Variable radius plot sampling- Know before you go!
Dr. Nan Pond
Dr. Nan Pond
22 July, 2015 min read

Variable radius plot sampling, also known as point sampling, is an awesome technique to use for fast, efficient cruising. Variable radius plots also provide a quick estimate of basal area. Because forest volume is closely related to basal area, cruising with variable radius plots makes it possible to do a back-of-the-envelope volume estimate for the stand, if you know the approximate ratio of volume to basal area for your forest type. In this blog post, we will clarify best practices for this technique and troubleshoot some common problems that can occur if it isn’t used properly.

When cruising with variable radius plots, it’s important to use the right basal area factor (i.e. the right size prism) for your forest type, or your estimate of trees per acre could end up far higher or lower than your expectations (and reality). Before you cruise with point sampling, it’s important to understand that under certain conditions, the ease of point sampling comes with a cost in precision in the calculation of trees per acre. Higher BAFs, clumpier forests, and lower minimum diameters result in lower precision in the measurement of trees per acre. (The mean estimate is still accurate, but the confidence interval around that mean is expected to be wider than, for example, a mean from the same number of plots cruised using a lower BAF prism.)

Using this method, every ‘in’ tree in your plot represents a constant value of basal area per acre. For example, if you’re cruising with a BAF 10 wedge prism, that value is 10 square feet. The contribution of any given tree to your calculation of trees per acre, however, varies. Think of it this way: around every tree there is an imaginary circle. The radius of that circle depends on the basal area factor of the prism you used and the diameter of the tree. Small trees have very small circles around them; larger trees have very large circles. If the imaginary circle around the tree would overlap with the center of your plot, that tree appears ‘in’ through your prism. In fixed area plots you multiply, for example, the number of trees in a 1/100th acre plot by 100 to get an estimate of trees per acre. Not so with variable radius plots. Imagine the circles around trees in your variable radius plot are small fixed-radius plots. A tree in a very small plot would represent a much higher estimate of trees per acre than a tree in a large plot.

Periodically, we get questions from Plot Hound users who are surprised by what seem like ‘unreasonably high’ trees per acre estimates from their cruise report. In most cases, these high tpa estimates are the result of measuring small-diameter trees using a relatively large basal area factor- for example, cruising with a BAF 20 prism. In this context, the high estimate of trees per acre isn’t necessarily accurate, but it should be expected, because the basal area factor chosen might not have been suited for that forest. For the most accurate results, use a larger BAF value in stands with predominantly larger trees, and a smaller BAF for stands with smaller ones.

Here’s a quick example of how to calculate trees per acre from a variable radius plot. When you download your cruise data from Plot Hound, you’ll see that we’ve calculated and included the ‘Tree Expansion’ value for you. This indicates the number of trees per acre that stem represents, within its plot.


The expansion factor equation for a given tree using a variable radius plot is BAF / basal area for the stem, or, 10 / (0.005454 * dbh2)

Then, we calculate the total TPA in each plot – by adding the expansion factor for all trees within a plot. In this example, we have:

Plot 1: 114.59 + 203.72 = 318.31 TPA
Plot 2: 28.65 + 28.65 + 22.64 + 114.59 = 194.53 TPA
Plot 3: 5.08 + 28.65 + 28.65 = 62.38 TPA

Because plot 1 had smaller trees in it, the trees per acre estimate for plot 1 is much higher than the other plots. When they are measured, they represent a large contribution in terms of trees per acre.

Then we average the TPA from each plot to get the average trees per acre for the stand – in this case, 191.74 trees per acre.
The basal area is much easier to calculate. It’s simply the basal area factor used multiplied by the number of trees in each plot.

Plot 1: 10 * 2 trees = 20 ft2
Plot 2: 10 * 4 trees = 40 ft2
Plot 3: 10 * 3 trees = 30 ft2

The average basal area for the stand is 30 ft2 per acre.

Variable radius plots are a quick and simple way to record inventory, which makes them very appealing. Just remember: it’s worth taking a minute to think about the forest type you’re cruising before you grab your prism and head to the woods. Using the appropriate basal area factor will help you get the most accurate representation of your forest from your cruise.

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about the author

Dr. Nan Pond

Dr. Nan Pond

Director of Certification
Dr. Nan Pond serves as the Director of Certification at NCX. She is responsible for ensuring that our natural capital products reflect the highest quality science as we hone our existing methods and expand into new credit types and new geographies. She is the recipient of the 2020 SAF Young Forester Leadership Award and has held multiple leadership roles within the Society of American Foresters. Dr. Pond earned a PhD in forest biometrics from Michigan Technological University and a Bachelor of Science in forest ecosystem science from SUNY ESF.