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Geometry

Slope Calculator

Slope from 2 points. Free online Slope Calculator. Calculate slope online — fast, accurate, mobile-friendly, no signup needed.

m = (y₂ − y₁) / (x₂ − x₁).
Slope
2
Y-intercept
0

Derivation

  1. ├── 01Givenx1 = 1, y1 = 2, x2 = 5, y2 = 10
  2. ├── 02FormulaSlope: {let t=e.x1,a=e.y1,n=e.x2;return(e.y2-a) / (n-t)}
  3. ├── 03Substitute{let t=e.1,a=e.2,n=e.5;return(e.10-a) / (n-t)}
  4. ├── 04Compute Slope2
  5. ├── 05FormulaY-intercept: a-(e.y2-a) / (n-t) × t
  6. ├── 06Substitutea-(e.10-a) / (n-t) × t
  7. └── 07Compute Y-intercept0.0000e+0
Did you know?

René Descartes introduced coordinate geometry in 1637 in La Géométrie, letting algebra solve geometric problems for the first time.

§01What is

Understanding the Slope Calculator

The Slope Calculator computes Slope from 4 inputs: x₁, y₁, x₂, y₂. Slope from 2 points.

Geometry is what turns raw measurements into useful answers about space — how much paint, how big a yard, how much material a project will need. Every craftsperson, architect, and DIYer reaches for these formulas regularly. The Slope Calculator sits in that toolkit — it slope from 2 points. Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

Slope = {let t=e.x1,a=e.y1,n=e.x2;return(e.y2-a) / (n-t)} | Y-intercept = a-(e.y2-a) / (n-t) × t

Where

x1
x₁
y1
y₁
x2
x₂
y2
y₂
Slope
Output value
Y-intercept
Output value
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: x₁ = 1, y₁ = 2, x₂ = 5, y₂ = 10.

  1. 01Start by noting the input — x₁: 1.
  2. 02Start by noting the input — y₁: 2.
  3. 03Start by noting the input — x₂: 5.
  4. 04Start by noting the input — y₂: 10.
  5. 05Substitute these values into the formula: Slope = {let t=e.x1,a=e.y1,n=e.x2;return(e.y2-a) / (n-t)} | Y-intercept = a-(e.y2-a) / (n-t) × t
  6. 06Compute Slope: the calculator returns 2.
  7. 07Compute Y-intercept: the calculator returns 0.
  8. 08Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common Slope Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

x₁ halved

x1 = 0.5 (from 1)

Keep every other input at its default and halve the x₁. See how slope responds.

  1. 01New x₁: 0.5
  2. 02Baseline Slope: 2
  3. 03New Slope: 1.77778
  4. 04Slope decreases by 11.1% → use this sensitivity to plan for real-world variation.
02 · PATTERN

x₁ doubled

x1 = 2 (from 1)

Keep every other input at its default and double the x₁. See how slope responds.

  1. 01New x₁: 2
  2. 02Baseline Slope: 2
  3. 03New Slope: 2.66667
  4. 04Slope increases by 33.3% → use this sensitivity to plan for real-world variation.
03 · PATTERN

y₁ halved

y1 = 1 (from 2)

Keep every other input at its default and halve the y₁. See how slope responds.

  1. 01New y₁: 1
  2. 02Baseline Slope: 2
  3. 03New Slope: 2.25
  4. 04Slope increases by 12.5% → use this sensitivity to plan for real-world variation.
04 · PATTERN

y₁ doubled

y1 = 4 (from 2)

Keep every other input at its default and double the y₁. See how slope responds.

  1. 01New y₁: 4
  2. 02Baseline Slope: 2
  3. 03New Slope: 1.5
  4. 04Slope decreases by 25% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
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