# Estimating the Number of Leaves on a Tree

The Big Oak Tree

How many leaves are on this tree? If you have ever wondered about this with a tree of your own acquaintance, here is at least one way to make a ball park estimate.

Lawn partially covered with leaves.

How many leaves does it take to cover the ground with a layer of leaves one leaf thick? The answer to this question will start us on our way.

Leaves on a paper plate

The first step is to cover a paper plate with a layer of leaves from the tree species of your choice. In this case, I have covered a 10-inch diameter paper plate with leaves from the big oak tree in my front yard.

Leaves from the paper plate

Determining the exact number of leaves requires some jig saw puzzle-solving skills, especially with dried and curled leaves. Using a range of leaf sizes from large to small, it took approximately 18 leaves from the big oak tree to cover the paper plate. I rounded this leaf number to 20 leaves to account for some of the small gaps between the leaves and to make the remaining calculations a little easier.

Using the formula, area = πr2, the 10-inch diameter paper plate has an area of 78.54 in2. Converted to square feet, the paper plate has an approximate area of ½-square foot. Thus 2 of these paper plates = 1 sq ft, and with 20 leaves per paper plate, that converts to approximately 40 leaves from the big oak tree needed to cover one sq. ft of ground surface.

The next step is to determine the approximate average diameter of the tree crown by pacing (or measuring with a tape). Do this by locating the outer edge of the leaves on one side of the tree and pacing to a similar location on the opposite side of the tree. If you want, you can refine this value by taking an average of several diameters paced from different points on the tree crown’s outline.

In my case, I paced one measurement that seemed typical and got a diameter of 90 feet. Again using the formula, area = πr2, and a radius of 45 feet, the big oak tree has an approximate crown area of 6,362 sq ft.

Multiplying the crown area in sq ft by the number of leaves necessary to cover 1 sq ft gives the approximate number of leaves on the tree if there were only one leaf per sq ft of ground area shaded by the tree’s crown (i.e., for the big oak, 6,362 sq ft times 40 leaves/sq ft = 254,480 leaves).

View up through the canopy of the big oak tree

What if the tree has more that one leaf in its crown for every corresponding leaf-sized area on the ground under the tree? In this case, which will generally be the rule rather than the exception, we need to know how many leaves actually overlap each other in the tree’s crown.

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A layer of leaves obscures the lawn

We will thus use the concept of Leaf Area Index (LAI) which is defined as the total leaf area (one surface only) divided by the ground area. The calculation of these values has been the subject of a number of ecological research projects, and we will use a set of estimates from the literature.

Barbour et al., (1999:199) [Terrestrial Plant Ecology, 3rd Ed., Addison Wesley Longman, Inc., Menlo Park, CA] present a summary table of LAI values for a number of vegetation types found throughout the world. Using their tabular values of 5 to 8 for deciduous forests (i.e., representing forests with trees such as ones similar to our big oak tree), I decided to use a LAI value of 6 for the big oak tree.

Thus our approximate value of 254,480 leaves for a layer of leaves one leaf thick becomes an estimate of approximately 1.5 million leaves for the big oak tree’s crown (i.e., 254,480 times 6 = 1,526,880 leaves). Using the range of estimates for deciduous forests of LAI = 5 to 8, the corresponding approximate range of estimated leaves on the big oak tree would range from 1.25 million leaves to 2 million leaves.

I am personally satisfied with this approximation and I think that I will forego counting the leaves after they fall in an attempt to verify the estimate. If you feel otherwise, let me know as I have a leaf rake that you can borrow.

1. Jeremy
Posted September 19, 2012 at 7:05 pm | Permalink

Oh my god, thank you so much for this, I’m in geometry and for my first project of the year, we have to find out how many leaves are on a tree. I had no idea how to tackle this problem but thanks to you, I do.

2. Kirana
Posted November 5, 2012 at 12:15 am | Permalink

Hi, thanks so much for this! I was raking leaves today and wondered. Best regards