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Stand Density Index Calculator

Free Stand density index Calculator for trees & forestry. Enter variables to compute results with formulas and detailed steps.

Reviewed by Daniel Agrici, Founder & Lead Developer

Reviewed by Daniel Agrici, Founder & Lead Developer

Formula

SDI = TPA x (QMD / 10)^1.605

Stand Density Index equals the number of trees per acre multiplied by the quadratic mean diameter (in inches) divided by 10, raised to the power 1.605. This normalizes stand density to a reference diameter of 10 inches.

Worked Examples

Example 1: Pine Plantation SDI

Problem:A loblolly pine stand has 300 trees per acre with a QMD of 8 inches. Calculate SDI and relative density (max SDI = 450).

Solution:SDI = 300 x (8/10)^1.605\nSDI = 300 x 0.8^1.605\nSDI = 300 x 0.7053\nSDI = 211.58\nRelative density = 211.58 / 450 = 47.0%

Result:SDI = 211.58, Relative density = 47.0% (fully stocked)

Example 2: Mature Hardwood Stand

Problem:A mixed hardwood stand has 150 TPA and QMD of 14 inches. Calculate SDI.

Solution:SDI = 150 x (14/10)^1.605\nSDI = 150 x 1.4^1.605\nSDI = 150 x 1.6284\nSDI = 244.26

Result:SDI = 244.26

Frequently Asked Questions

What is Stand Density Index (SDI)?

Stand Density Index is a measure of the stocking or crowding of a forest stand, developed by L.H. Reineke in 1933. SDI relates the current number of trees per acre to the quadratic mean diameter, providing a single number that describes how densely packed a forest is regardless of tree age or site quality. It is widely used in forest management to determine when thinning operations are needed, set target stocking levels, and predict future stand development.

What is relative density and why does it matter?

Relative density is the ratio of current SDI to the maximum SDI for a given species, expressed as a percentage. Maximum SDI values vary by species: Douglas-fir is around 600, loblolly pine is about 450, and red oak is approximately 400. Stands below 25% relative density are understocked, 35-55% is fully stocked (optimal growth), and above 60% signals overstocking where competition-induced mortality accelerates. Forest managers use relative density to time thinning operations.

References

Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy