Forest Stand Density Index and Relative Density Calculator

Table of contents

• How to use
• Common mistakes
• Definitions
• Methodology
• Limitations & assumptions
• Sources

Trees per acre: The expanded number of live trees in one acre of the stand.

Quadratic mean diameter (QMD): A stand-level diameter that gives more weight to larger trees. It is commonly reported in inches and is not usually the same as arithmetic-average DBH.

Stand density index (SDI): A Reineke density measure that expresses the stand as an equivalent number of 10-inch trees per acre. SDI is not unitless, so its area and measurement units matter when comparing values. [1]

Maximum SDI: The reference SDI used as the denominator for relative density. It can vary with species, forest type, region, and stand composition. [2]

Relative density: Current SDI divided by maximum SDI, shown by this calculator as a percent.

DBH: Diameter at breast height, usually measured at 4.5 feet above ground on the uphill side of a tree.

Mistake: Entering a tree count from a small sample plot as Trees per acre.
Fix: Expand the plot tally to trees/acre first, or use the trees-per-acre value from the cruise summary.

Mistake: Using arithmetic-average DBH for Quadratic mean diameter.
Fix: Use QMD from the inventory summary. Average DBH and QMD are different measurements.

Mistake: Leaving the example value in Maximum SDI for this stand without checking its fit.
Fix: Replace it with a documented value for the stand's species, forest type, region, and composition.

Mistake: Treating Relative density based on entered maximum SDI as a universal thinning prescription.
Fix: Use the percent as planning information and apply local silvicultural guidance to the stand.

Mistake: Comparing Stand density index at a 10-inch reference diameter with a value reported per hectare.
Fix: Compare only SDI values reported with compatible area and measurement units.

Mistake: Typing a malformed number such as 1,01 in Trees per acre.
Fix: Use commas only for thousands, such as 1,200, and use a decimal point for fractional values.

• This calculator uses one QMD and one trees-per-acre value, which is the direct even-aged stand workflow. Strongly uneven-aged, mixed, or multi-storied stands may need a diameter-class or tree-level SDI method.
• Relative density changes directly with the entered maximum SDI. The calculator cannot verify that the reference fits the stand.
• The result is in US units: trees per acre at a 10-inch reference diameter. Do not directly compare it with SDI reported per hectare or under a different diameter convention.
• Live-tree definitions, plot expansion methods, measurement error, and which trees are included in the inventory can change trees per acre, QMD, and the calculated SDI.
• A relative-density percent is planning information. It does not account for site conditions, species-specific objectives, tree health, harvest constraints, or local thinning guidance.

Calculation method

The calculator uses the conventional Reineke equation for a stand summarized by trees per acre and QMD. The reference diameter is 10 inches and the exponent is 1.605. [1]

SDI = trees per acre * (QMD in inches / 10) ^ 1.605

It then divides the calculated SDI by the maximum SDI you entered and changes the ratio to a percent.

Relative density percent = 100 * SDI / maximum SDI

The selected source category for maximum SDI is displayed with the interpretation, but it does not change either equation.

Worked example

For 300 trees/acre, a QMD of 12 inches, and a maximum SDI of 500 trees/acre, the calculated SDI is about 401.98 trees/acre. Relative density is about 80.40 percent because 401.98 divided by 500 times 100 equals 80.40.