Volume of a round log
Log volume by Huber's or Smalian's method, and mass if you know the density.
How it is calculated
Both methods treat the log as a cylinder (or a truncated cone) and calculate its volume as cross-section area × length, with area = (π/4) × diameter².
Huber: measures a single diameter, at the midpoint of the length, and treats it as constant along the whole log: volume = (π/4) × centre diameter² × length. It is quick (a single measurement) and fairly accurate for regularly shaped logs.
Smalian: measures the diameter at each end (base and tip) and averages the two cross-section areas, not the diameters: volume = length × (base area + tip area) / 2. It is somewhat more accurate for strongly tapered logs, because it avoids the error of averaging diameters instead of areas, but it requires measuring both ends, which are sometimes less accessible than the centre.
Huber example: a 3 m log, 30 cm diameter at the centre. Volume = (π/4) × 0.3² × 3 = 0.0707 × 3 = 0.212 m³.
Smalian example: a 4 m log, 40 cm at the base and 20 cm at the tip. Base area = (π/4)×0.4² = 0.1257 m². Tip area = (π/4)×0.2² = 0.0314 m². Volume = 4 × (0.1257+0.0314)/2 = 4 × 0.0785 = 0.314 m³. For 5 identical logs: 1.571 m³.
Keep in mind
- Always measure the diameter under the bark if you are going to use the wood as sawn timber (bark does not count as usable wood); measuring over bark gives a somewhat larger volume than the real one.
- For very irregular or curved logs, no simple method is exact: cut them into shorter, more uniform sections and add up the volumes.
- Wood density varies a great deal between species and, above all, between green wood (freshly cut, with a lot of water) and air-dried wood (months later): the same piece can weigh twice as much green as dry. If you do not know the density, leave the field blank and use the volume only.