Forest Basal Area & Stand Density Calculator (Plot or Prism)
Calculate basal area per hectare or acre from a list of tree diameters (DBH) on one or more fixed plots, or from a prism / angle-gauge count with any basal area factor (metric or BAF 10), with trees per hectare and acre, quadratic mean diameter, Reineke stand density index, relative density, stocking class, a diameter-class table and a thinning target from below, from above or by average tree.
How it works
tree basal area (m²) = π × (DBH cm ÷ 200)² = 0.00007854 × DBH² (imperial: ft² = 0.005454 × DBH in²) · BA/ha = Σ tree BA ÷ plot area (ha) · prism: BA/ha = (in-trees + ½ borderline) × BAF ÷ points · trees/ha represented by a prism tree = BAF ÷ tree BA · QMD = √(Σ DBH² ÷ n) · SDI = trees/ha × (QMD ÷ 25.4 cm)^1.605 · relative density = SDI ÷ maximum SDI · 1 m²/ha = 4.356 ft²/acre
Foresters describe how crowded a stand is by adding up the cross-sectional area of the stems at breast height (1.3 m or 4.5 ft), because a hundred saplings and ten veterans occupy very different amounts of growing space. Basal area per hectare (or per acre) rolls tree size and number into one figure that tracks competition, volume and the need to thin. On a fixed-area plot it is the sum of each tree’s circle scaled up to a hectare; you can pool several equal plots in one list. The quadratic mean diameter (the diameter of the tree of average basal area) links basal area back to tree count, and Reineke’s stand density index combines the two into the number of 10-inch trees the stand is equivalent to. Divided by the maximum SDI for the forest type it gives relative density: below about 35% the site is not fully used, between 35% and 60% trees grow well, and above 60% the stand self-thins. The prism or angle-gauge method selects trees with a probability proportional to their size, so every tree counted "in" stands for the same basal area, the basal area factor (BAF), whatever its diameter. Count the in-trees at several points, count borderline trees as half, and the average times the BAF is the stand basal area. List the diameters of the in-trees and the calculator also expands each one to trees per hectare. Metric BAFs are in m²/ha; the common US BAF 10 is 10 ft²/acre (2.30 m²/ha), and every input can be entered in metric or imperial units. For thinning, the calculator gives the basal area to remove to reach your target, the number of average-sized trees that represents and, for a plot list, how many of the smallest trees (thinning from below) or largest trees (from above) would have to go. Stocking classes by basal area are rough guides; regional stocking charts and yield tables for your species are better for decisions.
Worked example
Twelve trees with diameters from 22 to 45 cm on a 20 × 20 m plot (0.04 ha): the sum of DBH² is 12,922 cm², so the plot basal area is π ÷ 40,000 × 12,922 = 1.0149 m² and the stand basal area is 1.0149 ÷ 0.04 = 25.4 m²/ha (111 ft²/acre), a moderately stocked stand. That is 300 trees/ha (121 per acre) with a quadratic mean diameter of √(12,922 ÷ 12) = 32.8 cm, an SDI of 300 × (32.8 ÷ 25.4)^1.605 ≈ 453 per ha (183 per acre) and a relative density of 41% against a maximum SDI of 450. Thinning to 20 m²/ha removes 5.4 m²/ha, about 64 average trees per hectare: the 5 smallest trees on the plot (125/ha) or the 2 largest (50/ha). With a prism, nine in-trees at BAF 2 at one point would give 18 m²/ha.
Sources: University of Arkansas Extension FSA5036: basal area (0.005454 × DBH², BAF 10 prism) · Wikipedia: Stand density index (Reineke, slope 1.605, 10-inch reference) · USDA Forest Service: stand density thresholds (35% and 60% of maximum SDI) · Decision Maker basal area calculator (plot, prism, TPA/QMD modes)
Frequently asked questions
How do I calculate basal area of one tree?
Square the DBH and multiply by a constant: 0.00007854 for diameter in centimetres (result in m²) or 0.005454 for inches (result in ft²). A 30 cm tree has 0.0707 m²; a 12 inch tree has 0.785 ft².
Which basal area factor should I use?
Choose one that gives about 5–12 in-trees per point: BAF 1 or 2 m²/ha in young or open stands, 4 in dense mature conifers. In the US, BAF 10 ft²/acre (2.30 m²/ha) suits most hardwood and pine stands and BAF 20 dense, large timber.
What is a good basal area per acre?
It depends on species and goal. Roughly, under 60 ft²/acre (14 m²/ha) is understocked for timber, 70–110 ft²/acre (16–25 m²/ha) is well stocked for many pine and hardwood stands, and Douglas-fir can carry 140–200 ft²/acre. Wildlife and savanna goals often aim lower.
What is the quadratic mean diameter?
The diameter of the tree of average basal area: the square root of the mean of the squared diameters. It is always a little larger than the plain average DBH and links basal area and tree count (BA = trees × π × (QMD ÷ 200)²).
What does stand density index tell me?
SDI expresses the stand as the number of 10-inch (25.4 cm) trees per acre or hectare that would occupy the same growing space. Comparing it with the maximum SDI for the forest type gives relative density; about 35% marks full site occupancy and 60% the start of self-thinning, common thresholds for scheduling thinning.
Do I count borderline trees with a prism?
Count trees whose displaced image overlaps the stem as in, those clearly separated as out, and trees that look exactly borderline as half, or check them with a tape and the plot radius factor. Be consistent across points.
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