Distance Between Two Points Calculator
Find the straight-line distance between two points on a plane.
Results update as you type.
About this calculator
This calculator finds the straight-line distance between two points (x₁, y₁) and (x₂, y₂) using the distance formula, and also reports the horizontal change (Δx), the vertical change (Δy), and the midpoint of the segment, with a plot of the two points.
The distance formula, d = √((x₂ − x₁)² + (y₂ − y₁)²), is simply the Pythagorean theorem applied to a grid: the horizontal and vertical gaps are the two legs of a right triangle and the distance is the hypotenuse. Between (0, 0) and (3, 4), Δx = 3 and Δy = 4, so d = √(3² + 4²) = √(9 + 16) = √25 = 5. Because the differences are squared, the order of the points does not change the result, and negative coordinates work fine.
This is the everyday tool for map distances, the length of a line segment, the magnitude of a vector, and nearest-neighbour comparisons in data. Any two points on a plane have exactly one straight-line distance between them.
Frequently asked questions
What is the distance formula?
It is d = √((x₂ − x₁)² + (y₂ − y₁)²). Between (0,0) and (3,4) the distance is √(9 + 16) = √25 = 5.
How does it relate to the Pythagorean theorem?
The horizontal and vertical gaps form the two legs of a right triangle, and the distance is its hypotenuse — so the distance formula is Pythagoras on the grid.
What are Δx and Δy?
They are the horizontal and vertical differences between the points, x₂ − x₁ and y₂ − y₁ — the two legs of the right triangle behind the distance.
Does the tool show the midpoint?
Yes. Alongside the distance it gives the midpoint, the coordinate exactly halfway between the two points.
Does the order of the points matter?
No. The differences are squared, so swapping the two points gives the same distance.
Can it handle negative coordinates?
Yes. Any real coordinates work, including negatives and decimals — the squaring keeps every distance positive.
API — use this calculator from code
Call this calculator as a free JSON endpoint — no key required. Send the field values below as query parameters or JSON. Read the full API docs →
Endpoint
GET https://calculator.free/api/v1/distance-two-points/curl
curl "https://calculator.free/api/v1/distance-two-points/?x1=0&y1=0&x2=3&y2=4"JavaScript fetch()
const r = await fetch(
"https://calculator.free/api/v1/distance-two-points/?" + new URLSearchParams({
"x1": "0",
"y1": "0",
"x2": "3",
"y2": "4"
}));
const data = await r.json();
console.log(data.results);Results are estimates for general guidance only, not financial, medical or tax advice.