This slope calculator finds the slope of the line through two points — and everything that comes with it: the line’s equation, distance between the points, midpoint and angle. Enter the coordinates and get the full picture instantly.
What Is Slope?
Slope measures how steep a line is: for every unit you move right, how much does the line rise (or fall)? It is the “rise over run” of algebra class and the rate of change behind everything from road grades to speed on a distance-time graph. This calculator is part of our Math Calculators collection.
The Slope Formula
m = (y₂ − y₁) ÷ (x₂ − x₁)
Worked example (verified): points (2, 3) and (5, 11): m = (11 − 3) ÷ (5 − 2) = 8 ÷ 3 = 2.667. The line climbs 8 units for every 3 across. Its equation is y = 2.667x − 2.333, the distance between the points is 8.544, the midpoint is (3.5, 7), and the line’s angle is 69.44° — all shown above when you press Calculate.
Reading a Slope
- Positive slope: the line rises left to right (growth).
- Negative slope: the line falls left to right (decline).
- Zero slope: a horizontal line — y never changes.
- Undefined slope: a vertical line — x never changes, division by zero.
- Bigger |m| = steeper. A slope of 3 is steeper than a slope of 1.
Slope in Real Life
- Roads and ramps: grade is slope as a percentage — rise ÷ run × 100. A wheelchair ramp at 1:12 has slope 0.083 (8.3%).
- Graphs of change: on a distance-time graph, slope is speed; on a velocity-time graph, slope is acceleration.
- Roofs: pitch is quoted as rise over a 12-unit run (“6/12 pitch” = slope 0.5).
The distance between the two points comes from Pythagoras’ theorem — see the Pythagorean Theorem Calculator for the right-triangle side of the story, and keep fractions exact with the Fraction Calculator.
Related Tools
- Pythagorean Theorem Calculator — the distance formula’s root
- Fraction Calculator — exact rise/run fractions
- Scientific Notation Calculator
Frequently Asked Questions
How do I find slope from two points?
Subtract the y-values, subtract the x-values (same order), divide: m = (y₂ − y₁)/(x₂ − x₁).
What is the slope of a vertical line?
Undefined — the run is zero and division by zero has no answer. Vertical lines have equations like x = 4.
What is the slope-intercept form?
y = mx + b, where m is the slope and b is where the line crosses the y-axis. This calculator produces it directly.
Can slope be a fraction?
Yes — most slopes are. 8/3 and 2.667 are the same slope; the calculator shows both forms.
How is slope related to angle?
Slope = tan(angle). A 45° line has slope 1; the calculator converts with the arctangent.
Is this slope calculator free?
Yes — free, instant, no sign-up.