Slope Calculator

What slope means

Slope measures vertical change for each unit of horizontal change. It is often described as rise over run. A positive slope rises from left to right, a negative slope falls, a horizontal line has slope 0, and a vertical line has undefined slope.

The slope formula

For Point 1 (x₁, y₁) and Point 2 (x₂, y₂), use m = (y₂ − y₁) / (x₂ − x₁). Keep the subtraction order consistent in the numerator and denominator.

Exact fraction and decimal slope

The calculator keeps entered decimals and fractions as exact rational values for algebra. Repeating decimals are labeled approximate so a rounded display value never replaces the exact slope in the equations.

Line equations

For nonvertical lines, the calculator derives the y-intercept and shows both slope-intercept form and point-slope form. Vertical lines use the exact equation x = constant instead.

Percent grade and angle

Percent grade is slope × 100%. The angle is a signed angle from horizontal using arctangent. Physical grade is meaningful only when x and y use compatible, equal-scale units; this app is not a roadway, ramp, roof, or code-compliance checker.

Read the graph carefully

The graph uses the same units-per-pixel on both axes so the visual line does not distort the calculated slope. It supplements the exact values and calculation steps rather than replacing them.

Worked examples

• (2, 3) and (7, 6) give rise 3, run 5, and slope 3/5.
• (-2, 3) and (4, -1) give slope -2/3.
• (3, -2) and (3, 8) form a vertical line with undefined slope.

Common mistakes

• Reversing only one subtraction changes the sign incorrectly.
• Slope is rise divided by run, not run divided by rise.
• A vertical line is undefined, not zero.
• Two identical points do not determine one unique line.