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Stand measurement

Basal area calculator

Basal area is the single number a forester reaches for first. It is the cross-sectional area of a tree stem at breast height, and summed across an acre it says how much of your ground the trees are actually standing on - which is what decides whether a stand needs thinning, can carry more growth, or is about to start losing stems to competition.

All forestry calculators

Measure the stem, then the stand

Diameter at breast height is measured 4.5 feet (1.3 m) up the uphill side of the tree, over the bark. Type one tree for the single-stem figure, or a whole plot tally for the per-acre figure. Both can be filled in at once.

Units

Diameter over bark at 4.5 ft / 1.3 m.

Commas, spaces or one per line - paste it however your tally sheet is written.

A 37.2 ft radius circle is 1/10 acre; a 26.3 ft radius is 1/20 acre.

Nothing you type is stored or sent anywhere. The figures live in this page's address, which is what makes the link shareable.

Enter a diameter to see the basal area of one tree, or a plot tally and a plot size to see what the stand is carrying per acre.

The formulas on this page

One tree, imperial
BA = (pi / (4 x 144)) x DBH² ≈ 0.005454 x DBH²
DBH in inches, basal area in square feet.
One tree, metric
BA = (pi / 40,000) x DBH² ≈ 0.00007854 x DBH²
DBH in centimetres, basal area in square metres.
A stand
BA per acre = (sum of the plot's per-tree BA) / plot size
Measure every tree on a plot of known size; divide by the plot's area.

Taking the measurement

  1. Find breast height

    4.5 feet above ground on the uphill side of the tree, or 1.3 metres in metric. On a slope, measure from the high side; on a leaning tree, measure along the stem rather than vertically.

  2. Use a diameter tape

    A D-tape reads diameter directly from the circumference. A regular tape works too - divide the circumference by pi. Keep the tape level and snug, and clear loose bark first.

  3. Handle the awkward trees

    A fork below breast height is two trees; measure both. A swelling, burl or old wound at 4.5 feet means measuring just above it and noting why.

  4. Lay out the plot

    A 1/10-acre circular plot has a radius of 37.2 feet; a 1/5-acre plot, 52.7 feet. Measure every tree whose centre falls inside, then divide by the plot size to get the per-acre figure.

What the number is telling you

Picture cutting every tree on an acre off at 4.5 feet and measuring the stumps. Add up the area of all those cut faces and you have the stand's basal area per acre: how many square feet out of 43,560 the trunks themselves occupy. It is a small number - a heavily stocked Southern pine stand is still only carrying something in the low hundreds of square feet per acre - but it is the number that scales with competition better than any other single measurement.

That is why it turns up in every stocking guide, every thinning prescription and most harvest contracts. Two stands can carry the same basal area with completely different numbers of trees: a hundred big stems or a thousand small ones. Basal area does not care, and neither does the site - the trees are using the same amount of ground either way.

What it will not tell you on its own is which of those two stands you have. That takes a stem count and the quadratic mean diameter, which is the next calculator along.

Per tree
Cross-sectional area of one stem at breast height. A 12-inch pine carries about three quarters of a square foot.
Per acre
The stand's total. What a stocking guide, a thinning prescription and most cruise summaries are written in.
Not volume
Basal area is an area, not a quantity of wood. Height and taper decide volume, and neither appears in this formula.
Not a price
No basal area figure has a dollar value attached to it, on this site or anywhere else. What your stand is worth comes from the buyers within hauling distance of your gate.

Where 0.005454 comes from

The formula is nothing but the area of a circle with the units changed. Area is pi times the radius squared, or pi over four times the diameter squared. Diameter is in inches and the answer wants square feet, so divide by 144 square inches to the square foot. That leaves pi divided by 4 times 144 - which is 0.005454, to four significant figures.

This calculator does the arithmetic with the exact value rather than the rounded constant, and shows you the rounded one because that is what is printed in the field guides. The difference is invisible on one tree and becomes visible when a per-acre figure is expanded from a small plot, which is exactly the case where a forester would notice two calculators disagreeing.

The other way: a prism and a spin

Everything above is fixed-area plot work: pick a plot, measure every tree in it, divide by the area. The alternative is a wedge prism or an angle gauge, and it is what most cruisers actually carry. You stand at a point, sweep a full circle, and count the trees that look wider than the offset the prism produces. Multiply that count by the prism's basal area factor - a 10-factor prism is the common one - and you have basal area per acre directly, without measuring a single diameter.

It works because the prism counts a tree in proportion to its basal area, which is one of the quietly elegant results in forest measurement. It also means a prism sweep gives you basal area but not a stem count, and a fixed plot gives you both. If you already have a per-acre basal area from a prism and a stem count from a tally, take them straight to the stand density calculator.

Straight answers

Questions this calculator gets asked

How many square feet per acre should my stand be carrying?

That depends on species, site, age and what you are managing for, and this page will not hand you a target number dressed up as advice. A pine plantation grown for sawtimber, a naturally regenerated hardwood stand and a stand being managed for wildlife openings have genuinely different right answers.

The stocking guides published by your state extension service and by the Forest Service research stations give the target for your species and region. Your consulting forester will have them, and will have walked ground like yours.

Do I include every tree, or only the merchantable ones?

It depends on what the figure is for, and the important part is being consistent and saying which you did. A total basal area counts every stem above your measurement threshold. A merchantable basal area counts only stems above the diameter a buyer will take.

Cruise summaries usually state the threshold explicitly - 'all stems 5 inches DBH and larger', for instance. If somebody hands you a basal area with no threshold stated, ask.

Why measure at 4.5 feet?

Because it is roughly chest height on a standing person, above the root flare on most species, and it has been the convention long enough that every published table, guide and yield model assumes it. Metric practice uses 1.3 metres, which is about 4 feet 3 inches - close enough that the two systems' numbers are comparable, far enough apart that you should not mix them in one dataset.

Does this calculator store my measurements?

No. Everything runs in your browser, nothing is sent anywhere, and nothing is saved. The numbers appear in the page address so you can text the link to your forester or your buyer - that address is the only copy, and it goes wherever you send it and nowhere else.

What these calculators are, and are not

  • They are arithmetic on numbers you type. Nothing is stored, nothing is sent anywhere, and nothing here has seen your property.
  • They are estimates, not an appraisal, a cruise or a scale ticket. When money changes hands, the measurement should come from somebody whose name is on it.
  • They are not investment, tax or legal advice, and nothing on these pages is an offer to buy or sell timber.
  • They carry no price, rate, cost or yield assumption of any kind. Every input is yours, which is why nothing here can go stale.

Where these formulas come from

Every formula on this page is published forestry mathematics, not an AXE USA invention. These are the extension-service and Forest Service publications that teach them, with the date each publisher shows. Retrieved and checked 14 August 2026.

  1. Mississippi State University Extension Service

    Extension publications catalogue - forestry (opens in a new tab)

    Catalogue, continuously updated

    The source the owner's brief credits for the basal area formulation used on this site. MSU Extension's forestry publications are the plainest written introduction to stand measurement - and to log scaling - that a Southern landowner can get free of charge.

  2. Alabama Cooperative Extension System

    Forestry, wildlife and natural resources (opens in a new tab)

    Extension site, continuously updated

    The extension service for this site's home state, and the first phone call for an Alabama landowner who wants a person rather than a page. Their county foresters will walk a tract with you, and the difference between Doyle and International scale is standard teaching material in their forestry programme - nothing on the log rules page is a revelation, it is extension coursework with a calculator attached.

  3. USDA Forest Service Southern Research Station

    Southern Research Station (opens in a new tab)

    Station site, continuously updated

    The station whose work covers Southern pine: growth and yield, stocking guides, and the beetle risk that stands carried at high density run into.

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