559
55.9%
559
55.9%
The Stand Density Index (SDI) Calculator computes Reineke's Stand Density Index, a widely used measure of relative stand density in forestry. SDI quantifies how fully stocked a forest stand is by combining tree count and average tree size into a single number referenced to a standard size. It allows meaningful comparison of stocking levels across stands of different ages and tree sizes, making it invaluable for silvicultural prescriptions, thinning schedules, and growth modeling.
Enter the number of trees per hectare and the quadratic mean DBH to obtain the SDI and relative density as a percentage of a typical maximum SDI of 1000.
The calculator uses Reineke's SDI formula:
SDI = Trees/ha x (25 / QMD)-1.605
Where QMD is the quadratic mean diameter at breast height in cm, and 25 cm is the reference diameter. The exponent -1.605 is Reineke's constant, derived from the observed relationship between tree number and mean size in fully stocked stands. The formula is equivalent to: SDI = Trees/ha x (QMD/25)^1.605.
Maximum SDI varies by species (typically 600-1200 for common species), but 1000 is a useful general reference. Stands above 55% of maximum SDI are considered fully stocked, while those below 35% are understocked.
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Results
1200 trees/ha at 15 cm QMD gives SDI of 495 (about 50% of max), indicating moderate stocking.
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Results
400 trees/ha at 35 cm QMD yields SDI 683 (68% of max), indicating full stocking approaching need for thinning.
Reineke (1933) observed that in fully stocked, even-aged stands, the log of tree number decreases linearly as log of mean diameter increases, with a slope of approximately -1.605. This relationship holds remarkably well across many species and has been confirmed by numerous studies. Some species show slight deviations (slopes from -1.4 to -1.8), but -1.605 is the standard reference value used in most applications.
SDI guides thinning decisions. Stands are typically thinned when SDI reaches 55-60% of maximum (the onset of competitive stress) and thinned down to 35-40% of maximum. This creates growing space for remaining trees while maintaining site occupancy. The upper management zone (55-100% of max SDI) represents increasing competition and mortality risk, while the lower zone (below 35%) represents underutilized growing space.
Quadratic mean diameter (QMD) is the diameter of the tree of average basal area. It is calculated as the square root of the mean of squared DBH values: QMD = sqrt(sum(DBH²)/n). QMD is always larger than arithmetic mean DBH because it gives more weight to larger trees. It is the preferred measure of average tree size in forestry because basal area and volume calculations based on QMD are exact, while those based on arithmetic mean DBH are biased.
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