*Today’s post is part of a new effort to bring back some of the most successful context from turtlshel.org’s long history. These posts will cover the full range of past TS topics, including Japanese language learning resources, geography, Esperanto, international futbol, NERD stuff, bread baking, fly tying, and data science stuff. The original article was published on turtlshel.org in 2005. *

The area of a surface with square corners and straight edges on a map or photo can be found by multiplying the length of the surface by its width and then converting to real-world units using the scale of the image. What do you do if you need to find the area of an organic shape, or of a very complex geometric shape? One method that is widely used is the dot count using a dot grid.

A dot grid is a transparent sheet printed or drawn with dots arranged in a regular and even pattern such as a grid. When the dot grid is calibrated to the scale of the map or photo you are studying (finding the number of dots that falls in a known area), the area of an unknown surface can be found by laying the dot grid over the area, counting the number of dots that fall in and on the surface, and dividing that number by the number of calibrated dots per unit area. This gives you the area of the surface you are estimating in the units of your calibration.

As an example, let us suppose that I have calibrated my dot grid on an aerial photograph using a farmer’s field, bounded by section-line roads, as my known distance. How do I know the area of the farmer’s field? Often, fields are laid out along the US Public Land Survey System, with roads following the 1-mile edges of sections. A field bounded by such roads would be 1 square mile. These human features are obvious in aerial photos and on maps, and are very useful for establishing scale and for calibrating dot and square grids. Calibrating against the 1-square-mile field, suppose that I find that my dot grid is a size that there are 225 dots per square mile.

Now suppose that I have to find the surface area of a lake on the same photograph as the 1-square-mile field. Using the dot grid that I have just calibrated, I cover the lake with the dot grid and count 675 dots on the lake. The number of dots in my area-for-estimation (675), divided by my number of dots per unit area (225 dots per mile square) gives the lake an area of 3 square miles.

There are a few key points to using the dot grid:

- A dot count is a statistical method. It is important that you don’t line up the grid to get the best fit to count in your object. The whole point of the dot count is to see how many dots randomly fall within the area when the dot grid is placed in a random relationship to the area.
- When you are counting dots, each dot that falls completely within the area is given the weight of 1 full dot. Any dot that touches the side of the object, whether it is inside, outside, or one the line, gets a weight of 1 half dot. The number of whole dots plus the number of half dots (or the number of half dots divided by two, actually) is the total number of dots to be used in estimating the area of a surface.
- Once you have begun counting dots, don’t move the dot grid. If you do accidental move the grid, don’t just keep counting. You have to start over from the beginning.

I have created a dot grid for you to use in trying this method out. To use the dot grid, click on the image above to download “dotgrid1.pdf.” This file needs to be printed on plastic transparency, which is available for inkjet and laser printers, as well as copy machines for between $0.15 and $0.75.