Learn About Slope

The ideas behind the calculators, explained without the textbook voice. Read one of these first if the tools are giving you the right answer but you are not sure why.

Start here What Is Slope?

The complete guide: what slope measures, the formula, the four types, and where it turns up outside a maths class.

Read the guide →How to Find Slope

Three methods, worked through: from two points, from a graph, and from an equation in any form.

Read the guide →

The whole topic in one picture

If you take one thing from this section, make it this triangle. Slope is the vertical leg divided by the horizontal leg — everything else on the site is a variation on that.

Slope shown as a rise over run triangle between two points on a linexy(x₁, y₁)(x₂, y₂)run = Δxrise = Δym = rise ÷ run
Slope is the rise (vertical change) divided by the run (horizontal change) between any two points on the line.

Where should I start?

  1. What Is Slope? — start here if the word itself is new, or if positive, negative, zero and undefined still get muddled.
  2. How to Find Slope — read this when you know what slope is and need the method for a specific question type.
  3. The slope calculator — check your answers, and read the step panel to compare your working with the calculator's.

The four types at a glance

Four types of slope: positive, negative, zero and undefinedPositivem > 0 · goes upNegativem < 0 · goes downZerom = 0 · horizontalUndefinedrun = 0 · vertical
A line rises, falls, stays flat, or runs straight up — those four cases cover every slope you can meet.

Two of these cause almost all the confusion. A horizontal line has a slope of zero — it has a slope, and that slope happens to be nothing. A vertical line has an undefined slope — there is no number at all, because the run is zero and dividing by zero has no answer.

Studying for a test?

Three things are worth having automatic before an exam:

  • The formula, written the right way up: rise over run, not run over rise.
  • The difference between zero and undefined.
  • Perpendicular slopes multiply to −1, so you flip the fraction and change the sign.

Everything else you can rebuild from the triangle in about ten seconds.

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Slope vs Grade vs Pitch: The Same Number in Three TradesA math teacher calls it slope, a surveyor calls it grade, a roofer calls it pitch. They are the same ratio in ...Aug 20, 2026
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