Slope Calculator

Slope: A complete guide to lines, angles, and rise/run

Slope measures how steep a line is. It compares vertical change (rise) to horizontal change (run) between two points. This calculator standardizes the process and provides slope, angle of inclination, intercept, and the full line equation — ideal for students, engineers, analysts, and anyone working with linear trends.

What is slope?

Slope \(m\) is defined as \(m=\frac{y_2-y_1}{x_2-x_1}\). Positive slopes rise to the right, negative slopes fall to the right. Zero slope indicates a horizontal line, while an undefined slope indicates a vertical line where \(x_1=x_2\).

Line equations

• Point-slope: \(y - y_1 = m(x - x_1)\).
• Slope-intercept: \(y = mx + b\), where \(b = y_1 - m x_1\).
• Standard form: \(Ax + By = C\), with \(A,B,C\) integers.

Angles and metrics

• Angle of inclination: \(\theta=\arctan(m)\) in degrees.
• Rise/run: Rise \(=y_2-y_1\); Run \(=x_2-x_1\).
• Distance: \(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\).

Best practices

• Check special cases: Handle vertical/horizontal lines explicitly.
• Use consistent units: Ensure \(x\) and \(y\) units align for meaningful slopes.
• Round appropriately: Keep enough precision for angles and intercepts.

Worked example