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Basal Area Calculator
Turn a diameter tape into real forestry numbers. Enter DBH (diameter at breast height) to get a tree’s basal area in cm², m², in² and ft² — then tally a whole fixed-area plot and scale it to m²/ha and ft²/acre, with trees-per-hectare, quadratic mean DBH, Reineke SDI and a stocking class.
Measured with a diameter tape or caliper at breast height.
BA = π × (DBH ÷ 2)² · metric shortcut: BA(m²) = 0.00007854 × DBH(cm)² · imperial: BA(ft²) = 0.0054542 × DBH(in)²
Blank lines are ignored; invalid lines are counted and reported.
Expansion factor = 10000 ÷ plot area (m²) · TPH = trees × expansion factor · BA/ha = TPH × mean BA · SDI = TPH × (Dq ÷ 25.4)1.605
How it works
Basal area is the cross-sectional area of a tree trunk at breast height (1.3 m / 4.5 ft). The calculator applies BA = π×(DBH/2)² per tree. For a fixed-area plot it sums every tree, then multiplies by the expansion factor (10000 ÷ plot m²) to get basal area per hectare — and converts to ft²/acre (×4.356).
Stocking uses Reineke’s stand density index: SDI = TPH × (Dq/25.4)1.605, where Dq is the quadratic mean DBH. Stocking % is SDI relative to the species maximum (default 230; typical species maxima range 230–900 — set it for your species). Classes are approximate rules of thumb: under 35% understocked, 35–60% fully stocked, 60–100% overstocked, above 100% exceeds the species maximum.
A tree age calculator and a tree value calculator cover age and valuation; this tool is dedicated to basal area measurement and stand density.
Frequently asked questions
What is the basal area formula for a tree?
Basal area is the cross-sectional area of a trunk at breast height: BA = pi times (DBH divided by 2) squared. For example, a tree with a DBH of 30 cm has a basal area of pi times 15 squared = 706.86 cm2, which is 0.0707 m2. In imperial units, a 12 inch DBH tree has pi times 6 squared = 113.10 in2, or 0.7854 ft2.
Is there a shortcut formula for metric basal area?
Yes. Because BA in m2 equals pi over 4 times DBH squared divided by 10000, you can use BA(m2) = 0.00007854 times DBH(cm) squared. For a 30 cm DBH tree: 0.00007854 times 900 = 0.0707 m2, identical to the full formula.
What is the imperial shortcut for basal area?
In imperial units, BA in ft2 = 0.0054542 times DBH(in) squared, because pi over 4 divided by 144 square inches per square foot. For a 48 inch DBH tree: 0.0054542 times 2304 = 12.57 ft2. The calculator shows both metric and imperial results for every input.
Can I compute basal area from trunk circumference instead of DBH?
Yes. Divide the circumference by pi to get DBH, then apply the formula. A circumference of 94.25 cm gives DBH = 94.25 divided by pi = about 30.0 cm, so basal area = 706.86 cm2. The calculator has a circumference mode that does this conversion for you.
How do I scale a fixed-area plot up to basal area per hectare?
Multiply the summed basal area of the plot by the expansion factor: 10000 divided by plot area in m2. A 500 m2 plot has an expansion factor of 20. One 30 cm DBH tree (0.0707 m2) in a 500 m2 plot therefore represents 1.41 m2 per hectare and 20.00 trees per hectare.
How do I convert m2 per hectare to ft2 per acre?
Multiply by 4.356: 1 m2/ha = 4.356 ft2/acre. For example, a stand of 13.91 m2 per hectare equals 60.58 ft2 per acre. The calculator reports both units automatically.
What is Reineke stand density index (SDI) and stocking percent?
SDI combines tree count and size into one density number: SDI = trees per hectare times (quadratic mean DBH in cm divided by 25.4) to the power 1.605. Stocking percent is SDI divided by the species maximum SDI, times 100. Example: six trees averaging about 24.8 cm DBH on a 500 m2 plot give 120.00 trees per hectare, a quadratic mean DBH of 24.87 cm, SDI = 116.00, which is 50.44 percent of the default maximum SDI of 230 — a fully stocked stand.
How do I read the stocking classes?
Below 35 percent of maximum SDI is understocked, 35 to 60 percent is fully stocked, 60 to 100 percent is overstocked, and above 100 percent means the stand exceeds the species maximum you set — double-check the max SDI value. These are approximate rules of thumb; the calculator lets you change the maximum SDI, since species maxima typically range from 230 to 900.
What is quadratic mean DBH and why use it instead of the average DBH?
Quadratic mean DBH (Dq) is the square root of the mean of the squared DBHs. It gives the diameter of the tree of average basal area, so it weights larger trees correctly. Example: DBHs of 28, 32, 30, 25, 35, 29, 31, 27, 33 and 26 cm have an arithmetic mean of 29.6 cm but a quadratic mean of 29.76 cm.
Does this work with inches and acres?
Yes. Enter DBHs in inches and plot area in ft2 and you get basal area per acre as well. Example: five trees of 11 to 14 inches DBH on a quarter-acre plot (10890 ft2) give 15.93 ft2 per acre, equal to 3.66 m2 per hectare, at 49.42 trees per hectare.
Why is DBH measured at breast height, 1.3 m or 4.5 ft?
Breast height is a standard, convenient point that avoids the swollen trunk base while staying easy to reach. Measuring every tree at the same height makes basal areas comparable between trees, plots, and inventories. Measure on the uphill side on slopes, and above any deformity if one occurs exactly at breast height.
Which trees should I include in a plot tally?
Follow your inventory protocol, but the common rule is to tally every live tree at or above the minimum DBH for your survey, often 5 or 10 cm. Record dead standing trees separately. Skipped lines in the DBH list are counted and reported so you can spot data-entry mistakes.
Is basal area the same as timber volume?
No. Basal area is a cross-sectional area, while volume also needs height and a form factor. Basal area per hectare is, however, the main density input that foresters combine with height to estimate stand volume and to decide on thinning.
Can this replace a professional forest inventory?
It is an educational and field-check tool, not a substitute for a professional cruise. Real inventories use randomized plot designs, species-specific volume tables, and error estimates. For timber sales, carbon credits, or legal boundary work, hire a qualified forester.
Free tool by NRTechStudio