Perimeter by Coordinates Calculator
Paste the vertices, such as A(1, 1), B(4, 5), C(7, 1), to get the perimeter, each side's length with its distance-formula working, the exact radical answer and the enclosed area.
To find a perimeter from coordinates, use the distance formula d = √((x₂ − x₁)² + (y₂ − y₁)²) for each side, including the side from the last vertex back to the first, and add the lengths.
Use the Perimeter by Coordinates Calculator
Coordinates
Result
Enter coordinates to see the perimeter
Side lengths
| Side | Δx, Δy | Length |
|---|
Shape Preview
Preview updates after calculating
Quick answer
List the vertices in order around the shape. For each pair of neighbouring vertices compute d = √((x₂ − x₁)² + (y₂ − y₁)²), close the shape with the side from the last vertex back to the first, and add all the side lengths. With integer coordinates, simplify each root (√20 = 2√5) and add like radicals for an exact answer. The area of the same polygon comes from the shoelace formula, A = ½|Σ(xᵢ·yᵢ₊₁ − xᵢ₊₁·yᵢ)|. For GPS latitude and longitude points, use great-circle (haversine) distances instead of the flat distance formula.
Examples
| Vertices | Side lengths | Perimeter | Area |
|---|---|---|---|
| (1,1), (4,5), (7,1) | 5, 5, 6 | 16 | 12 |
| (0,0), (4,0), (4,3), (0,3) | 4, 3, 4, 3 | 14 | 12 |
| (0,0), (2,4), (6,2) | 2√5, 2√5, 2√10 | 4√5 + 2√10 ≈ 15.27 | 10 |
| (−2,1), (3,1), (3,−4) | 5, 5, 5√2 | 10 + 5√2 ≈ 17.07 | 12.5 |
Paste your points above; the perimeter, side lengths, exact form and area update as you type.
Summary
This calculator finds the perimeter of any polygon from its corner coordinates. Paste points in almost any format (x, y per line, A(1, 2), a CSV with a header, or one line of pairs) and it applies the distance formula to every side, closes the shape back to the first point, and adds the lengths. For integer coordinates it also shows the exact simplified radical answer used in geometry classes, plus the enclosed area by the shoelace formula. Switch off "Closed shape" to measure an open path, or switch to latitude/longitude to get great-circle perimeter and area for GPS points in km, miles, metres, feet and nautical miles.
How it works
- Paste or type the vertices in order, one point per line: "x, y", "A(1, 2)", "1 2" or a CSV with a header row all work.
- Leave "Closed shape" on for a polygon (the last point joins back to the first), or turn it off for an open path.
- For GPS points choose Latitude / longitude and the column order; distances then follow the Earth's surface (haversine formula).
- Each side is computed with d = √((x₂ − x₁)² + (y₂ − y₁)²) and the lengths are added for the perimeter.
- Read the perimeter, the exact radical form (integer points), the area from the shoelace formula, and the side-by-side table; copy the result if needed.
Use cases
- Finding the perimeter of a triangle, rectangle or quadrilateral from its vertices for geometry homework.
- Getting an exact answer such as 4√5 + 2√10 instead of a decimal.
- Measuring the boundary length and area of a plot from surveyed corner coordinates.
- Estimating fencing for a field from GPS points taken with a phone.
- Checking the length of an open route or path through waypoints.
- Verifying polygon edge lengths exported from CAD or GIS software.