Trees per acre, often abbreviated as TPA, represents the density of a forest stand by measuring the number of individual trees on a single acre of land. This metric is a fundamental component of forest management, providing quantitative data needed for planning operations like thinning, harvesting, and planting new stock. The standard definition of an acre is a plot of land covering 43,560 square feet. The method used to determine TPA depends entirely on whether the stand is a new plantation with uniform spacing or an established natural forest.
Determining Density Based on Spacing
The simplest method for calculating TPA applies to tree plantations or orchards where the trees are intentionally placed in a consistent, grid-like pattern. This calculation relies solely on the known distance between the planted trees and rows, requiring no field measurement of existing trees.
The method uses the total square footage of an acre divided by the area occupied by a single tree and its surrounding space, which is the product of the row spacing and the tree spacing. For example, if trees are planted 10 feet apart within the row and the rows are 10 feet apart, the area per tree is 100 square feet. The formula is therefore 43,560 square feet divided by the spacing area per tree.
A plantation set at a 10-foot by 10-foot spacing yields 435.6 TPA, calculated by dividing 43,560 by 100. Similarly, a denser planting of 8 feet by 8 feet results in 64 square feet per tree, equating to 680 TPA. This simple arithmetic provides an immediate, highly accurate TPA count for new stands, which serves as a baseline for all subsequent management decisions.
Fixed-Area Sampling Methods
For established forests where tree placement is uneven and natural, foresters cannot rely on a simple spacing calculation and must employ a sampling technique. Fixed-area sampling involves laying out small, consistently sized plots across the stand, counting the trees within them, and then extrapolating that count to a full acre. This process avoids the impracticality of counting every tree in a large forest.
The most common approach uses circular plots, typically a fraction of an acre, such as a one-tenth or one-twentieth acre size. A one-tenth acre circular plot has a fixed radius of 37.2 feet, while a one-twentieth acre plot has a radius of 26.3 feet. To perform the calculation, the number of trees counted within the plot is multiplied by the inverse of the plot size fraction, known as the expansion factor.
For instance, if a forester counts 40 trees within a one-tenth acre plot, the expansion factor is 10. Multiplying the tree count by the expansion factor (40 trees multiplied by 10) results in an estimate of 400 TPA for that specific plot location. Multiple plots are measured across the stand, and the individual TPA estimates are then averaged together to provide a reliable estimate for the entire forest, ensuring the sample represents the natural variability in tree density.
Variable Radius Plot Sampling
Professional foresters often use a more specialized and efficient technique called variable radius plot sampling, sometimes referred to as point sampling, particularly when estimating timber volume is the primary goal. Unlike fixed plots, this method does not use a fixed-size boundary but instead selects trees based on their size and proximity to a central point. The technique relies on a concept known as Basal Area (BA), which is the cross-sectional area of a tree stem measured at breast height and is expressed in square feet per acre.
The selection of trees is accomplished using an angle gauge or an optical wedge prism, a specialized tool that refracts light to offset a tree’s image. The observer holds the prism over the plot center and rotates 360 degrees, tallying a tree as “in” if the refracted image still overlaps with the main trunk, indicating the tree is large enough or close enough to be included in the sample. Each tree tallied in this variable plot represents a specific amount of basal area per acre, determined by the Basal Area Factor (BAF) of the prism being used.
The BAF is a predetermined constant that dictates the relationship between a tree’s diameter and its maximum distance from the plot center to be counted. To calculate TPA using this method, foresters first determine the basal area per tree (Tree BA) for every tallied specimen using the formula: Tree BA = 0.005454 multiplied by the diameter at breast height squared. The final TPA is determined by dividing the Basal Area Factor by the individual tree’s basal area, which yields a unique expansion factor for each tree. These expansion factors are then summed to reach the total TPA for the plot.