the first point.
- x2, y2: The coordinates of the second point.
- theta: The angle between the line connecting the two points and the positive x-axis, measured in radians or degrees.
Special Cases:
- Vertical Line:
- If x2 – x1 = 0, the angle is:
- 90 degrees (pi/2 radians) if y2 > y1.
- -90 degrees (-pi/2 radians) if y2 < y1.
- If x2 – x1 = 0, the angle is:
- Horizontal Line:
- If y2 – y1 = 0, the angle is:
- 0 degrees (0 radians) if x2 > x1.
- 180 degrees (pi radians) if x2 < x1.
- If y2 – y1 = 0, the angle is:
Pre-Calculated Values Table
This table provides reference values for common coordinate pairs:
| Point 1 (x1, y1) | Point 2 (x2, y2) | Delta y = y2 – y1 | Delta x = x2 – x1 | Angle (degrees) | Angle (radians) |
|---|---|---|---|---|---|
| (0, 0) | (1, 1) | 1 | 1 | 45 | 0.785 |
| (0, 0) | (1, 0) | 0 | 1 | 0 | 0.000 |
| (0, 0) | (0, 1) | 1 | 0 | 90 | 1.570 |
| (1, 1) | (2, 3) | 2 | 1 | 63.43 | 1.107 |
| (2, 3) | (1, 1) | -2 | -1 | -116.57 | -2.034 |
Example of Coordinate Angle Calculator
Scenario:
Calculate the angle between the line connecting points A (3, 4) and B (7, 10) and the positive x-axis.
Step-by-Step Solution:
- Identify coordinates:
- Point A: x1 = 3, y1 = 4
- Point B: x2 = 7, y2 = 10
- Calculate differences:
- Delta y = y2 – y1 = 10 – 4 = 6
- Delta x = x2 – x1 = 7 – 3 = 4
- Apply the formula: theta = arctan(Delta y / Delta x) theta = arctan(6 / 4) = arctan(1.5)
- Find the angle: Using a calculator, arctan(1.5) is approximately 56.31 degrees or 0.983 radians.
Result:
The angle is approximately 56.31 degrees or 0.983 radians.
Most Common FAQs
Yes, the calculator works with all coordinate values, including negative ones, as long as the points are well-defined.
Angles are measured counterclockwise from the positive x-axis. Negative angles represent clockwise directions.
This calculator is useful in navigation, robotics, physics, and graphics, where understanding direction or orientation is essential.