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Math calculator

Coordinate Geometry Calculator

Distance, midpoint, and slope of two points in the plane. Not the Pythagorean-only page. Runs locally.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary Engine tested · Specification checked · 10/10 tests · Production surface contract 3/3 · v1.0.0
Input interpretation
Enter values to calculate.
Result
—
Model
Distance, midpoint, and slope of two plane points.
Scope
Euclidean plane
Verification
Engine tested · 10/10 tests · Production surface contract 3/3 · Specification checked · v1.0.0
Named expert review
Optional · Not performed
Specification basis
  • ISO 80000-2:2019 Quantities and units — Mathematics
Specification basis
Evidence
4 golden · 1 boundary · 5 property · Production surface contract 3/3 · Artifact integrity PASS
Production
Embedded snapshot: unpublished · Build schema 1.0.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status PASS (0 stale; 164 CURRENT) @ 2026-09-16T06:44:24.909Z
Semantic contract
PASS

Formulas

Core equations used by this calculator.

Distanced = √((x₂−x₁)²+(y₂−y₁)²)
MidpointM = ((x₁+x₂)/2, (y₁+y₂)/2)
Slopeslope = (y₂−y₁)/(x₂−x₁)
iShare URLs use x1,y1,x2,y2 — not m (reserved). Vertical lines report undefined slope.

How to use

1

Choose distance, midpoint, or slope

Enter both points. Slope of a vertical line is undefined.

2

Read the scalar or the point

Distance of (0,0) to (3,4) is 5, the same number as a 3-4-5 triangle, on a different model.

Example calculations

Common configurations with formula and result.

ϟ

3-4-5 distance

(0,0) to (3,4)

√(9+16)
5
ϟ

Slope 2

(0,1) to (2,5)

4/2
2

Coordinate Geometry calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
The Euclidean distance between (x₁, y₁) and (x₂, y₂) is √((x₂−x₁)²+(y₂−y₁)²). The midpoint is the average of the coordinates. Slope is Δy/Δx when the line is not vertical.
What it calculates
Distance, midpoint, and slope of two plane points.
Inputs
  • mode
  • x1
  • y1
  • x2
  • y2
Outputs
  • distance
  • mx
  • my
  • slope
  • vertical
Formula
d = √((x₂−x₁)²+(y₂−y₁)²)
Assumptions
  • Euclidean plane
  • Not 3-D / spherical
Units
  • length (consistent units)
Boundary conditions
  • missing coordinates → MISSING_REQUIRED_INPUT
  • unknown mode → INVALID_MODE
Example
distance (0,0)(3,4) → 5
Validation cases

2 published on this page · 10/10 tests · Production surface contract 3/3 · View evidence

  • mode=distance x1=0 y1=0 x2=3 y2=4 → distance=5
  • mode=slope x1=2 y1=0 x2=2 y2=5 → vertical=true
Specification basis
  • ISO 80000-2:2019 Quantities and units — Mathematics
Calculation version
1.0.0

Other calculators in this family: Pythagorean, Circle, Linear equation .

a²+b² Pythagorean › ○ Circle › ax+b Linear equation ›
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Frequently asked questions

Key distinctions behind the calculation.

Is this the Pythagorean calculator?

No. This page takes coordinates. /calc/math/pythagorean solves a right triangle from two sides.

Where does this run?

Locally in the browser by default. REST and MCP call the same coordinate-geometry engine.