2 Slope in Degrees Calculator

This calculator helps you find the angle between two points in degrees using the 2-point slope formula. Whether you're working with coordinates in a coordinate plane or measuring the angle between two locations, this tool provides an accurate and easy-to-use solution.

What is 2-point slope?

The 2-point slope, also known as the slope between two points, is a measure of the steepness and direction of a line connecting two points in a coordinate plane. It's calculated using the vertical change (rise) and horizontal change (run) between the two points.

When converted to degrees, the 2-point slope represents the angle that the line makes with the positive direction of the x-axis. This angle is crucial in various fields including geometry, physics, and engineering.

How to calculate 2-point slope in degrees

To calculate the angle between two points in degrees, follow these steps:

Identify the coordinates of the two points: (x₁, y₁) and (x₂, y₂)
Calculate the horizontal change (Δx) and vertical change (Δy) between the points
Use the arctangent function to find the angle in radians
Convert the angle from radians to degrees

This process gives you the angle that the line connecting the two points makes with the positive x-axis.

Formula

The formula to calculate the angle θ between two points (x₁, y₁) and (x₂, y₂) in degrees is:

θ = atan2(Δy, Δx) × (180/π)

Where:

Δy = y₂ - y₁ (vertical change)
Δx = x₂ - x₁ (horizontal change)
atan2 is the two-argument arctangent function
π is the mathematical constant pi (approximately 3.14159)

The atan2 function automatically determines the correct quadrant for the angle based on the signs of Δy and Δx, providing an accurate result between -180° and 180°.

Worked example

Example calculation

Let's calculate the angle between points A (2, 3) and B (5, 7):

Δy = 7 - 3 = 4
Δx = 5 - 2 = 3
θ = atan2(4, 3) × (180/π) ≈ 53.13°

The angle between points A and B is approximately 53.13 degrees.

This example demonstrates how to apply the formula to find the angle between two specific points. The calculator automates this process for any coordinates you input.

FAQ

What is the difference between slope and angle?

Slope is a ratio of vertical change to horizontal change (Δy/Δx), while angle is the measure of the direction of the line relative to the positive x-axis. The angle can be calculated from the slope using the arctangent function.

How do I convert slope to degrees?

To convert slope (m) to degrees, use the formula: θ = atan(m) × (180/π). This gives you the angle that the line makes with the positive x-axis.

What if the angle is negative?

A negative angle indicates that the line is descending from left to right. The absolute value represents the magnitude of the angle, while the sign indicates the direction.