By Norma Kline, Oregon State University Extension Forester for Coos and Curry Counties
This is the 6th article in the Writing a Forest Management Plan series. The objective of this series is to break the process of writing a forest management plan into simple steps intended to make the process accessible and straight forward regardless of your previous skills and knowledge. If you already have a management plan, use these steps to help review and update your plan.
The first articles cover how to generate the basic property information and maps for your forest management plan from web-based mapping resources, map forest cover (stands) based on stand age and species, describe stand characteristics and take simple plot measurements and make simple calculations of stand averages from your plot data. The links to the first five topics are at the end of this article.
In this article, we will describe how to use the basic fixed plot data calculations from the fourth article to describe stand density. Assessing stand density can help determine whether a stand is overcrowded. Depending on a landowner’s management objectives, overcrowded stands can be thinned to maintain stand health, tree growth and wildlife habitat characteristics.

In areas of your forest that are crowded or dense, your first observation might be the lack of sunlight reaching the forest floor and the presence of little to no understory vegetation. Looking up at the canopy in these areas, you will find that overcrowded trees have small live crowns compared to their total height (we described how to measure live crown ratio in the third article in this series). Trees growing in these crowded conditions are competing with each other for resources and some trees will start to die from this competition. Conversely in areas with less crowding, tree crowns will be fuller (have longer live crowns) and there will be the presence of a shrub understory. In fact, if you are in Oregon’s coast range, it might be difficult to walk through these stands because of the thick brush present in the understory (Figure 1). While casual field observations are useful, calculating relative density (RD) using your stand data and referencing an appropriate stand density table will take the guesswork out of knowing whether a stand is overly dense. Stand density tables will also help you determine the best time to thin a stand for stand health.
We will use stand density tables in the Competition and Density in Woodland Stands Extension Publication, link below, to determine if our example stand is becoming overcrowded. Since our stand consists of primarily Douglas-fir, we will use the Douglas-fir density table. Our first step will be to use our basic fixed plot calculations (from the fourth article) to locate the position in the table indicating how the relative density of the stand is ranked in regard to competition. The relative density scale has descriptive names for the different zones of competition. The lowest density is Crown Closure, then the Enthusiastic Growth Zone, Lower Goldilocks Zone, Upper Goldilocks Zone, Danger Zone, Zone of No Return and finally the Maximum density. As you would expect, a stand in the Danger Zone is very dense and will likely have tree mortality.
From our previous basic fixed plot data calculations, we calculated an average of 160 Trees per Acre (TPA), and an average 11.18 inches (arithmetic mean) Diameter at Breast Height (DBH). Now we will use these two values to determine the stand’s location in the density table. This will require some approximation. You will notice that the table uses a diameter referred to as quadratic mean diameter (QMD). The QMD will always be somewhat higher than the arithmetic mean because it is weighted towards larger trees. It is typically used in forestry calculations instead of the arithmetic mean. The calculated QMD for our stand is 11.43 inches. Just keep this in mind if you use the average DBH for your stand to determine the relative density. Otherwise, you can calculate the QMD using the formulas at the end of this article.

In our example, after locating the position of our stand on the Douglas-fir density table, we see that it is in the Lower Goldilocks Zone. In other words, the stand is still growing without severe competition. Our landowner wants to plan a thinning before the stand reaches the Danger Zone, which is when trees become crowded and start dying. The green arrow depicted in Figure 2 shows the future trajectory of the stand as it increases in diameter (and density). We see that when the stand reaches the Upper Goldilocks Zone it has a diameter of about 13 inches with an average spacing of about 16 feet between trees. The stand will then be thinned so that the density is reduced back to the Lower Goldilocks Zone. The red arrow represents the thinning, which will reduce the number of trees per acre to about 120, the spacing between the remaining trees will be about 20 feet on average between trees. For more information on charting a stand using the density tables refer to the detailed descriptions in the Competition and Density in Woodland Stands publication.
The landowner has determined that the thinning should likely occur within the next 5 years (this will be when the stand reaches the Upper Goldilocks zone). Additional factors to consider in the planning process include determining the number of acres in the thinning project, estimating cost and any potential revenue, and steps required for regulatory compliance (e.g., Power Driven Machinery Permit, Forest Practices Notification). For information on Oregon’s Forest Practice Act and to find your ODF Stewardship Forester, see links in the Resources section below.
The Schedule of Planned Management Actions (starting on page 31 of the Forest Management Template) is a helpful tool to consider all of the necessary steps needed to plan a successful thinning project. Once the landowner has a rough timeline for the project, they can start searching for the right contractors to accomplish the work. For example, scheduling a logger that has expertise and the right equipment for thinning (or a consulting forester that can arrange the work) should all be done well in advance of the planned activity.
Thinning is just one type of management action that the Schedule of Planned Management Actions is used for. Other management actions might include clearcut harvests, road construction, salvage logging, invasive weed eradication, among others.
In the next article of the series we will discuss how to find the information to complete the other parts of the plan including soils, water resources and fish and wildlife. These are allimportant factors that can help inform management actions on your woodland.
Calculations (for those that are interested)
To calculate the Quadratic Mean Density (QMD) we will need to make a few preliminary calculations. Insert the following formulas into a spreadsheet to make quick calculations.
Our first calculation will be to determine the basal area (BA) of each tree. The BA is the cross-sectional area at breast height (4.5 ft above ground). Tree Basal Area (BA) = 0.005454 * (DBH)2 (using inches as the unit for DBH)
In the plot data form below, the BA has been entered for each tree. For the first tree in Plot 1, the Tree Basal Area = 0.005454 * (11) 2 = 0.005454 *121 = 0.66 square feet.
The next step is to calculate the Basal Area per acre that the tree represents by multiplying the Tree Basal Area by the expansion factor. (the expansion factor is the denominator of the plot size). For our example we selected a 1/20th acre fixed plot size which gives us an expansion factor of 20.
BA/acre = Tree BA X Expansion Factor
BA/acre = 0.659 square feet X 20 = 13.20 square feet per acre (represented by the first tree in the first plot).
Sum the plot TPA and the plot BA/ac
From the previous article, the sum of the plot TPA is 480.
Plot 1. 7 trees. 7 x 20= 140 trees per acre (TPA).
Plot 2. 9 trees. 9 x 20 =180 TPA
Plot 3. 8 trees. 8 x 20 =160 TPA
The sum of plot TPA = 480
The sum of the plot BA/ac, from the table is 99.37 + 127.30 + 115.41 = 342.07. Use these sums to calculate the average basal area per tree:
Average basal area per tree= sum of plot TPA ÷ sum of plot BA/ac
Average basal area per tree= sum of plot TPA (480) ÷ sum of plot BA/ac (342.07) = .713
This is used to calculate the quadratic mean diameter of a stand:
QMD = √(Average basal area per tree/0.005454)
In our example, the QMD is square root (.713/0.005454)= 11.43
Plot Data
Plot # | Tree # | Species | DBH (Inches) | Height (Feet) | Live Crown Ratio | Tree Basal Area (sq ft) | Basal Area per acre (sq ft) | Sum of Basal Area per acre (Sq fit) |
1 | 1 | DF | 11 | 90 | 30 | 0.66 | 13.20 | |
2 | DF | 14 | 95 | 60 | 1.07 | 21.38 | ||
3 | DF | 13 | 95 | 50 | 0.92 | 18.43 | ||
4 | DF | 10 | 85 | 30 | 0.55 | 10.91 | ||
5 | DF | 9 | 80 | 25 | 0.44 | 8.84 | ||
6 | DF | 10 | 90 | 35 | 0.55 | 10.91 | ||
7 | DF | 12 | 90 | 45 | 0.79 | 15.71 | ||
99.37 | ||||||||
2 | 1 | DF | 9 | 85 | 25 | 0.44 | 8.84 | |
2 | DF | 8 | 85 | 25 | 0.35 | 6.98 | ||
3 | DF | 14 | 95 | 50 | 1.07 | 21.38 | ||
4 | DF | 16 | 100 | 60 | 1.40 | 27.92 | ||
5 | DF | 15 | 100 | 55 | 1.23 | 24.54 | ||
6 | DF | 8 | 90 | 25 | 0.35 | 6.98 | ||
7 | DF | 9 | 90 | 30 | 0.44 | 8.84 | ||
8 | DF | 10 | 95 | 30 | 0.55 | 10.91 | ||
9 | DF | 10 | 95 | 30 | 0.55 | 10.91 | ||
127.30 | ||||||||
3 | 1 | DF | 16 | 100 | 50 | 1.40 | 27.92 | |
2 | DF | 13 | 90 | 45 | 0.92 | 18.43 | ||
3 | DF | 13 | 90 | 45 | 0.92 | 18.43 | ||
4 | DF | 10 | 85 | 30 | 0.55 | 10.91 | ||
5 | DF | 9 | 85 | 25 | 0.44 | 8.84 | ||
6 | DF | 9 | 85 | 25 | 0.44 | 8.84 | ||
7 | DF | 11 | 90 | 35 | 0.66 | 13.20 | ||
8 | DF | 9 | 80 | 30 | 0.44 | 8.84 | ||
115.41 |
Resources
Basic Forest Inventory Techniques for Family Forest Owners. https://pubs.extension.wsu.edu/basic-forest-inventory-techniques-for-family-forest-owners
Competition and Density in Woodland Stands https://extension.oregonstate.edu/catalog/pub/em-9206-competition-density-woodland-stand
Measuring Your Trees. https://extension.oregonstate.edu/catalog/pub/em-9058-measuring-your-trees
Oregon Forest Management Plan Template and Guidance. https://blogs.oregonstate.edu/forestplanning/templates/
Oregon Forest Practice Act Resources https://www.oregon.gov/odf/working/pages/fpa.aspx
Find an ODF Forester https://www.oregon.gov/odf/working/Pages/findaforester.aspx
Articles in the Writing a Forest Management Plan Series:
1 – Start with the Easy Sections. https://blogs.oregonstate.edu/southcoastfieldforest/2024/02/15/writing-a-forest-management-plan-start-with-the-easy-sections/
2 – Mapping Stands.
3 – Measuring Plots to Describe Your Woodland.
4 – Summarizing Plot Measurements to Describe Your Woodland.
5 – Describing Stand Characteristics.