SOLVETUTORMATH SOLVER

Instrument MI-08-079 · Construction

Log Weight Calculator

Enter a log's diameter, length, and wood density to estimate its weight — modeled as a simple cylinder, a close approximation for a fairly uniform log.

Instrument MI-08-079
Sheet 1 OF 1
Rev A
Verified
Type 08 — Materials & Weight SER. 2026-08079

Estimated weight (lb)

837.8

volume = pi x radius(ft)^2 x length (simple cylinder)

16.755 Log volume (cubic ft, simple cylinder)
The working Every figure verified twice
  1. volFt3 = π·pow(16 ⁄ 12 ⁄ 2, 2)·12 = 16.755
  2. weightLb = 16.755161·50 = 837.8
Worksheet log
  1. No entries yet — change an input to log a scenario.

How this instrument works

A log's weight is simply its volume times its density, but neither number is quite as fixed as it sounds. This calculator models the log as a perfect cylinder — π × radius² × length — which is a close approximation for a fairly straight, uniform-diameter log, but real logs taper from butt to tip, so a log measured at its average diameter will give a more accurate result than one measured at its widest end.

Wood density is where the real variation lives, and it's left fully editable here rather than fixed to one number. Green, freshly cut, unseasoned wood density varies substantially by species and moisture content — Penn State Extension's published species tables put green softwoods (fir, pine, spruce, cedar) roughly in the 35-65 lb/ft³ range and green hardwoods (oak, hickory, maple) roughly in the 40-70 lb/ft³ range, with the densest, wettest species running higher still. The 50 lb/ft³ default here is a rough 'average green hardwood' illustrative figure, not a value that applies to your specific log — the actual number depends heavily on species and how recently the tree was cut.

Because both the cylinder approximation and the density figure are estimates, treat the output as a working figure for planning handling, transport, or firewood-splitting logistics, not a precise scale weight. A log that tapers significantly, has substantial rot or a hollow section, or has begun drying out from its green state will weigh meaningfully less than this formula suggests.

volFt3 = π × (diameterIn/24)² × lengthFt
weightLb = volFt3 × densityLbFt3
diameterIn — log diameter in inches, ideally measured near the midpoint · lengthFt — log length in feet · densityLbFt3 — wood density in lb/ft³, roughly 35 (lighter green softwood) to 70 (dense green hardwood) — check a species table for accuracy · volFt3 — volume as a simple cylinder, a real-log simplification since actual logs taper.
  • Enter Log diameter (in) — measure at roughly the midpoint of the log for the best average-diameter estimate.
  • Enter Log length (ft) — the log's overall length.
  • Enter Wood density (lb/ft³) — green wood varies roughly 35-70 lb/ft³ by species; check a species-specific table for a more accurate figure than the default.
  • Read Log volume (cubic ft) and Estimated weight (lb) — a cylinder-based approximation, not an exact scale weight.

Worked example — a 16in-diameter, 12ft log

Set Log diameter to 16in, Log length to 12ft, and Wood density to 50 lb/ft³, an illustrative 'average green hardwood' figure. Volume = π × (16/24)² × 12 = π × 0.4444 × 12 = 16.755 cubic ft. Weight = 16.755 × 50 = 837.8 lb.

That's a cylinder-model estimate, not a scale reading — a real log tapering from a wider butt to a narrower tip would weigh somewhat less than this figure if 16in was measured at the wide end rather than the midpoint. A larger 24in-diameter, 16ft log at a denser green-oak-range figure of 62 lb/ft³ comes out to 50.265 cubic ft and 3,116.5 lb, showing how strongly diameter, which enters the formula squared, drives the total weight compared to length.

Questions

Why does this calculator model a log as a simple cylinder?

Because it's the simplest closed-form approximation that only needs two easy field measurements, diameter and length, and it's reasonably accurate for a fairly straight, uniformly tapered log measured at its midpoint. Real logs taper from a wider butt end to a narrower tip, so the true volume is somewhat less than a cylinder of the same midpoint diameter; for a precise volume, foresters use taper-corrected formulas like Smalian's or Huber's, which need multiple diameter measurements along the log's length.

What density should I use for green, freshly cut wood?

It depends heavily on species. Penn State Extension's published data puts many oak and hickory species around 60-70 lb/ft³ green, while lighter softwoods like fir and spruce more typically run 35-50 lb/ft³ green, and the true figure also shifts with how recently the tree was felled, since green wood loses weight as it dries. If you know the species, look up its specific green density rather than relying on this calculator's 50 lb/ft³ generic default.

Does this account for bark, branches, or hollow or rotten sections?

No — it computes a solid cylinder purely from the diameter and length you enter, with no adjustment for internal defects. If a log has significant rot, a hollow core, or you measured diameter over the bark when you meant under it, the real weight will differ from this estimate. For a log you suspect has internal defects, treat the calculated weight as an upper bound rather than an exact figure.

Why does diameter affect weight so much more than length?

Because volume scales with the square of the radius but only linearly with length — doubling a log's diameter roughly quadruples its volume and weight, while doubling its length only doubles them. That's simple cylinder geometry, V = π × r² × L, and it's why a modest-looking increase in diameter can add far more weight than the same percentage increase in length.

How accurate is this for estimating equipment needs, like trailer capacity?

Treat it as a planning estimate with a safety margin, not a precise figure to run right up against a hard weight limit. Between the cylinder approximation, which can overstate volume for a tapered log, and the density uncertainty, which can swing two times or more between species and moisture levels, the real weight could differ meaningfully from this calculator's output — when equipment capacity or safe handling is on the line, weighing the actual log, or using a conservative density estimate, is the safer approach.

References