Slope Calculator

Calculate the gradient between two points and find the line equation

Slope Calculator

Point 1 (x₁, y₁)
Point 2 (x₂, y₂)
Calculation Results
Slope (m):
Angle of Inclination (θ):
Line Equation:
Distance Between Points:
Formulas Used:
Slope (m) = (y₂ - y₁) / (x₂ - x₁)
Angle (θ) = arctan(m) in degrees
Line Equation: y - y₁ = m(x - x₁)
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

About Slope Calculator

The slope or gradient of a line describes its steepness, incline, or grade. A higher slope value indicates a steeper incline. Our slope calculator helps you find the slope between two points, determine the line equation, calculate the angle of inclination, and find the distance between points.

Key Concepts

Practical Applications

1. Roof Pitch Calculation

Example: A roof rises 6 inches for every 12 inches of horizontal distance.

Slope: 6/12 = 0.5 (or 26.57° angle)

2. Road Gradient

Example: A road climbs 100 meters over 1 kilometer of horizontal distance.

Slope: 100/1000 = 0.1 (or 5.71° angle)

3. Physics Problems

Example: A position-time graph with points at (0s, 0m) and (5s, 20m).

Slope: (20-0)/(5-0) = 4 m/s (velocity)

Frequently Asked Questions

A slope of 1 means the line rises 1 unit vertically for every 1 unit of horizontal distance. This creates a 45° angle with the x-axis. In practical terms, it represents a 1:1 ratio, like a ramp that rises 1 foot for every foot of horizontal run.

A negative slope means the line decreases (falls) as you move from left to right. In real-world terms, this could represent:
  • Decreasing temperature over time
  • Depreciation of an asset's value
  • Downhill sections on a hiking trail

In mathematics, "slope" and "gradient" are often used interchangeably to describe the steepness of a line. However, in some contexts:
  • Slope typically refers to the incline of a line in two dimensions
  • Gradient can refer to the slope in any number of dimensions and is also used in vector calculus
For most practical purposes, especially in 2D coordinate geometry, they mean the same thing.
Tip: For vertical lines (undefined slope), enter the same x-coordinates for both points. For horizontal lines (zero slope), enter the same y-coordinates.