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Enter your values, then click Calculate result.How this calculator helps
Estimate an ideal tapered log’s volume and mass from two measured end diameters, length and independently supplied bulk density. The calculator treats a log as a straight circular frustum, connecting the two supplied circular end sections. It assumes a linear change in radius along the length. A bent trunk, flared butt, hollow section or irregular cross-section departs from this model. Measure representative end diameters consistently and document whether bark is included rather than silently mixing inside- and outside-bark measurements.
How to use it
- 1
Prepare the independently established inputs in the units shown, starting with taper model.
- 2
Review diameter conversion and the supported scope before submitting; example defaults demonstrate the arithmetic rather than a personal recommendation.
- 3
Click Calculate result to submit the current values. Input edits retain the previous submitted result until you calculate again.
- 4
Read the labeled output with the worked example, then check handling limits before using the result in another record.
Formula and methodology
Circular-frustum volume = π·length·(r²+rR+R²)/3, with radii in feet. Estimated mass = volume × supplied density.
The calculator applies the displayed arithmetic to the values entered on this device. It does not silently load a local tax rate, currency conversion or commercial assumption.
Worked calculation example
A 10 ft log with end diameters 12 and 18 in has radii 0.5 and 0.75 ft. Its frustum volume is about 12.43547 ft³. At a supplied density of 40 lb/ft³, its illustrative weight is about 497.419 lb, or 225.625389 kg.
How to interpret your result
A 10 ft log with end diameters 12 and 18 in has radii 0.5 and 0.75 ft. Its frustum volume is about 12.43547 ft³. At a supplied density of 40 lb/ft³, its illustrative weight is about 497.419 lb, or 225.625389 kg. Ideal circular frustum with independently supplied bulk density. No species/moisture inference, load-rating decision or lifting recommendation. Compare the labeled intermediate outputs with the input units and convention before carrying a number into another worksheet.
For different inputs or formulas, use Firewood Calculator — Full Cords from a Stack; Cylinder Volume Calculator.
Related questions this calculator covers
- log weight calculator
Scenario comparison
| Scenario | What it shows |
|---|---|
| Cylinder check | equal 12 in ends and 10 ft length give 2.5π ft³. |
| Density change | doubling supplied density doubles mass while geometric volume is unchanged. |
| Length change | halving length with identical ends and density halves both volume and mass. |
Common mistakes to avoid
- Converting diameter to feet but forgetting to halve it into a radius.
- Using dry density for an unverified wet or bark-inclusive log.
- Using calculated mass to approve equipment loading or lifting.
An illustrative mass does not establish a crane, sling, trailer, axle or vehicle capacity. Real lifting plans require verified weight and appropriately qualified assessment of equipment and conditions. Use this worksheet to understand how taper, length and supplied density affect arithmetic, then verify an actual mass independently when a safety-critical operation or commercial weigh ticket requires it.
Authoritative reference. Method reference reviewed on 4 October 2026. The displayed worksheet and examples are SolvePilot’s own bounded implementation. The reference does not certify an individual calculation. Review by Mohammad Qasim is editorial and technical, not patient-specific, financial, structural or equipment approval.What can affect the result?
Taper model
The calculator treats a log as a straight circular frustum, connecting the two supplied circular end sections. It assumes a linear change in radius along the length. A bent trunk, flared butt, hollow section or irregular cross-section departs from this model. Measure representative end diameters consistently and document whether bark is included rather than silently mixing inside- and outside-bark measurements.
Diameter conversion
Both diameters are entered in inches and converted to radii in feet by dividing by twenty-four. Length remains in feet, so the volume is cubic feet. Dividing a diameter by twelve changes units but does not make it a radius. That error can multiply the calculated volume by four and is worth checking before considering the density input.
Density basis
Density must describe the actual wood and moisture condition on a compatible mass-per-volume basis. A generic dry-species value may understate a fresh or saturated log, while bark and voids can change the effective bulk value. The calculator supplies no density table and cannot infer species from diameter. If density is uncertain, run separately labeled low and high scenarios using independently supported values.
Mass versus stacked volume
A solid geometric log volume differs from a firewood cord, which describes a stacked volume containing spaces. Do not multiply a cord volume by solid-wood density without separately establishing the solid fraction. The adjacent cord tool answers a different measurement question. Keeping the distinction visible avoids treating two forestry quantities with the same unit label as equivalent physical volumes.
Handling limits
An illustrative mass does not establish a crane, sling, trailer, axle or vehicle capacity. Real lifting plans require verified weight and appropriately qualified assessment of equipment and conditions. Use this worksheet to understand how taper, length and supplied density affect arithmetic, then verify an actual mass independently when a safety-critical operation or commercial weigh ticket requires it.
Privacy and browser processing
Values entered on this page are processed in the current browser session. SolvePilot does not require an account and does not receive the values entered into the calculator. Refreshing or closing the page clears the working values unless the browser itself restores a previous session. Avoid entering identifying or account information because the calculation needs summary values only.
Accuracy and verification
Accuracy depends first on input quality. Confirm definitions, scales, dates and source information before entering a value. Keep an independent record of any result used for planning because this page does not create an official statement or retain a calculation history.
Limits of this estimate
Ideal circular frustum with independently supplied bulk density. No species/moisture inference, load-rating decision or lifting recommendation. The entered values are not independently verified. Numerical output does not establish the suitability of its assumptions for a real situation. Calculator inputs are processed locally in the browser interface; avoid entering identifying records and retain the relevant measurement or source basis with any result you save.
Sources and review information
Frequently asked questions
Does the calculator know wood species?＋
No. You supply a suitable density; species and moisture are not inferred.
Can both end diameters be equal?＋
Yes. The frustum then reduces to a cylinder with the same radius and length.
Is this a firewood cord calculator?＋
No. It estimates solid frustum volume and mass, while cords measure stacked wood including gaps.
Does it approve a lifting plan?＋
No. A geometric estimate cannot establish safe equipment loading or handling.
What happens when density doubles?＋
With the same geometry, the estimated mass doubles and the displayed geometric volume stays unchanged.