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Slope Calculator | Compute slope and slope-intercept form from two points

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Find the slope between two points as rise over run, then get the complete line equation in slope-intercept form with the intercept shown. Ideal for algebra homework, rate-of-change problems and graphing — the tool displays the full working for each step.

Last updated: June 2026 · Free · No sign-up required

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Results

Enter values above and click Calculate to see your result instantly.

Quick reference

Slope and its meaning:

Slope (m)Line behavior
PositiveRises left to right
NegativeFalls left to right
ZeroHorizontal line
UndefinedVertical line (x1 = x2)

functions Shows the working, not just the answer

For students and teachers, the final number is only half the value. Every math tool here exposes the formula it applied, the intermediate steps, and the rounding rule, so you can follow along, check your homework, or use the answer in a proof or report with confidence.

calculate Accurate to the spec

Calculations use 64-bit floating point with sensible rounding for the domain (currency to 2 decimals, percentages to 4 decimals, algebra to 6 significant figures). Where exact rational arithmetic matters — fractions, factorials, simplification — we use a dedicated BigNumber path so 1/3 + 1/6 returns ½, not 0.49999.

school Free for classroom use

Educators are welcome to link to any math calculator on CalcaTools from a class site, Google Classroom, or worksheet. The pages are mobile-friendly, free, ad-supported (so we can keep them free) and have no sign-up wall — students just click and use them in class or at home.

tips_and_updates Pair with the spoke articles

Below the calculator we link a small set of plain-English explainer pages — "What is a percentage?", "Why does PEMDAS matter?", and so on. They cover the underlying concept in 4–6 short paragraphs. Read those before the calculator if the topic is new, or after if you want the extra context.

Interpretation guide

From two points to the equation:

QuantityFormula
Slope m(y2 - y1) / (x2 - x1)
Y-intercept by1 - m x1
Line equationy = m x + b
Anglearctan(m)

lightbulb Worked example: checking a 1:12 ramp

A ramp runs from (0, 0) to (12, 1) in meters. Does it meet the 1:12 ratio? Slope m = (1 − 0) / (12 − 0) = 1/12 ≈ 0.08333. Y-intercept: b = 0 − (1/12)(0) = 0, so the equation is y = x/12. Incline angle = atan(1/12) ≈ 4.76°. Grade = 8.33%. Ramp length = √(12² + 1²) = √145 ≈ 12.042 m.

Result: Slope 1/12 ≈ 0.0833; equation y = x/12; incline ≈ 4.76°.

What this means: Rise-over-run is exactly 1:12 — the steepest ratio commonly permitted by accessibility guidelines. Any ramp with m > 1/12 over this run would exceed it. The equation y = x/12 also predicts the height at any point: 0.5 m at x = 6 m, for instance.

Formula & methodology

Formula: m = (y2 - y1) / (x2 - x1) = rise / run; y = m x + b

How slope is computed

Slope measures a line's steepness as rise over run between two points (x₁, y₁) and (x₂, y₂):

m = (y₂ − y₁) / (x₂ − x₁)

  • The y-intercept follows: b = y₁ − m·x₁, giving the equation y = mx + b.
  • Inclination angle = atan(m); distance between the points = √((x₂−x₁)² + (y₂−y₁)²).
  • A vertical line (x₂ = x₁) has undefined slope — division by zero.

Reading the result

Positive m rises left to right, negative m falls, m = 0 is horizontal. Points (0, 0) and (12, 1) give m = 1/12 ≈ 0.0833 — an 8.33% grade, or about 4.76° of incline.

Authoritative source: Wolfram MathWorld

Frequently asked questions

How do I calculate slope from two points?
Enter the required values into the input fields and press the calculate button. The tool applies the formula m = (y2 - y1) / (x2 - x1) = rise / run; y = m x + b and returns the result with a short explanation of each step, so you can check the working yourself.
What does a negative slope mean?
The Slope Calculator is a free online tool that enter two points (x1, y1) and (x2, y2) and this tool computes the slope as rise over run, then converts it into slope-intercept form (y = mx + b). it also reports whether the line is rising, falling, horizontal, or vertical, and shows the step-by-step. You enter a few values, and it returns an accurate result together with a step-by-step explanation, so it works as both a calculator and a quick reference for the underlying concept.
Why is a vertical line's slope undefined?
The Slope Calculator is free, private, and accurate: it runs entirely in your browser (no uploads, no accounts), applies the standard calculation, and explains each step so you can verify the result. Enter two points (x1, y1) and (x2, y2) and this tool computes the slope as rise over run, then converts it into slope-intercept form (y = mx + b). It also reports whether the line is rising, falling, horizontal, or vertical, and shows the step-by-step There is no limit on usage, and it works on any device.
How do I find the equation of the line?
The Slope Calculator uses the standard m = (y2 - y1) / (x2 - x1) = rise / run; y = m x + b. You enter your values, and the calculator applies the formula step by step, showing the working so you can verify the math and understand how the result is derived rather than trusting a black box.
What is rise over run?
Rise over run is the ratio of the vertical change to the horizontal change between two points on a line — the definition of slope. From (1, 2) to (4, 11), the rise is 9 and the run is 3, so the slope is 3. The phrase is a memory aid: rise (Δy) divided by run (Δx), which the calculator applies directly when you enter two points.
What slope does a 1:12 wheelchair ramp have?
Rise over run = 1/12 ≈ 0.0833, or 8.33% grade. Through points (0, 0) and (12, 1): m = (1−0)/(12−0) = 1/12, y-intercept 0, equation y = x/12, inclination angle atan(1/12) ≈ 4.76°. A 1:12 ratio is the steepest slope commonly permitted by accessibility guidelines.
How do you tell if two lines are parallel from their slopes?
Parallel lines have identical slopes — y = 2x + 1 and y = 2x − 5 never meet. Perpendicular lines have slopes that multiply to −1 (negative reciprocals): a line of slope 2 is perpendicular to one of slope −1/2. The calculator's equation output makes both checks immediate.
What does a slope of zero look like?
A perfectly horizontal line, like y = 4 — zero rise over any run. It is the flattest possible non-vertical line, with an inclination angle of 0°. Do not confuse it with undefined slope: zero slope is a real number, undefined slope (a vertical line) is not.
How is slope used in economics?
Demand curves slope downward (negative m: higher price, lower quantity) while supply curves slope upward. The steepness encodes elasticity — a flat demand curve means buyers are price-sensitive. Rise-over-run on a price-quantity plot is literally the same m = Δy/Δx calculation.

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