More about Lumber Volume MeasuresOverview

Measuring Volume of Growing Trees

Determining Height

Determining the Diameter and Calculating Volume

Measuring Lumber

Lumber Dimensions

Board Foot

Cords

Cubic Feet or Meters

Computer Models

Measuring Weight Instead of Volume

OverviewWood that is cut down for human needs is referred to as

Measuring Volume of Growing TreesWhen estimating volume of lumber from the trees that are still growing, one can collect measurements of a sample plot, and then approximate these calculations for the entire plot. Traditionally these plots are circular, although not always. In other situations sample trees are selected individually throughout the woodland area instead of measuring all of the trees on sample plots. If the total area of woodland that needs to be measured is small, it is possible to measure all of the trees there, but this approach is less common.

BC is the usable height of the tree — anything above point C will be discarded. This height equals the tangent of the angle A multiplied by AB.

Determining HeightFirst, it is important to determine which part of the tree can be used commercially, and which part is to be discarded. The height of the log, also known as

Let us consider the illustration to see how we can determine the height of a tree. Here point B is at the base of the tree and point C marks the end of the usable trunk of the tree. We will not use anything above point C, once the tree is logged. Thus, BC is the height that we need to calculate. Climbing the tree to do so would not be reasonable or easy to do, so we will use trigonometric formulas for calculating the side of a right-angled triangle ABC. We will walk away from the tree until point A, noting the distance from A to B, and then find the angle A using a protractor or similar tools. Here BC is the opposite side of the triangle, and AB is the adjacent side, so we can calculate BC by multiplying the tangent of our angle A by AB.

A hypsometer allows the user to calculate the height of an object by providing the value for the height above the eye level, height A, and the height below the eye level, height B. The two are then added together.

It is also possible to measure the height of a tree using tools known as

Determining the Diameter and Calculating VolumeOnce the height is known, the diameter of the tree is measured. Sometimes tools such as

Measuring LumberThere are many different units for measuring the volume of lumber — the choice depends on the intended use of the lumber and on the length of each piece of wood. Larger pieces of 2.4 meters or 8 feet are called logs, while the smaller sections are bolts and sticks, although we will refer to all logged wood as “logs” collectively, for simplicity.

How the logs would be cut depends on the specific needs of the buyer. The tree on the left is cut into two logs, A and B, while the tree on the right is cut into a single log C. The total volume of logs A and B is larger than that of log C, but log C is longer, which is beneficial in some cases. Bark and wood that is discarded are labeled in brown and pink.

Lumber undergoes a number of changes during the processing from the initial rough-green stage, especially as it is being dried and cut. Prior to cutting the wood is scaled. Scaling is a process of determining what amount of wood can be cut into sawlogs or boards, and how much usable wood will be yielded. The yield is estimated using one of the many rules about cutting a log, and the choice of the rule depends on the local legislation, the intended use for the lumber, and on what rule the purchaser and the seller can agree on. When the wood is later cut, the surface of logs or boards is made more uniform by removing the uneven parts and the volume diminishes as a result. Scaling provides the estimate of usable wood while taking these reductions in volume into consideration.

You can see a very simple example of scaling on this illustration. Here one log is scaled in two different ways. Blue lines represent the cut, brown is the bark that will be discarded, pink is the rest of the discarded wood, and yellow are the logs after scaling. In the picture on the left the scaling is more economical, rendering two separate logs, A and B. In the picture on the right the total volume of log C is smaller, but this log is longer. Sometimes longer logs are needed and loss in volume is justified.

It is important to note that if the estimate is made without cutting the logs into boards, there is a possibility that the volume of usable wood is even smaller, once cut, due to the defects of the wood. That is why some buyers of uncut wood scrutinize it carefully to detect any potential defects, and negotiate a price reduction if they doubt the quality.

Volume of lumber also decreases as it dries, and the change in volume depends on the kind of lumber that is being processed, and can sometimes decrease by 30% or more. Therefore, when considering measurements for lumber we have to keep in mind at what stage the volume of the lumber was measured. Some volume measurement units can only be used with wood, processed in a specific way, for example for pre-cut wood.

Lumber DimensionsOne could calculate the volume of lumber cut into boards by multiplying their width by the height and by the length. It is important to note, however, that the specified dimensions often refer to the nominal size, not the actual size of the boards. This is especially true for the width and the height of a board. For example, the actual size of a 4 inches by 6 inches board is 3.5 inches by 5.5 inches. This is because the nominal sizes are for the boards only processed initially, but the drying of the boards and the final processing to make them smooth, reduces the nominal size. For dimensions less than 2 inches, this difference is 0.25 inches, for dimensions under 8 inches — 0.5 inches, and for anything larger it is 0.75 inches. When calculating the volume using the dimensions of the lumber, it is important to use the actual dimensions, not the nominal ones.

Board FootWithin the allowed diameter of the smallest width at the top of the log, marked in blue, a log can be cut into boards in a variety of ways. The rectangles in different shades of yellow mark possible cuts for boards in cross-section. Pink and brown sections are the discarded wood and bark respectively.

Board foot is a unit generally used in the USA and Canada for uncut wood, but with the assumption that the wood is cut into boards of specified height and width, determined by the selected rule. The length could be arbitrary. This means that the “extra” wood to be discarded or outside this size is not included in the calculations. One board foot is the volume of 1×12×12 inches. The calculations for uncut wood are usually done as estimates, and the formulas within a given rule take the dimensions of the log and produce the output. The illustration shows some possibilities of cutting the same log. Here we are looking at the cut on the wider bottom part of the tree, and the blue circle indicates the limitations due to the smaller diameter at the top of the tree. The pink areas are discarded, and various cuts for the final boards are shown in different shades of yellow. Here the cuts shown are rough cuts only — as we have discussed earlier, these boards will be further reduced during the final processing.

Some of these formulas are more accurate for specific dimensions, for example for a specified range of diameters. In general, using board feet is not always accurate when measuring uncut wood, because the way a board is processed affects the total volume of lumber, and the processing may differ greatly based on equipment and skill.

Firewood

CordsUnprocessed wood used for firewood or production of paper, which is stacked together is measured in cords. One cord represents the volume of a stack of 8 feet by 4 feet by 4 feet. Measurements in these units include not only the wood but the space between logs as well. Therefore this measure is not as accurate because it depends on how well the logs are stacked, but this method provides a value that is easy, cheap, and fast to calculate — this is why it is popular. There are also ways to calculate the volume of a stack of wood that uses other units besides cords, for example cubic meters of feet, but they are not commonly used.

Cubic Feet or MetersUnlike board feet, cubic feet or cubic meters are often used to measure entire logs including the parts that will later be discarded during processing, but excluding space between the logs if they are stacked, and often excluding the volume of the bark. This gives a less accurate estimate of the actual amount of wood that will remain after processing than with board feet, but at the same time this measurement is more consistent and easy to perform. Generally it is calculated using the values for height and diameter. If the logs are longer than 20 meters, they are usually divided for the purpose of measurement, and diameter is measured for each part. 100 cubic feet are also known as a cunit.

Pulpwood is commonly measured in cubic meters or feet. It is also possible to measure lumber in cubic meters or feet after it was scaled and cut. This is done less commonly but it is very easy to calculate, as long as you keep in mind the actual dimensions of the boards and not the nominal ones.

Computer ModelsCurrent technology allows for cost-effective three-dimensional modelling of logs. A three-dimensional model is created based on the data, to allow for more accurate volume calculations. The precision that three-dimensional models allow helps when working with expensive wood.

Measuring Weight Instead of VolumeIn some cases it is more reasonable to measure lumber by weight. Weight is often measured for lumber carried in trucks, by putting the entire truck on the scales. This is done to avoid extra work of unloading the lumber on the scale and then loading it back. In this case the weight of the truck is substituted from the total weight. While the measurements are taken, the truck is stationary and without the passengers or the driver inside. Weight measurements are simple and cheap to perform and are often used for the less valuable wood.

In some cases weight and volume measurements are combined. Doing so is very labor-intensive, but may be necessary when higher precision is needed. It is important to note that weight is affected by the moisture content of the wood, so additional calculations may be needed to account for this.

Measuring Volume of Growing Trees

Determining Height

Determining the Diameter and Calculating Volume

Measuring Lumber

Lumber Dimensions

Board Foot

Cords

Cubic Feet or Meters

Computer Models

Measuring Weight Instead of Volume

OverviewWood that is cut down for human needs is referred to as

**“lumber”**in American English and**“timber”**in British English. There are some other specific distinctions and contexts in which each word is used, but for the purposes of this article we will use the word “lumber”. In the industry, the amount of lumber is commonly measured by volume. The usable volume can be estimated even before the trees are cut, and it is also measured during different stages of processing. Estimating volume may be important for people, who grow trees for logging, for example when selling or purchasing a new plot of woodland, or to estimate the price for selling the lumber, as well as potential income. It is worth noting that these surveys often include an evaluation of the quality of the wood to estimate how much of it may be unusable, and consider the additional costs of offsetting the environmental effects of logging.Measuring Volume of Growing TreesWhen estimating volume of lumber from the trees that are still growing, one can collect measurements of a sample plot, and then approximate these calculations for the entire plot. Traditionally these plots are circular, although not always. In other situations sample trees are selected individually throughout the woodland area instead of measuring all of the trees on sample plots. If the total area of woodland that needs to be measured is small, it is possible to measure all of the trees there, but this approach is less common.

BC is the usable height of the tree — anything above point C will be discarded. This height equals the tangent of the angle A multiplied by AB.

Determining HeightFirst, it is important to determine which part of the tree can be used commercially, and which part is to be discarded. The height of the log, also known as

**merchantable tree height**would depend on what the wood is intended for, and on how wide the tree is. Once it is decided which part of the tree is to be used, one can measure the actual height from the ground to the top of the usable part of the tree, using trigonometric formulas.Let us consider the illustration to see how we can determine the height of a tree. Here point B is at the base of the tree and point C marks the end of the usable trunk of the tree. We will not use anything above point C, once the tree is logged. Thus, BC is the height that we need to calculate. Climbing the tree to do so would not be reasonable or easy to do, so we will use trigonometric formulas for calculating the side of a right-angled triangle ABC. We will walk away from the tree until point A, noting the distance from A to B, and then find the angle A using a protractor or similar tools. Here BC is the opposite side of the triangle, and AB is the adjacent side, so we can calculate BC by multiplying the tangent of our angle A by AB.

A hypsometer allows the user to calculate the height of an object by providing the value for the height above the eye level, height A, and the height below the eye level, height B. The two are then added together.

It is also possible to measure the height of a tree using tools known as

**hypsometers**. They generally use the same trigonometric formulas for calculating the side of a right-angled triangle, except there are several triangles considered, because the measurement is not done at the ground level but at eye level. To use a hypsometer, one generally needs to pre-set the known values, then look through the hypsometer at the object being measured, and check the pre-calibrated scale for the result. The latter operation is usually done in two steps. First we would determine the height of the tree from the eye level up, height A in the illustration, marked in fuchsia. Following that, we will calculate the height from the eye level and down to the base of the tree. This height B is marked in yellow on the illustration. We will then add the two heights together to get the overall height.Determining the Diameter and Calculating VolumeOnce the height is known, the diameter of the tree is measured. Sometimes tools such as

**dendrometers**are used to do this. Generally the diameter is calculated not at the base of the tree near the ground, but at the height of 4.5 feet or 1.37 meters above ground. If the tree grows on an incline, then this height is measured from the uphill side of the tree. This value is known as**diameter at breast height**, because 4.5 feet is roughly the breast height for an average person. It is often written as**DBH**. With this information one can then estimate the volume using formulas for volume calculations of simple geometric objects. There are also tables available that provide the volume for a given height and DBH.Measuring LumberThere are many different units for measuring the volume of lumber — the choice depends on the intended use of the lumber and on the length of each piece of wood. Larger pieces of 2.4 meters or 8 feet are called logs, while the smaller sections are bolts and sticks, although we will refer to all logged wood as “logs” collectively, for simplicity.

How the logs would be cut depends on the specific needs of the buyer. The tree on the left is cut into two logs, A and B, while the tree on the right is cut into a single log C. The total volume of logs A and B is larger than that of log C, but log C is longer, which is beneficial in some cases. Bark and wood that is discarded are labeled in brown and pink.

Lumber undergoes a number of changes during the processing from the initial rough-green stage, especially as it is being dried and cut. Prior to cutting the wood is scaled. Scaling is a process of determining what amount of wood can be cut into sawlogs or boards, and how much usable wood will be yielded. The yield is estimated using one of the many rules about cutting a log, and the choice of the rule depends on the local legislation, the intended use for the lumber, and on what rule the purchaser and the seller can agree on. When the wood is later cut, the surface of logs or boards is made more uniform by removing the uneven parts and the volume diminishes as a result. Scaling provides the estimate of usable wood while taking these reductions in volume into consideration.

You can see a very simple example of scaling on this illustration. Here one log is scaled in two different ways. Blue lines represent the cut, brown is the bark that will be discarded, pink is the rest of the discarded wood, and yellow are the logs after scaling. In the picture on the left the scaling is more economical, rendering two separate logs, A and B. In the picture on the right the total volume of log C is smaller, but this log is longer. Sometimes longer logs are needed and loss in volume is justified.

It is important to note that if the estimate is made without cutting the logs into boards, there is a possibility that the volume of usable wood is even smaller, once cut, due to the defects of the wood. That is why some buyers of uncut wood scrutinize it carefully to detect any potential defects, and negotiate a price reduction if they doubt the quality.

Volume of lumber also decreases as it dries, and the change in volume depends on the kind of lumber that is being processed, and can sometimes decrease by 30% or more. Therefore, when considering measurements for lumber we have to keep in mind at what stage the volume of the lumber was measured. Some volume measurement units can only be used with wood, processed in a specific way, for example for pre-cut wood.

Lumber DimensionsOne could calculate the volume of lumber cut into boards by multiplying their width by the height and by the length. It is important to note, however, that the specified dimensions often refer to the nominal size, not the actual size of the boards. This is especially true for the width and the height of a board. For example, the actual size of a 4 inches by 6 inches board is 3.5 inches by 5.5 inches. This is because the nominal sizes are for the boards only processed initially, but the drying of the boards and the final processing to make them smooth, reduces the nominal size. For dimensions less than 2 inches, this difference is 0.25 inches, for dimensions under 8 inches — 0.5 inches, and for anything larger it is 0.75 inches. When calculating the volume using the dimensions of the lumber, it is important to use the actual dimensions, not the nominal ones.

Board FootWithin the allowed diameter of the smallest width at the top of the log, marked in blue, a log can be cut into boards in a variety of ways. The rectangles in different shades of yellow mark possible cuts for boards in cross-section. Pink and brown sections are the discarded wood and bark respectively.

Board foot is a unit generally used in the USA and Canada for uncut wood, but with the assumption that the wood is cut into boards of specified height and width, determined by the selected rule. The length could be arbitrary. This means that the “extra” wood to be discarded or outside this size is not included in the calculations. One board foot is the volume of 1×12×12 inches. The calculations for uncut wood are usually done as estimates, and the formulas within a given rule take the dimensions of the log and produce the output. The illustration shows some possibilities of cutting the same log. Here we are looking at the cut on the wider bottom part of the tree, and the blue circle indicates the limitations due to the smaller diameter at the top of the tree. The pink areas are discarded, and various cuts for the final boards are shown in different shades of yellow. Here the cuts shown are rough cuts only — as we have discussed earlier, these boards will be further reduced during the final processing.

Some of these formulas are more accurate for specific dimensions, for example for a specified range of diameters. In general, using board feet is not always accurate when measuring uncut wood, because the way a board is processed affects the total volume of lumber, and the processing may differ greatly based on equipment and skill.

Firewood

CordsUnprocessed wood used for firewood or production of paper, which is stacked together is measured in cords. One cord represents the volume of a stack of 8 feet by 4 feet by 4 feet. Measurements in these units include not only the wood but the space between logs as well. Therefore this measure is not as accurate because it depends on how well the logs are stacked, but this method provides a value that is easy, cheap, and fast to calculate — this is why it is popular. There are also ways to calculate the volume of a stack of wood that uses other units besides cords, for example cubic meters of feet, but they are not commonly used.

Cubic Feet or MetersUnlike board feet, cubic feet or cubic meters are often used to measure entire logs including the parts that will later be discarded during processing, but excluding space between the logs if they are stacked, and often excluding the volume of the bark. This gives a less accurate estimate of the actual amount of wood that will remain after processing than with board feet, but at the same time this measurement is more consistent and easy to perform. Generally it is calculated using the values for height and diameter. If the logs are longer than 20 meters, they are usually divided for the purpose of measurement, and diameter is measured for each part. 100 cubic feet are also known as a cunit.

Pulpwood is commonly measured in cubic meters or feet. It is also possible to measure lumber in cubic meters or feet after it was scaled and cut. This is done less commonly but it is very easy to calculate, as long as you keep in mind the actual dimensions of the boards and not the nominal ones.

Computer ModelsCurrent technology allows for cost-effective three-dimensional modelling of logs. A three-dimensional model is created based on the data, to allow for more accurate volume calculations. The precision that three-dimensional models allow helps when working with expensive wood.

Measuring Weight Instead of VolumeIn some cases it is more reasonable to measure lumber by weight. Weight is often measured for lumber carried in trucks, by putting the entire truck on the scales. This is done to avoid extra work of unloading the lumber on the scale and then loading it back. In this case the weight of the truck is substituted from the total weight. While the measurements are taken, the truck is stationary and without the passengers or the driver inside. Weight measurements are simple and cheap to perform and are often used for the less valuable wood.

In some cases weight and volume measurements are combined. Doing so is very labor-intensive, but may be necessary when higher precision is needed. It is important to note that weight is affected by the moisture content of the wood, so additional calculations may be needed to account for this.