Forestry mathematics
Basal area, stand density, and the three board-foot rules a load can be scaled on. These are the figures a forester quotes across a tailgate and assumes you follow. Every formula is printed, every step of the arithmetic is shown with your own numbers in it, and nothing you type leaves your browser.
No calculator here prints a dollar figure. Timber is priced by species, quality, haul distance and the week it sells - a number typed into a website would be wrong before you read it. What these tools give you is the measurement the price is negotiated against. The rest of the negotiation is on the guide to selling standing timber, and the buyers those measurements end up in front of are in the mill directory.
Stand measurement
Cross-sectional area of a single stem at breast height, and the square feet per acre your whole stand is carrying.
Stocking
The diameter of the tree of average basal area, and the stocking index that tells you whether your stand is about to start killing its own stems.
Scaling
The same log scaled under all three board-foot rules at once, with the difference between them in plain percentages. The rule named in your contract decides what you are paid on.
Scaling
Cubic feet or cubic metres of wood in a log from its two end diameters and its length - the measure pulpwood, chip and export trade runs on.
Board feet in a 16-foot log at each small-end diameter, under all three rules. The last column is Doyle as a percentage of the International 1/4-inch scale - the gap is widest on small logs and closes as diameter grows, which is why the rule named in a contract matters most in a thinning.
| Small end | Doyle | Scribner | Int'l 1/4" | Doyle vs Int'l |
|---|---|---|---|---|
| 6 in | 4 | 12 | 19 | -79.1% |
| 8 in | 16 | 31 | 39 | -58.7% |
| 10 in | 36 | 55 | 65 | -44.3% |
| 12 in | 64 | 86 | 97 | -34.0% |
| 14 in | 100 | 123 | 136 | -26.2% |
| 16 in | 144 | 166 | 181 | -20.2% |
| 18 in | 196 | 216 | 232 | -15.5% |
| 20 in | 256 | 272 | 290 | -11.6% |
| 22 in | 324 | 334 | 354 | -8.4% |
| 24 in | 400 | 403 | 424 | -5.7% |
Figures are the rules' own arithmetic, rounded to whole board feet. A scale difference is not money owed either way - a buyer prices against the rule he scales on, and the two are negotiated together.
The money side of forestry - growth and yield, net present value, land expectation value and risk. Each needs figures only you have: your own yield table, your own discount rate, your own view of the market. They are listed here so you can see what is coming, and so you can see that it is not here yet.
Coming next
Where your stand's average annual growth peaks, and the age at which MAI meets PAI - the biological rotation age.
Needs your own yield figures at two or more ages - from a cruise, a growth model or your forester. No yield table will ship with it, because a yield curve borrowed from another site and another species is a wrong answer with a graph attached.
Coming next
Faustmann's bare land value, the present worth of a rotation, and the annual figure that lets timber be compared against crop rent.
Every revenue, every cost and the discount rate will be yours to type. AXE USA will ship no default price, rate or cost assumption in it - the whole reason these formulas belong on this site is that they do not go stale, and a defaulted number would make them stale on the day it was written.
Coming next
Weighing a fire, beetle or hurricane scenario against a clean rotation, and building a discount rate from your own view of the market.
Probabilities, scenario outcomes, the risk-free rate and beta will all be inputs. Timberland beta has historically run low against the broad market, and that will be said as an attributed observation - never pre-filled as a default.
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.
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.
Purdue University Extension
Log and Tree Scaling Techniques (FNR-191) (opens in a new tab)
No publication date printed on the copy retrieved; the file's own metadata records it as prepared in December 2001
Works through Doyle, Scribner and International side by side with worked examples, and explains why the three disagree. If you read one thing after using the log rules calculator, read this.
USDA Forest Service Research and Development
Forest Service research publications (opens in a new tab)
Archive, continuously updated
Where Reineke's 1933 stand density index and the density-management literature built on it live. Maximum stand density index by species and region comes from work published here and by the regional stations - never from a default typed into a website.
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.
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.
Journal of Agricultural Research
L. H. Reineke, 'Perfecting a stand-density index for even-aged forests' (1933)
1933
The original paper behind the SDI calculator. Cited here by name rather than by link: it predates the web and copies live behind various library front doors. The 1933 date is the one the owner's source brief gives.