Calculator Tools
Calculate rise, run and slope from two coordinate points or direct changes. See a simplified exact fraction, concise decimal and line equation, with correct handling for horizontal and vertical lines.
Formula
m = (y₂ − y₁) ÷ (x₂ − x₁) = rise ÷ run
Simple workflow
How to use Slope Calculator
- 1Choose Two points or Rise and run.
- 2Enter the labelled coordinates or changes as integers or decimals.
- 3Select Calculate slope to see rise, run, exact slope, decimal and the line equation where available.
Good to know
Frequently asked questions
What is the slope formula for two points?
Subtract the y-values for rise and the x-values for run, then divide: m = (y₂ − y₁) / (x₂ − x₁).
What is the slope of a vertical line?
It is undefined because the run is zero and division by zero is not defined. Two-point mode instead shows the vertical equation x = constant.
What is the slope of a horizontal line?
It is 0 because the y-values do not change, so rise is zero while run is nonzero.
Why show both a fraction and decimal?
The simplified fraction preserves the exact ratio. The decimal is convenient for reading but may be rounded when the value repeats.
Practical guide
Calculate rise over run from two points or direct changes
Slope describes how y changes as x changes. From two points, subtract y₁ from y₂ for the rise and x₁ from x₂ for the run, then divide: m = (y₂ − y₁) / (x₂ − x₁).
Two-point mode also calculates the y-intercept for y = mx + b. Rise-and-run mode can find the slope without enough information to determine a unique intercept.
Worked example
Find the line through (1, 2) and (3, 6)
- Start with
- x₁ = 1, y₁ = 2, x₂ = 3 and y₂ = 6.
- Choose
- Choose Two points and calculate.
- You get
- Rise = 4, run = 2, slope = 2 and the line equation is y = 2x.
Tips for a useful result
- A horizontal line has a rise of zero and slope 0.
- A vertical line has a run of zero, so its slope is undefined and its equation is x = constant.
- A fractional slope is shown exactly and with a concise decimal equivalent.
Precision and limitations
Ordinary decimal inputs are converted to integer fractions before the calculation. This avoids binary floating-point artifacts in subtraction, simplification and the line equation.
The tool calculates straight-line slope in a Cartesian plane. It does not fit a trend line to a collection of data points or estimate measurement uncertainty.
Coordinates and results remain local to this page and are not stored or transmitted.
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