Quadratic Mean Diameter (from a Tally)
The QMD the Reineke stand density index requires, straight from the tally sheet.
Example
You enter
- DBH tally (one token per tree "12" or per class "12:40"; commas or new lines) 8, 10, 10, 12, 14
You get
- Quadratic mean diameter 10.99 in
- Arithmetic mean (for contrast) 10.8 in
- Trees tallied 5
- Total basal area (tallied trees) 3.29 ft^2
Checked against published worked examples from: USDA Forest Service forest-mensuration practice.
Details, formula, and sources
ScopeQMD = sqrt(sum(count x DBH^2) / trees). Enter a diameter tally (one token per tree "12" or per class "12:40") and get the QMD, the arithmetic mean beside it (so the gap is visible), the tree count, and the tallied basal area. QMD is the diameter of the tree of average basal area, always at or above the arithmetic mean - the number a plain average gets wrong. A mensuration helper, not a cruise compilation.
Formula or tableQMD = sqrt( sum(count x diameter^2) / sum(count) ); arithmetic_mean = sum(count x diameter) / sum(count); basal_area_ft2 = 0.005454 x sum(count x diameter^2).
Source and editionUSDA Forest Service forest-mensuration practice (quadratic mean diameter), by name.
Free accessThe quadratic-mean-diameter definition is standard forest mensuration; the forester and the cruise design govern the compilation.
What governsEstimate. AHJ and licensed professional govern.
API field namestally, qmd_in, arithmetic_mean_in, tree_count, basal_area_ft2
- Quadratic vs arithmetic QMD is the diameter of the tree of average basal area, always >= the arithmetic meanUSDA FS forest mensuration
- Basal-area constant per-tree basal area is 0.005454 x DBH^2 ft^2 for DBH in inchesforestry mensuration