Knowing your plot’s stage of development or stand class size can help you and foresters decide how best to manage a stand of trees.
Calculating the “average DBH” of each species in your plot is an important next step. Unlike a traditional arithmetic average, foresters use the Quadratic Mean Diameter (QMD) as a different type of average. The QMD calculation gives more weight to the larger trees in a plot than a traditional average would.
- FIND OUT MORE: Why you should not use the average DBH
Calculate the Quadratic Mean Diameter
Follow these steps to find the Quadratic Mean Diameter of your plot, and to create a bar graph that shows the Quadratic Mean Diameter of each species in your plot using one year of data
1. Download your data
- Find your plot on the ALL PLOT DATA page
- When you find your plot, download the year(s) of data you plan to work with
2. In Excel or Numbers, calculate the basal area of each tree you measured:
- FIND OUT MORE: What is basal area?
To calculate basal area in square feet for a tree, enter this calculation in column K of your spreadsheet: =0.00545415 x (DBH in inches)^2.
Click & drag the calculation the length of your tree list to get the basal area of each tree:
3. Sum up all of the basal areas you just calculated using the formula =sum(…)
4. Find the average basal area per tree:
- Count up the number of trees in the column
- Divide the sum of basal area (your answer to step 3) by the count of trees
5. Find the (calculated) DBH that represents the average basal area
- Reverse the basal area calculation:
Basal area = 0.00545415 x (DBH in inches)2
QMD (calculated DBH) = √((avg basal area per tree)/0.00545415)
- Do the math to find your QMD
Example: if your average basal area per tree is 0.68978 square feet,
QMD (calculated DBH) = √(0.68978/0.00545415)
QMD (calculated DBH) = 11.2”
Interpret your QMD results
Is your QMD in the range of 1.0” to 4.9”?
- You have a sapling stand.
- You have mostly young trees that – for the most part – are not yet merchantable.
- It is very unlikely to have a QMD in this range because FIG plots have a minimum DBH of 5.0” for tallying and measuring.
- However, if you establish a satellite sapling plot, the QMD of that separate sample can then be likewise calculated.
Is your QMD 5.0” to 9.9”?
- You have a poletimber stand.
- Your stand can be harvested for pulpwood.
Is your QMD 10.0” or larger?
- You have a sawtimber stand.
- Depending upon actual tree quality, your stand can be harvested for sawlogs and pulpwood.
Build a bar chart that shows the QMD for each species in your plot
Make a new table off to the right of your data:
| Species Name | sum of basal areas (sqft) | average of basal areas | QMD |
| Species 1 | |||
| Species 2 | |||
| Species 3 |
To fill in each column, use the same calculations you used above:
- Sum of basal areas: =sum(…select values for only one species…)
- Average of basal areas: =sum of basal areas / count of that species only
- QMD (calculated DBH) =√((avg basal area per tree)/0.00545415)
Insert a bar chart:
- Select the SPECIES NAME column and the QMD column
- Click INSERT > 2D bar chart
Ta-dah!
FIND OUT MORE
Why can’t I do a traditional math average (arithmetic mean, sum of values divided by count of values) of my DBH measurements?
DBH measures the diameter (straight-line distance) of a circular area.
An arithmetic average would then represent the average straight-line distance of the sampled trees.
In using basal area for averaging we are giving more weight to the larger sampled trees, because if you double the DBH, you would quadruple the circular area (basal area)
Example 1
To make sense of this, imagine the circular area of two 5” diameter trees. Your two 5” diameter trees do not have the same circular area as one 10” tree.
Basal area = 0.00545415 X (DBH)^2
A single 5” DBH Tree = 0.1364 square feet, so two 5” trees would have 0.2727 square feet. A 10” DBH tree = 0.5454 square feet, being 4 times larger in area than a single 5” DBH tree and is 2 times larger than the 2 – 5” DBH trees.
Example 2
Another example highlights the different outcome between an arithmetic average and QMD.
Tally 2 trees:
- 6” DBH
- 12” DBH
Calculate and compare the arithmetic average to the Quadratic Mean Diameter:
| Arithmetic average | Quadratic Mean Diameter |
| (6”+12”)/2 = 9.0” | 6” basal area = 0.1963 square feet |
| 12” basal area = 0.7854 square feet | |
| Average basal area per tree: (0.1963+0.7854)/2 = 0.4909 square feet | |
| QMD: √(0.4909/0.00545415) = 9.5” |
Within a given FIG plot, the QMD will almost always be larger than the arithmetic average DBH, in some rare cases it will be identical to the arithmetic average, and can never be less than the arithmetic average.
What is basal area?
Imagine cutting off your plot trees at the DBH mark, the circular area of those surfaces, is called basal area by foresters. In the side view below, are some trees on a plot, in the top view, we are looking down on the surface area of those same trees, at the DBH mark. Using the standard mathematical formula we can calculate the area of each tree’s circle (Area of a circle = A=πr^2), but foresters, again are different and need to have these circular areas expressed in square feet.
