Slope Calculator

Slope fundamentals at a glance

Slope measures how quickly a line rises or falls as it moves horizontally. It is a cornerstone of analytic geometry and appears throughout physics, engineering, and data analysis.

Key ideas

• Slope definition: Slope m quantifies the steepness or inclination of a line. Positive slopes rise as x increases, negative slopes fall, and a slope of zero corresponds to a perfectly horizontal line.
• Formula meaning: The slope formula m = Δy / Δx compares vertical change (y₂ − y₁) to horizontal change (x₂ − x₁). It is often summarized as rise over run.
• Angle of inclination θ: θ ranges from 0° to 180°. The relationship m = tan(θ) links slope to angle. At θ = 90° the line is vertical, Δx = 0, and slope is undefined because division by zero is not possible.
• Distance along a line: When you know a starting point, slope (or angle), and a distance, the calculator produces both points located that distance away in opposite directions. Vertical lines shift only in y, while other lines move in both x and y according to the slope.
• Practical significance: Slope expresses rates of change such as velocity in physics or gradient on a hiking trail. For example, the points (0, 0) and (2, 4) yield m = 2, meaning y increases two units for every unit of x.