Polygon Area Calculator

How to use the Polygon Area Calculator

1. 1Enter the corner points, one x, y pair per line.
2. 2Pick the units or options from the menus if the polygon area tool offers them.
3. 3Read the polygon area in the large result box.
4. 4Look at the extra rows for related figures.
5. 5Press Copy result to keep the answer.

When you need the polygon area

Surveyors, gardeners and students use it to find the area of a plot from measured corner points, and game or map developers use it to size shapes.

List the corners in a continuous order, clockwise or anti-clockwise. The sign of the sum tells which way you went, and the tool reports it. Use the same unit for all coordinates; the area is then in that unit squared.

How the polygon area is worked out

Area = ½ × |Σ (xᵢ × yᵢ₊₁ − xᵢ₊₁ × yᵢ)|, going round the corners and back to the first. The perimeter adds the lengths of all sides. The corners (0, 0), (4, 0), (4, 3), (0, 3) give a rectangle with an area of 12 and a perimeter of 14. The centroid is at (2, 1.5).

Every answer on this page comes from that one rule, so you can check any result by hand with a calculator. The figures shown underneath, such as other units, are conversions of the same answer.

• Any number of corners
• Centroid and perimeter included
• Detects the point order

Mistakes to avoid with polygon area

If the sides of the shape cross each other, like a bow tie, the shoelace formula gives the net area, not the total. Entering corners out of order is the usual mistake: you would get a smaller area from a self-crossing path.

On phone and computer

On a phone, type into the boxes one after another and read the polygon area underneath; Copy result puts it on the clipboard for a message or a note. On a computer the inputs sit on the left and the answer on the right, so you can change one figure and watch the polygon area move. The polygon area calculator works the same on both.

Checking your polygon area by hand

A good habit is to test the polygon area calculator with a case you already know. The corners (0, 0), (4, 0), (4, 3), (0, 3) give a rectangle with an area of 12 and a perimeter of 14. The centroid is at (2, 1.5).

If your own figures give a surprising answer, repeat the working yourself: Area = ½ × |Σ (xᵢ × yᵢ₊₁ − xᵢ₊₁ × yᵢ)|, going round the corners and back to the first. The perimeter adds the lengths of all sides. Small differences usually come from rounding, from mixing units, or from a typing slip in one of the inputs. A polygon can often be split into simple shapes. Check the pieces with the Triangle Calculator, find a circle's part with the Circle Calculator, and measure sides with the Distance Calculator.

Features

• List corners in order
• Same unit for x and y
• Crossing sides give a net area
• Clear messages when the polygon area inputs make no sense
• Copy the result with one tap
• Private: nothing is uploaded

Frequently asked questions