In this article we will discuss about how to measure the diameter, height and volume of a tree.

**How to Measure the Diameter of a Tree ? **

The size of the tree is best described with the diameter of the tree. The diameter of the tree provides a measure of tree performance and is a useful starting point for estimating tree volume. It is the linear measurement, the main objective of which is to estimate the volume of the trees. The volume of a tree is dependent on diameter or girth at breast-height, total height and form factor.

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It is not only necessary for calculation of volume of logs, but also necessary for making inventory of growing stock as well as to correlate height, volume, age, increment of trees. In forestry, diameter should always be used for the description of the tree. In the past, girth has been used but this is no longer recommended.

A carefully defined point should be used for measuring the diameter of the tree. In many countries, especially India, this will be at 1.37 m above the base of the tree where the tree meets the ground. By convention, the diameter of forest trees is measured in centimeters at 1.37 m above the ground and is termed the “Diameter at Breast Height” or DBH. Because trees are measured with the bark on, this is also called the Diameter at Breast Height Over Bark (DBHOB).

When measuring live trees most information is presented as over bark dimensions. Diameter at Breast Height (DBH) is the most common parameter used in the measurement of standing timber. Generally DBH is not measured on dead trees or on those of less than 7 cm DBH. Universally adopted standard height for measuring girth, diameters and basal area of standing trees is 1.37 m and being practiced in India, Burma, America, Union of South Africa and other British Colonies. In Europe, Australia and UK, DBH is taken as 1.3 m which is recommended by FAO as standard. In New Zealand, DBH is measured at 1.4 m.

**The Significance of DBH: **

i. Convenient height for taking measurement.

ii. Avoids the fatigue caused unnecessarily.

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iii. Saves extra expenditure from not clearing the base.

iv. Abnormalities, e.g., root swell, disappear below breast-height.

v. Standardizes diameter measurement giving a uniform point of measurement. Diameter measurement at stump height is preferred, but standardization is lost because height of stump depends upon skill of the labour and the commercial value of the tree.

**Standard Rules Governing Breast Height Measurement DBH should be measured using calipers or tapes and the following conventions: **

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i. Breast height point should be marked by intersecting vertical and horizontal lines 12 cm long, painted with white paint.

ii. On flat ground, breast height (BH) should be marked by means of a measuring stick on standing trees at 1.37 m or 4 ft 6 inch above the ground level.

iii. On sloppy ground, BH should be measured from uphill side after removing any dead leaves or needles lodged there.

iv. In case of leaning trees on flat ground, BH is measured along the tree stem and not vertically on the side of the lean of the trees. On sloppy ground, BH on leaning trees should be measured from the uphill side along the leaning side of tree stem but not vertically.

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v. In abnormal trees, BH mark should be shifted little up or down as little as possible to a more normal position of stem and diameter is measured.

vi. If tree is forked above BH, it should be considered as a single tree. If tree is forked below the BH, each fork should be treated as separate tree. If forking renders the BH point abnormal, foregoing rule should be applied and the tree is counted as one or two depending on the place of measurement.

vii. BH of the tree with aerial root/ buttress formation is measured by shifting BH mark a little above the buttress formed.

viii. Callipers should be held in such a way that the arm of the calipers is at right angles to the stem.

ix. Tapes should maintain a loop, at right angles to the stem, around the tree. Obstacles such as branches, climbers, loose bark etc. should be removed before measurement so that they do not distort the result.

**DBH vs Girth **

DBH = Diameter at Breast Height = 2r

Where, r is the radius of stem

GBH = Perimeter of Stem at Breast Height = 2πr

Thus, GBH = DBH x π

**Under Bark vs Over Bark: **

DUB = DOB – 2t

GUB = GOB – 2πt where, t is the bark thickness

**Instruments such as diameter callipers, tapes and wooden scales are most commonly used and the details of their descriptions are presented below: **

**1. Diameter Callipers: **

It is generally made of wood and consists of a graduated rule and two arms. One is fixed at right angles to one end of the rule and the other movable parallel to the fixed rule. Size more than 120cm in length is rarely used. The use depends on the desired accuracy.

Callipers marked are painted to differentiate the reading. In some callipers, the arms are made parallel by screw adjustment. Metal callipers made of aluminum alloy are now in use. They are not heavier than wooden callipers and easy to keep clean and adjustment.

**The different types of callipers are: **

**i. Flurry Callipers: **

Arms from aluminum and graduated rule from wooden and bound with brass of sizes available in lengths of 80, 60, 35cms.

**ii. Fommes Calipers: **

All aluminum and same size as Flurry.

**iii. Indian Aluminum Callipers: **

They are variable in the length of 50 cm, 75 cm & 100 cm and they are graduated to show cm and mm.

Callipers are used to measure diameter of standing trees and logs. Diameters can be read directly in cm and mm thus making the instrument applicable for precise scientific work. If just one measurement is taken, an assumption is made that the cross-section at that point on the stem is perfectly circular. More than one measurement may be taken at that point on the stem. The average reading of these measurements is used as an estimate of the mean diameter.

The measurement of more than one diameter and the subsequent estimation of mean diameter are made easier with the use of electronic calipers. A single calliper measurement has the potential to both over or under estimate the true mean diameter. With increasing numbers of measurements using calipers, evenly spread around the stem, the deviation of the estimate of mean diameter from the true mean will decrease.

**2. Tapes: **

It is a band of cloth, reinforced cloth, plastic or steel about 1.5 cm wide and of varying length and is used to measure girth of trees and logs. It is usually graduated one side in cm and mm but sometimes it is graduated on both sides to give measurements in metric system on one side and those in British system on the other.

The ends of the tape are always plated some metal to prevent their tearing off but in case of longer tapes which are kept encased in some cover by winding it in or in some other cases too, the beginning of tape has a metal ring to hold it. In western countries, tapes are often provided with hook enables one person to measure large trees with tapes lying flat in correct position on the tree.

**The different types of tapes are: **

**i. Cloth Tape: **

The tapes are made of cloth, though they may be painted with some paint on both sides to give better look and correct them from the influence of water. They are also affected by fluctuations in length due to expansion in use.

**ii. Metallic Tape: **

The better quality of tapes are usually reinforced inside by metal wires and are, therefore called metallic tapes. They are painted with some durable paint. So, they are more durable and reliable.

**iii. Steel Tape: **

Steel tapes are used for precise work and are mostly used in forest for measurement in sample or research work.

**iv. Nylon and Fiberglass Tapes: **

In western countries, nylon coated steel tapes and fiberglass tapes are available.

The tree measuring tapes are generally 3 m long or at the most 5 m. But land measurement tapes may be 5 m, 10 m, 30 m or even 50 m long. The tree measuring tapes, which are usually small, do not generally have cases to cover them, though some steel tapes are 2 or 3 m long are kept in cases with some spring device to wind them back when not in use. Diameter is best measured with a diameter tape, which is a tape marked with units that convert the girth to the diameter. It is important to make sure that a correctly calibrated tape is used.

**3. Biltmore Stick: **

The Biltmore stick is a rule graduated to indicate the diameter of a tree. The rule is placed against the trunk of the tree at a tangent. With the eye about 25 inches away (average arm length), the diameter may be read by lining up the end of the stick with the line of vision to one side of the trunk and sighting across the rule to the other side. At the point where the line of vision crosses the stick, the graduation will indicate the diameter of the tree (CCC 2009).

**4. Wooden Scales: **

It is a flat wooden piece marked in cm and mm. Wooden scales are used to measure diameter of stumps or end sections of logs exposed as a result of cross- cutting. It is also used in stump and stem analysis for measuring radius at successive decade marks. The diameter should be measured along the passing through pith. In case of eccentric stumps or logs, two diameters, one along major axis and other at right angles to it should be measured.

As the end of the scale gets worn off by continuous use, the measurement should be taken from first centimeter and not from zero and one cm is deducted from the reading. The scale should be placed on edge so that the ends of the line to be measured coincide with marks of the scale. While reading measurement, the eye should be just above the mark. If this is not done, some error will creep in the measurement which is called error of parallax.

**Two types of wooden scales are available provided with folding arrangements at every 15 cm length: **

i. 30 cm long and 3 cm width

ii. 60 cm long and 1.5 cm width

**5. Wheeler’s Pentaprism Caliper: **

The pentaprism is a moderately expensive instrument used for measuring the diameter of the stem at heights normally above reach from the ground. The Wheeler’s pentaprism is an optical caliper that has two pentaprisms: a fixed one and a movable one. The construction allows generating parallel beams that correspond to the arms of a mechanical caliper. The sighting is situated at the position of the fixed prism and is separated into two parts.

Through the upper part, the observer aims directly at the left hand side of the trunk. The second beam goes through the two prisms where the movable prism is moved back and forth in such a manner that the second beam aims at the right hand side of the stem. This is achieved by simultaneously looking through the lower part of the sighting where the picture of the trunk in the prism is mirrored to the left along the left side of the tree.

**6. Spiegel Relaskop: **

The Spiegel Relaskop, also known as a Relaskop, is a sophisticated instrument that can be used to measure stand basal area and tree height and diameter at any point up a tree bole. In conjunction with other equipment, the Relaskop can be used in the estimation of distance (range) to an object and the number of trees per ha. The Relaskop has a peep-hole at the rear and a clear window at the front.

Three additional windows in the lower half of the instrument allow light to enter and illuminate the scale. A brake button, bottom half at the front of the instrument, allows a weighted wheel within the Relaskop to rotate. When looking through the peephole, a circular field of view is seen. The scales are seen in the bottom half of this field of view and scale readings are taken where the scale touches the line halfway up the field of view.

**Determination of the Stem Diameter for a Known Height on the Tree:**

First depress the brake button and move back until the tree stem appears to cover all of band 1 and the 4 quarter bands, i.e. the left side of the tree is aligned with the left of band 1 and the right side of the tree is aligned with the right side of the right most quarter band. Measure the horizontal distance (D in m) to the tree (directly beneath the point of interest). This method provides a maximum precision for determining diameter with the Relaskop.

Calculate the stem diameter (d in cm) as d = 4 x D

**Measurement of both height and diameter at same time at one or more points up the stem: **

1. Measure out a horizontal distance (D in m) appropriate for the height of the tree.

2. Sight to the base of the tree and the point of interest and determine height using the appropriate scales and calculations.

3. With the brake button depressed, align the right side of the tree with the right side of band 1 and ensure that the left side of the tree falls within the quarter bands. If the left side of the tree goes beyond the quarter bands, you will need to move further away from the tree – you will need to be 5 m away for every 20 cm of diameter. If the left side does not make it to the quarter bands, i.e., it falls within band 1, align the right side of the tree with the left side of band 1.

4. Estimate the number of quarter bands that are covered by the tree bole (between 0 and 4).

**Experienced operators can read down to fifths of a quarter band: **

1/5 just into the quarter band

2/5 almost half a quarter band

3/5 at least half a quarter band

4/5 almost the whole quarter band

5. **Calculate diameter (d in cm) as:**

d = 2 x D x [b + (q/4)]

where

b equals 1 if band 1 is covered and 0 otherwise,

q denotes the number of quarter bands (read down to one fifth of a quarter band).

6. The precision (p) in per cent of the estimate depends on the distance from the tree (D in m) and the estimated diameter (d in cm):

p = 10 x D/d

**How to Measure the Height of a Tree ? **

Total height of the tree is the straight line distance from the tip of the leading shoot (or from the highest point of the crown where there is no leader) to the ground level, usually measured on slopes from the uphill side of the tree. It is the straight-line distance from the highest point of the crown to the ground level. It is used to find out tree volume. It is also essential to read volume tables, form factor table, yield tables, etc. Tree height is normally used to find out productive capacity of the site and site quality of a locality.

**There are different measurements of height on trees: **

**i. Bole Height: **

It is the distance from the ground level to the position of the first crown forming living or dead branch.

**ii. Commercial Bole Height: **

The height of bole that is usually fit for utilization as timber is called commercial bole height.

**iii. Height of Standard Timber Bole: **

It is the height of the bole from the ground level up to the point where average diameter over bark is 20cm.

**iv. Timber Height: **

It is the vertical distance from the base of the tree to the point on the main stem where the diameter is 7 cm for conifers. For hardwoods, timber height is the vertical distance from the base of the tree to the point on the main stem where the diameter is 7cm or where the main stem becomes the crown, whichever is the lower.

**v. Stump Height: **

It is the height of the top of the stump above ground and it is normally 20-30 cm.

**vi. Crown Length: **

It is the vertical measurement of the crown of a tree from the tip to the point half way between the lowest green branches forming green crown all round and the lowest green branch on the bole.

**vii. Crown Height: **

It is height from the ground level to the point half way between the lowest green branches forming green crown all round and the lowest green branch on the bole.

**viii. Breast Height: **

If refers to the usual point of measurement of standing tree or stem diameter (1.37 m or 1.3 m) above ground on the uphill side of the tree.

**ix. Mean Crop Height: **

The mean height of all the trees growing in forest.

**c. Top Height: **

Mean height of the trees with the largest dbh in a stand.

**Height Measurement Principles: **

**Trigonometric Principle: **

Trigonometry is a branch of mathematics dealing with measurements of the angles and sides of triangles and functions based on these measurements.

**Tangent Law: **

The height of the tree is calculated with the help of the tangents of the angles to the top and base of the tree and the distance of the observer from the tree. Simple example is of standing tree in plane ground.

Tree Height (BD) = AE + ED Tan α

**Sine Law: **

In trigonometry, in any triangle, sines of angles are proportional to the opposite sides. The three basic trigonometric functions that we are concerned with here (sine, cosine and tangent) are ratios of the lengths of two sides of a triangle. These ratios are the trigonometric functions of an angle, theta, such that here, opposite side refers to tree height.

**Principle of Similar Triangles: **

Two triangles are said to be similar when the corresponding angles are equal and the corresponding sides are proportional. ADE and ABC are similar triangles.

Thus, BC: DE = AC: AE

Tree Height (BC) = DE x (AC/AE)

Where, DE and AE are known and AC can be measured in ground

Height sticks are used to measure the height of small trees. Hypsometers, altimeters and clinometers are used to measure height of tall trees (CCC 2009).

**i. Hypsometers: **

Used for determining the height of standing tree from observations taken at some distance from the tree.

**ii. Altimeters: **

Generally altitude measuring instruments, which can be devised to determine heights of tree.

**iii. Clinometers: **

It measures angle of slope. Any instrument which measures angles of slope can be used for height of tree by trigonometrical methods.

**iv. Laser Dendrometers: **

They basically rely on the same geometric principles as the hypsometers.

Some clinometers designed for this purpose called hypsometers are based on geometrical principles of similar triangles or based on relations between the sides of right angled triangles. Christen Hypsometer, Improved Callipers, Smythies’ Hypsometer, Improved Smythies’ Hypsometer are the instruments based on similar triangles. They are very slow, fatigue, heavy and rough information. These instruments are very easy to use manually in the field even by unskilled labour.

Abney’s Level, Brandis Hypsometer, Relaskop, Topographical Abney’s Level, Haga Altimeter, Blume-leiss Hypsometer are the height measuring instruments based on trigonometrical principles. They are manufactured scientifically and repair is difficult on spot. They are used only by skilled labour and limited use and expensive. It is fast, easy to carry and accuracy is maintained. They are easily available in markets and adopted by many countries.

**1. Christen Hypsometer: **

The Christen hypsometer is a simple instrument consisting of a rule or scale about 10 inches long which may be folded and carried in the pocket. It is made of metal, thin wood or even card board of about 2.5 cm thickness having two flanges to be used with a staff of known length. Upper flange will suspend by thread and next one to be suspended with weight to prevent swinging. It is based on similar triangles and usual length of instrument is 33cm (1.3 feet) used with a staff of 3.6 m (12′).

The estimator, facing the tree at sufficient distance to permit him to see its top and base, holds the instrument vertically before him. An assistant holds a 12-feet pole upright at the base of the tree. The estimator moves the scale nearer or away from the eye until the whole length of the scale just covers the entire view (in height) of the tree. The marking on the scale which is on the line of sight with the top of the upright pole indicates the height of the tree.

**2. ****Abney’s Level: **

It is commonly used tree height measuring instrument based on trigonometrically principles. It gives accurate angle of elevation and depression. Readings can be taken after sighting the tree without disturbing the index arm. The instrument is small and light and can be used even in hills without difficulty. It has eye piece (hollow telescopic piece), magnifier glass, protector, wire and screw. It is an instrument with hollow tube with an eye piece at one end and a short sighting tube fitted at the other.

Eye piece consists of 2 or 3 telescopic hollow tubes and a sighting tube is a small detachable tube fitted with a horizontal wire at the centre. A mirror behind the horizontal wire covering only half of the tube so fitted that it makes 45°. A spirit level is fitted to the main tube, which can be rotated by one screw. Wheel is for quicker movement and screw is for final adjustments. An index arm is also attached to the spirit level.

As the spirit level rotated, index arm moves on a graduated semi-circular arc. The angles of elevation and depression are noted in graduated arc in degrees up to 90°. On either side of the zero mark at middle, each division gives the reading of 10′.

The horizontal distance from the base of the tree is measured to a location where the required point on the tree (e.g., tree tip) can be seen. The tree tip is sighted through the eye piece and this makes the instrument inclined and the bubble is not seen in the mirror.

Therefore, while sighting the top, the screw is rotated to bring the spirit level in a horizontal position. The spirit level is continued to be moved slowly to the position when the bubble image is bisected by the line of horizontal wire on the mirror and in the other half the tree top is seen touching the horizontal wire.

The spirit should be balanced by tuning with screw as well as moving to and back ward. The degrees and minutes for angle of elevation- (a) are read. Again the base of the tree is sighted through eye piece and angle of depression (P) is measured.

**If the base of the tree is level with the observer or below observer (i.e., observer on the upward slope), total tree height is calculated using following formula: **

Tree Height = Horizontal Distance x [Tan (α) + Tan (β)]

**If the base of the tree is above the observer (i.e. observer on the downward slope), the following formula is used to get a total tree height: **

Tree Height = Horizontal Distance x [Tan (α) – Tan (β)]

**3. ****Suunto Clinometer: **

The Suunto Clinometer (clino) is a tool commonly used by foresters to measure tree heights and also slope angles. Tree height is measured using the principle of triangulation with a clinometer. Of all the forestry tools, the clinometer requires the most practice and skill. It is assumed that the tree grows at a right angle to the ground (even on a slope). At the rear of the clino is a peephole, which shows a percentage scale and a horizontal line. First, the horizontal distance between the base of the tree and the operator is measured.

Looking through the peephole, the horizontal line is lined up with the top of the tree and the corresponding number from the percentage scale, which is on the right hand side is read off (top reading). The scale on the left is in degrees and should not be used. Similarly, the corresponding percentage scale for base of the tree (bottom reading) is measured. If the base of the tree is level with the observer or below observer (i.e., observer on the upward slope).

**Total tree height is calculated using following formula: **

Tree Height = Horizontal Distance x [Top Reading + Bottom Reading]

If the base of the tree is above the observer (i.e., observer on the downward slope),

**The following formula is used to get a total tree height: **

Tree Height = Horizontal Distance x [Top Reading – Bottom Reading]

**4. ****Haga Altimeter: **

Haga altimeter is based on the trigonometrically ratio. It is very easy to use and read height directly. This instrument is based on the principle of ‘sight the object and shoot’. It has eye piece, pronges, scale, trigger button, release trigger button and tuning knob. It has several percent of usual scales: 15, 20, 25, and 30 for the corresponding horizontal distance from the tree: 15 m, 20 m, 25 m, and 30 m.

For example, if the observer is standing at a distance of 20 m from the base of the tree, then he must use the percentage scale of 20 for measuring the reading. First, the observer stands at a distance of 20m from the tree and looks the top of the tree through eye piece. He sees the tip of the tree through eye piece and coincides it with the pronge of the instrument.

At this position, trigger is pressed to arrest the pointer on the scale and now the reading on percent scale 20 is noted (top reading). Now the pointer is released by pressing trigger release button. Again the base of the tree is viewed through eye piece and corresponding reading on 20 percent scale is noted (bottom reading).

**The total tree height is calculated using the formula: **

Tree Height = Top Reading + Bottom Reading

Ravi altimeter/multimeter and Blume Leiss altimeter also work with the above same principles and readings are taken in the same manner of Haga Altimeter.

**5. ****Vertex IV and Transponder T3: **

The vertex IV is primarily designed to measure the height of standing objects and most often trees. The instrument can also be used to measure distance, horizontal distance, angle and inclination. The vertex instrument with its ultrasonic measuring technique proved to be specially useful in dense terrain with thick undergrowth, where conventional methods such measuring tapes, laser instrument and mechanical height measures are difficult to use.

To define a reference point in a secure and reliable way, the vertex IV works with the transponder T3. The vertex IV communicates with the transponder. This communication eliminates any mix up of signal from other instruments or places (echos) in an efficient way.

The measuring operation will not be disturbed by objects in between the vertex IV and the transponder T3 in any significant way. The reference point i.e., the T3 is used as a sight mark for height measuring and can be placed at optional height. The reference point height is set in a special menu in the vertex instrument and automatically added to the measured height.

The vertex IV uses ultrasound to measure distance. Unlike measuring tapes and laser instrument, ultrasound can be used also when there is no free aim to the reference point. The ultrasound will not pass through an obstacle, but looks for the shortest way. Heights are calculated trigonometrically using the variables contained when measuring angle and distance.

The vertex IV automatically assumes that the measuring object is perpendicularly positioned to the ground. With the vertex IV, an unlimited number of heights or objects can be measured. The instrument display can show the four lastly measured heights per object at a time. When using a telescopic method to measure, an in built BAF function can be used for the vertex IV instrument to control the minimum diameter for trees.

The function is useful when some trees in an area are covered by other, making the decision whether to include the tree or to exclude it from the area, difficult. By simply measuring the distance between the tree and plot centre, the vertex IV can calculate the minimum diameter the tree should have in order to be included into the counting. Data can be sent through IR or Bluetooth and results can be stored and processed in the digitech professional calliper, other PC or handheld computer.

**6. ****Spiegel Relaskop: **

The standard metric Relaskop has three scales for measuring (vertical) height. The appropriate scale will depend on the horizontal distance from the tree.

i. Left-most scale – 20 m from the tree.

ii. Middle-left – 25 m from the tree.

iii. Middle-right – 30 m from the tree.

After depressing brake button, one should look straight up or down and the appropriate distance values can be seen alongside their scales. A point must be selected that is 20, 25 or 30 m (horizontal) from the tree of interest. Other horizontal distance can be selected for which the final scale reading must be doubled or halved or multiplied with respective conversion factors. The base and tip (or any other points of interest) must be clearly visible from the selected point.

If the tree is leaning, the point where you observe the tree should be at 90 degrees to the plane of the lean. If the lean is severe (i.e., more than 10 degrees from vertical), the point directly beneath the tip of the tree should be located (e.g. using a plumb-bob) and the horizontal distance taken from this point. The actual distance chosen is related to an initial estimate of the tree height.

Once the observation point is found and the appropriate scale selected, sight through the peephole to the base of the tree. Tap the brake button several times until the scale settles then read the height directly from the appropriate scale. If you are looking down towards the base of the tree, this reading is the vertical height that the base of the tree is beneath your eye. Sight to the top of the tree (or other point) and again tap the brake button until the scale settles.

The scale is a direct reading of the height above your eye to this new point. Add the two heights together if the base of the tree was below your eye to determine total (vertical) height. If the base of the tree was initially above your eye (i.e., the base if above you on sloping ground) subtract the initial height from the upper height to determine (vertical) height.

**How to Measure the Volume of a Tree ?**

Volume is the most widely used measure of wood quantity and is usually estimated for the assessment of economic value or commercial utilization potential. The wood volume of a tree includes stem, branches, stump and roots. For standing trees, aboveground volume production is generally based on stem wood volume for conifers, but may include branch volume for broad-leaved tree species.

Depending on measurement objective and local traditions, measurements or predictions of wood cubic volume may refer to, for example, total stem volume, total tree volume (stem and branches), or volume above a certain merchantable limit. Volume estimates may include or exclude bark and, for aboveground estimates, include or exclude the stump. Volume is always a cubic measure and usually expressed in cubic meters. Merchantable volume, however, is sometimes expressed in other units related to commercial use.

Volume is usually estimated for standing trees from such measurements as diameter, or diameter plus merchantable height, using a volume equation or a log rule. Volume may be measured directly on felled trees or logs, but is often estimated from dimensions such as minimum diameter or piece length. Direct measurement of volume is usually done by sectioning the tree into smaller pieces assumed to be cylinders.

**The general formulas for calculating the volume of standing trees are: **

i. Volume = BA x H x Form Factor

ii. Volume = πr^{2}H x Form Factor

iii. Volume = D^{2}H x Form Factor

Where,

BA = Basal area of the tree

r = radius of the tree

H = Height of the tree

D = Dbh of the tree

**Stem/Log Volume Measurements: **

It is possible to utilize geometric relationships to approximate volume. The volume of a cylinder is simply the area of the base times the height, and the volume of a cone is one-third of the volume of a cylinder with the same area of the base and height. Trees are neither cones nor cylinders, but empirical analyses often indicate that the volume of a single-stemmed tree is between that of a cone and a cylinder, with tree volume often lying between 0.40 and 0.45 times that of an equivalent cylinder.

Volume of Cylindrical Stem = S x L

Volume of Conical Stem = 1/3 x S x L

Volume of Paraboloid Stem (Huber’s Formula) = S_{m} x L

Volume of Paraboloid Stem (Smalian’s Formula) = (S_{1} + S_{2}) x L/2

Volume of Neiloid Stem (Newton’s Formula) = (S_{1} + 4S_{m }+ S_{2}) x L/6

Where,

V = Volume of log

L = Length of log

S = Cross-Sectional area of cylinder or cone

S_{m} = mid cross-sectional area of log

S_{1} = Cross-sectional area at the smaller end

S_{2} = Cross-sectional area at the larger end

G = Mid Girth of log in inches

Volume Calculation of Sawn Timber

V = L x B x H (cubic meter or cubic feet)

**Volume Calculation of Firewood/Stacked Wood: **

Volume may be estimated for stacks of logs or processed products by measuring dimensions. In these cases, local knowledge is often needed for appropriate estimation of volume.

**Firewood is stacked in the form of rectangular parallel piles and the volume of the stacked firewood is calculated by: **

Volume = Length (L) x Height (H) x Breadth (B) of the stack expressed in cubic meter or cubic feet.

**Stem Form: **

Form is defined as the rate of taper of a log or stem. Taper is the decrease in diameter of a stem of a tree or of a log from base upwards. The taper varies not only with species, age, site and crop density but also in the different parts of the same tree.

**Form Factor: **

Form factor is defined as the ratio of the volume of a tree or its part to the volume of a cylinder having the same length and cross-section as the tree.

**The form factors are of the following types: **

**i. Artificial Form Factor: **

This is also known as the breast height form factor. Here, the basal area is measured at breast height and the volume refers to whole tree both above and below the point of measurement.

**ii. Absolute Form Factor: **

For this form factor, basal area is measured at any convenient height and the volume refers only to that part of the tree above the point of measurement.

**iii. Normal Form Factor: **

In this form factor, basal area is measured at a constant proportion of the total height of the tree.

**Form Quotient: **

It is the ratio of diameter to diameter at breast height.

**Form quotients are of two types: **

**i. Normal Form Quotient: **

It is the ratio of mid-diameter of a tree to its diameter at breast height.

**ii. Absolute Form Quotient: **

It is the ratio of a stem diameter at one half its height above the breast height to the diameter at breast height.

**Form Height: **

It is the product of form factor and the total height of the tree.

Form Height = Volume of tree/Basal area

**Form Class: **

It is one of the intervals in which the range of form quotient of trees is divided for classification and use.

**Form Point Ratio: **

Form point is the point in the crown where wind pressure is estimated to be centered. Form point ratio is the relationship of height of the form point above ground level to the total height of the tree, usually expressed as percentage.

**Tree Basal Area Measurements: **

Tree Basal Area (TBA) is the cross-sectional area (over the bark) at breast height measured in square meter (m^{2}). TBA can be used to estimate tree volumes and stand competition. To determine tree basal area simply measure the diameter at breast height in centimeters (DBHOB) and calculate the basal area (m^{2}) using an equation based on the formula for the area of the circle (area = πr^{2} where r = radius). The formula below also converts the diameter in centimeters to the basal area in m^{2}. The same technique can be used to calculate the cross sectional area of the tree at any point along the stem.

Tree Basal Area (TBA) in m^{2} = (DBH/200)^{2} x 3.142

Where, DBH is the Diameter at Breast Height in centimeters and 3.142 is π