## The issue

If you are using photoshop to create your maps, like I do, you find difficult sometimes to do things that some specialized mapping software do.

I am designing a map for our project and **I wanted to be able to calculate the surface area of a kingdom in order to calculate the amount of population it can support** based on the data we’ve gathered from the Doomsday Book.

## The lazy solution: Surface area of a rectangle

If it was square or rectangular that would have been easy. You multiply X by Y, and as long as you know your scale … presto! You could then break down the rectangle into smaller interconnected ones in order to calculate the surface area of more irregular shape.

But kingdoms, duchies, counties or any demesne (domain) are hardly ever even close to rectangular; so how do you do it?

## The real solution: Surface area of an irregular shape

For this example we will calculate what was the surface area that it was used for habitation on this medieval village.

### Step 1: Define your territory

Create a new layer on top of your map. Let’s call it “Domain” and using a black brush **(make sure the colour is #000000) **Paint over the area you want to calculate.

### Step 2: Establishing scale

Create a new layer, call it “**total area**” under the domain layer and fill it with white.

From the previous example we know that **150px equal 450 feet** on this map.

This image is 1140×852 pixels which means that the X of the box can be calculated by a simple cross multiplication.

If the long side of the rectangle is 1140 pixels and we know that 150px equal 450 feet

X (in feet) = (1140 * 450) / 150 =

3420 feet

In the same way we can calculate that the short side of the rectangle is equal to **2556 feet**.

Using the method we used above we can calculate that the total surface area of the map is X * Y = 3420 * 2556 = 8.741.520 square feet = **200.6 acres**

Your file should now look like this:

### Step 3: The magic

Now for the magic trick.

**Select the “domain” and “total area” layers we created and merge them**- With the new layer selected, Go to
**Filters > Blur > Average** - Select the colour dropper from the menu and click on your grey layer.
- Click on the foreground colour to open thedialogueandlocate the brightness value.

### Crunch them

87% is the coverage of the area outside your Domain area.

Thus 100 – 87 = 13% (of the total 200.6 acres)

In order to calculate the surface area of our housing district we use once again cross multiplication

*206.6 * 13 / 100 *= **27 acres of housing **

– Your colours are pure white #ffffff and pure black #000000

– Your Document is set to RGB (Image > Mode > RGB Color

## Conclusion

What did you think of this method? Do you have a better one?

Does this work on GIMP or other programs with Blur > Average filter. Please do let us know!

## Further reading

## Notes

Thank you mostlyignorant for spotting the calculation issue!

I use another method, figure out the scale of a pixel, then with the wand or lasso tool select your territory. In the expanded histogram (histogram, options, expanded view) it will tell you how many pixels you have selected, after that figuring out the total area is a matter of one single formula (pixels x pixel area)

Thank you for this article! In the past I used a similar technique as @Miguel Bartelsman. However, using the author’s methods, has anyone had any success when calculating the surface area of multiple “kingdoms” at once? Is it still possible to merge the “total area” layer and maintain individual kingdoms? Or is it necessary to have one “total area” layer per “kingdom”?

Hey Patagonian Scientific,

You won’t be able to get individual kingdom AND total kingdoms but you can get total kingdoms. Alternatively you can just use the same technique in multiple layers and then just sum the results.