# How to Calculate Trees Per Acre

Trees per acre, also known as TPA, is one of the most important metrics for determining the timber density of a forest, particularly in softwood silviculture. Luckily, it is also one of the easiest metrics to measure. **To calculate trees per acre, simply use a fixed radius plot to count trees within a given area and multiply the number of trees by the denominator of the fraction of an acre the plot represents. **If that sounds confusing, don’t worry: It’s actually quite simple. We’ll explain how to do it in depth in this article. Alternatively, if you want to convert a spacing regie into a TPA measure or vice versa, there is a chart at the bottom of the article that can help you. But first, let’s explain the fundamentals of what exactly a fixed radius plot is and how they can be used to calculate trees per acre.

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## What Is a Fixed Radius Plot?

Fixed Radius plots are a method of sampling in which every individual within reach of a specified, consistent radius is tallied or measured. The area of the circles created by the radius represents a given fraction of a larger area, such as a 1/100th of an acre circle, and this is the sample area. By measuring trees within that plot, we can then extrapolate and estimate data about the population of the larger area. By sampling enough of these plots and averaging them, we can get a decent idea of the true numbers across large areas that are otherwise impractical to measure.

## Using Fixed Radius Plots to Calculate Trees Per Acre

Using fixed radius plots properly is more than just drawing circles and counting trees, however. It requires good, consistent technique, an appropriate radius, and a non-biased sampling method. Let’s take a closer look at every step of the process.

### How to Take a Plot

To take fixed radius plots to calculate trees per acre, you need only three materials:

- A tape measure
- Rope or cable
- Sturdy wooden stake or metal rod
- A notepad or digital recording device
- (
**Optional**) Laser Distance Measure

To begin, place the stake or rod firmly in the ground so it does not easily move from side to side. This is your plot center. Next, affix a cable or rope to the plot center in such a way that it moves freely around the rod and does not wind (looping it around the stake, for example). Measure the rope to the desired length and cut it or mark it at the correct length (for now, we will use 11.8′, or 1/100th of an acre). Now we are ready to begin tallying.

- Find a place to begin. Hold out the rope, and begin moving clockwise.
- Any tree with a center that lands within reach of the rope falls within the plot and should be tallied. If the center falls outside of reach, the tree should not be counted. reference the diagram above to see what trees should and should not be counted.
- Once you count your first tree, be sure to mark it with a ribbon or paint so you don’t lose track of where you started counting.
- Proceed to move in a complete circle and tally every single tree that falls within the plot. Stop Counting when you return to your starting point.

When you are done, multiply the tally by the denominator of the fraction of acreage your plot represents. This number represents the total trees per acre. for example, in the diagram above, the 8 trees tallied in a 1/100th acre plot represent 800 trees per acre, as 8*100=800. However, 8 trees tallied in a 1/50th of an acre plot represent only 400 trees per acre.

#### Alternative Method

If you are dealing with larger radius plots, it can be easier to use a laser distance measure instead of a rope or cable to find distances. Simply stand at plot center and shoot a laser at trees, going around in a circle. Trees that fall within the specified distance, such as 11.8′, are tallied. Using this method can be a much faster and more convenient way to calculate trees per acre.

### Choosing Plot Radius

How do you know what plot radius to use? Generally, the larger the trees on a given plot of land, the larger the radius needed. As trees grow, they outcompete smaller trees, and so TPA decreases as mean diameter increases. The relationship is demonstrated with the graph below.

When trees are fewer and farther between, a larger plot is needed to ensure enough trees are counted to generate useful data. If a plot size is too large, however, collecting data can be difficult and needlessly tedious. **It is important to choose the proper size plot**. Below is a table of three common plot sizes and the type of timber they should be used for.

Acreage of Plot | Plot Radius | Optimum Timber Type |

1/100 | 11.8′ | Regeneration |

1/10 | 37.2′ | Small Sawtimber and pulpwood |

1/5 | 52.7′ | Large Sawtimber |

### How Many Plots Should Be Taken?

To be able to calculate trees per acre accurately, you need to take several plots on a given piece of land, but how many, exactly, should be taken? There is no clear rule, and there may be additional considerations if confidence interval or statistical integrity is important to your project. That said, in my years as a forester, I have found that **one plot for every five acres (with a three plot minimum) is a good rule of thumb to generate usable data. **

### How to Choose a System For Random Sampling

In collecting data, it can be easy to greatly bias data by picking and choosing (even if it is done unconsciously) the areas you sample. For example, when walking in the woods, it is easy and natural to choose the path of least resistance and walk through more open areas, but doing so may cause you to sample areas with less trees, greatly skewing trees per acre calculations downward. It is important you devise a system to sample randomly **before you head out to the field.**

One of the easiest systems to use is to set up a grid system and take plots at predetermined intervals. You could walk a line eastward and take a plot every 400 feet, walk south 400 feet, and then walk to the west taking another plot every 400 feet. The result is a 400’x400′ grid collection scheme.

Alternatively, you can relatively randomly place points on a GPS or Google Earth and navigate to them in the field. However, This method can be slightly prone to bias.

It is up to you to determine how random your points need to be, your tolerance for potential bias, and **what method best suits your needs.**

### Averaging Plot Totals

Once all plot data is collected, averaging out the data is simple. Add up the calculated trees per acre for each plot and then divide by the total number of plots taken. Below is a sample table of collected data and the resulting average.

Plot | TPA |

Plot 1 | 800 |

Plot 2 | 900 |

Plot 3 | 600 |

Plot 4 | 500 |

Plot 5 | 800 |

Average | 720 |

In this example, the average of the data from the five plots is 720 trees per acre, and so this represents the estimate for trees per acre across the sampled piece of land.

## Converting Tree Spacing to Trees Per Acre

If you are involved in plantation forestry, it can also be useful to know the conversions between spacing regimes and trees per acre. Spacing regies refer to the dimensional spacing between trees, but how this translates into trees per acre depends on whether these trees are spaced equilaterally (hexagonally) or in a square arrangement. The difference between these regimes can be seen in the diagram below.

Understanding this difference, you can see the conversions between spacing (in feet) and trees per acre using the chart below. If you do not know the arrangement, or if it is a more natural condition (such as a stand that was pre-commercially thinned, assume equilateral spacing.

## Why Is It Important to Calculate Trees Per Acre?

Trees per acre is one of the most important measures to use to determine the density of a forest. Trees per acre can be used to help determine spacing for pre-commercial thinning regimes to maximize the amount of timber growing on each acre and ensure trees have enough room to grow. Additionally, TPA can be useful when timber is being grown on a small-tree-specific basis, and trees are selected for harvest individually, such as for individual firewood consumption.

## When to Use Trees per Acre and When to Use Basal Area

Trees per acre has limitations as a useful metric, however. It is a measurement of the density of individual trees only. It has no relation to total timber volume. Thus, TPA is best used in even-aged stands with more or less uniform timber. In such cases, each tree can be assumed to contain a certain amount of volume, and TPA can be more easily used to make management decisions or make assumptions about timber inventory. Where this is not the case and trees are uneven-aged, non-uniform, and variable, basal area, a measurement of timber area per acre, is a much more useful metric. So if you decide to calculate trees per acre, be sure it is a metric that suits your needs.

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