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

Calculating 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.

The layer called domain is painted with 100% black on top of the areas that we want to calculate their surface area.

Step 2: Establishing scale

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

Surface area of an irregular shape in Photoshop: Total area

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.

1. Select the “domain” and “total area” layers we created and merge them
2. With the new layer selected, Go to Filters > Blur > Average
   

   This should leave you with a greyish box. That’s good!
3. Select the colour dropper  from the menu and click on your grey layer.
4. Click on the foreground colour to open thedialogueandlocate the brightness value.
   

   The brightness value is marked with the red box

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 

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

Medieval land measuring units

Notes

Thank you mostlyignorant for spotting the calculation issue!