Angle Between Two Points Formula

Angle Calculation Formula:

\[ \theta = \arctan\left(\frac{y_2 - y_1}{x_2 - x_1}\right) \]

Point 1 X-coordinate (x₁):

Point 1 Y-coordinate (y₁):

Point 2 X-coordinate (x₂):

Point 2 Y-coordinate (y₂):

Angle (θ) between points:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Angle Between Two Points?

Definition: This calculator determines the angle (θ) formed between two points in a 2D plane relative to the positive x-axis.

Purpose: Useful in geometry, physics, engineering, and computer graphics for determining direction or orientation between points.

2. How Does the Calculator Work?

The calculator uses the arctangent function:

\[ \theta = \arctan\left(\frac{y_2 - y_1}{x_2 - x_1}\right) \]

Where:

θ — Angle in degrees between the line and positive x-axis
(x₁, y₁) — Coordinates of the first point
(x₂, y₂) — Coordinates of the second point

Explanation: The function calculates the ratio of vertical change (Δy) to horizontal change (Δx) and returns the corresponding angle.

3. Importance of Angle Calculation

Details: Knowing the angle between points is essential for determining direction, slope, orientation in navigation systems, and many engineering applications.

4. Using the Calculator

Tips: Enter the coordinates of two points in meters. The calculator will determine the angle from point 1 to point 2 relative to the positive x-axis.

5. Frequently Asked Questions (FAQ)

Q1: What range of angles does this produce?
A: The calculator returns angles between -180° and +180° (full circle).

Q2: What happens if the points have the same x-coordinate?
A: Vertical lines return ±90° depending on the y-direction.

Q3: How is this different from slope calculation?
A: Slope gives the ratio (Δy/Δx) while this gives the actual angle in degrees.

Q4: Can I use this for 3D points?
A: No, this is for 2D only. 3D requires additional calculations for azimuth and elevation.

Q5: Does the angle represent compass bearing?
A: Not directly. For compass bearings, you'd need to adjust for the reference direction (North).