What it does
In a forest inventory you measure every tree in a number of small plots of the same size, then scale up to the whole stand. This tool takes that tally and gives:
- Stems per hectare (or per acre): trees in a plot × 10,000 ÷ plot area in m², averaged over the plots.
- Basal area per hectare: the trunk cross-sections at breast height (π × DBH² / 4), scaled the same way. It is the usual measure of how stocked a stand is.
- Standard error and a 95 % range for both, from the spread between plots (treating them as a simple random sample, with Student’s t).
- Quadratic mean diameter (QMD): the DBH of the tree of average basal area, √(basal area per tree × 4/π). It is always a little larger than the plain mean DBH.
- Lorey’s mean height: the mean height weighted by basal area, from the trees you measured heights for.
- A table by species: stems, basal area with its standard error, share of basal area, QMD and Lorey’s height.
- A diameter distribution: stems per hectare in each DBH class, stacked by species.
How to use it
- Paste or open the tally: one row per tree with plot, species, DBH and, if measured, height. Columns headed plot, species, DBH (or diameter) and height are found by name; without headers they are taken in that order. With only two columns they are plot and DBH.
- Choose units: metric (cm, m, m²/ha) or imperial (inches, feet, ft²/acre).
- Give the plot size: its area, or the radius of a circular plot (11.28 m gives 400 m²; 37.24 ft gives 1/10 acre).
- Number of plots: leave blank to use the plots that appear in the tally. If some plots had no trees, type the total number so those plots count as zeros; otherwise the stand looks denser than it is.
- Class width: 5 cm or 2 inches are common.
Worked example (made-up tally)
Six 400 m² plots hold 37 trees of pine, spruce and birch. Each tree stands for 25 per hectare. The stand has 6.28 m²/ha of basal area (± 1.05, or 16.7 %; 95 % range 3.59 to 8.97) and 154 stems/ha (± 18.7). The quadratic mean diameter is 22.8 cm and Lorey’s mean height, from the 23 trees with heights, is 14.6 m. Pine makes up 73.5 % of the basal area (4.62 m²/ha, QMD 27.3 cm), spruce 15.8 % and birch 10.7 %. The diameter distribution peaks in the 25 to 30 cm class with 41.7 stems/ha.
If a seventh plot had no trees, typing 7 plots lowers basal area to 5.39 m²/ha and widens the standard error.
Tips
- Use the same minimum DBH on every plot and say what it was when you report.
- The standard error only reflects the plots you took; plots placed subjectively (for example, in “typical” spots) make it look better than it is.
- To see how many plots you need for a target precision, use the sample size planner with the standard deviation shown here.
FAQs
Why is QMD bigger than the mean DBH? Basal area grows with the square of DBH, so the average basal area belongs to a slightly larger tree than the average diameter.
Can I use variable-radius (prism) plots? Not here: this tool is for fixed-area plots. The tree height and basal area calculator handles prism sweeps.
Is my data uploaded? No. Everything runs in your browser.
Where the numbers come from
- Fixed-area plot expansion, basal area, quadratic mean diameter, Lorey's mean height and the standard error of the mean across plots (simple random sampling): standard forest inventory methods, as in Husch, Beers and Kershaw, Forest Mensuration, and Avery and Burkhart, Forest Measurements. Method only.
- Checked in the tests against an independent pandas and SciPy calculation. The example tally is made up.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-09.