Map area calculator

Worked example: one degree of latitude and longitude

Draw a four-corner box from 40° N to 41° N and from 100° W to 99° W. The tool's polygon formula gives 3,630.1 square miles. The exact area of that box on a sphere is R² · Δλ · (sin 41° − sin 40°) = 3,630.1 square miles, so the two agree.

The same box at 60° N is much smaller, because meridians converge toward the pole. That is why areas measured by counting grid squares on a map are unreliable away from the equator.

How to use it

1. Zoom in to the area you want to measure so each click lands where you mean it.
2. Click the first corner, then each corner in order around the edge. A line joins the first two clicks.
3. After the third corner the shape closes and fills, and the card shows its area in square kilometers, square miles, acres, and hectares, the perimeter in kilometers, and the number of corners.
4. Press Undo to remove the last corner, or Clear to start again.

How the area is computed

The corners you click form a ring of latitude and longitude points. The tool sums a term for each edge, based on the change in longitude and the sines of the two latitudes, then multiplies by the square of the Earth's mean radius. This is the standard spherical polygon area method used by many web mapping libraries. It handles any size of shape, from a field to a country.

The perimeter is the sum of great-circle lengths of the edges, including the closing edge back to the first corner.

Units

One square mile is 640 acres. One hectare is 10,000 square meters, so one square kilometer is 100 hectares. One acre is about 0.405 hectares. The tool converts from square kilometers with fixed factors and shows every unit at once, so you can copy whichever the form in front of you asks for.

Accuracy and good practice

Your clicks are the main source of error. Zoom in before placing corners along a curved boundary, and add more corners where it bends. The sphere model itself is within a fraction of a percent of the ellipsoid for areas of any practical size.

Edges that cross each other make an invalid shape, and the area of a figure-eight is not meaningful. Place corners in order around the outside. For official land areas of counties, use the Census figures on each county page, which are measured from boundary files.