How this instrument works
Volume doubling time (VDT) estimates how many days it would take a lung nodule to double in volume, assuming it keeps growing at its current pace. The measurement radiologists actually take from a CT scan is a diameter, not a volume, so the formula has to convert one into the other. A sphere's volume scales with the cube of its diameter — double the diameter and volume rises eightfold, not twofold — so a small rise in the measured diameter implies a much larger rise in true tumor volume. That is why the calculation divides by three times the natural log of the diameter ratio rather than by the log alone: the factor of 3 is what turns a diameter measurement into genuine volume-doubling arithmetic.
The underlying math traces to a 1961 paper by Michael Schwartz, who modeled tumor growth as exponential and worked out how a doubling time in volume relates to a change in a linear measurement over a known interval. Clinically, VDT sits at the center of how a growing nodule gets read: nodules that double in under about 20 days usually turn out to be infection or inflammation rather than cancer, most malignant nodules fall somewhere between roughly 20 and 400 days, and nodules that grow slower than that, or not at all, lean strongly toward benign. The American College of Chest Physicians' evidence-based guideline on pulmonary nodules draws on exactly this kind of growth-rate evidence when it sets follow-up intervals.
A genuine limitation worth stating plainly: two-point measurements are noisy. Diameter on a CT slice depends on window settings, slice angle, and which radiologist drew the boundary, and a millimeter or two of disagreement between two readings can swing a computed doubling time substantially — more so for small nodules and short intervals, where the ratio between the two diameters is close to 1 and the log in the denominator is small. A single VDT calculation is a data point to track over serial scans, not a verdict from one pair of numbers.
- Enter Earlier diameter (mm) — the nodule's diameter on the first CT.
- Enter Later diameter (mm) — its diameter on the follow-up CT; it must exceed the earlier value.
- Enter Days between scans — the interval separating the two studies.
- Read Volume doubling time (days): shorter figures indicate faster growth, longer figures indicate slower growth.
Worked example — 6 mm to 8 mm over 180 days
A nodule measures 6 mm on the initial CT and 8 mm on a scan taken 180 days later. The diameter ratio is 8 / 6 = 1.333, and its natural log is about 0.2877. Multiply by 3 to convert to a volume basis: 3 × 0.2877 = 0.8630. The doubling formula gives (180 × 0.6931) / 0.8630 ≈ 144.6 days — inside the roughly 20-to-400-day band many guidelines treat as concerning for malignancy, and fast enough to warrant tissue sampling or close short-interval follow-up rather than routine rescanning.
Contrast that with slower growth: a nodule moving from 5.0 mm to only 5.2 mm across a full 365-day year computes to a doubling time near 2150 days — more than five years, comfortably past the slow end of the malignant range and reassuring. And a nodule growing from 8 mm to 12 mm in just 90 days computes to about 51.3 days, a rapid pace that sits well within the concerning band and typically prompts urgent evaluation rather than watchful waiting.
Questions
Why does the formula divide by three times the log, instead of just the log?
Because the measured quantity is a diameter but the biology of interest is volume. A sphere's volume is proportional to the cube of its diameter, so tripling the exponent in the denominator (equivalently, dividing by 3·ln of the ratio) is what converts a change measured in millimeters into a doubling time expressed in true tumor volume. Skip that factor and the result describes how fast the diameter is doubling, a much slower and less clinically meaningful pace.
What volume doubling time counts as concerning for cancer?
As a rough guide drawn from decades of nodule-growth literature, doubling times under about 20 days usually reflect infection or inflammation rather than a tumor, doubling times from roughly 20 to 400 days raise concern for malignancy, and doubling times beyond that — including nodules that appear stable — lean toward benign. These are population patterns, not individual diagnoses, and a radiologist weighs VDT alongside nodule shape, density, and a patient's risk factors.
How much does measurement error affect this calculation?
More than it should, especially for small nodules and short scan intervals. A CT diameter reading can vary by a millimeter or two between radiologists or even between two reads by the same person, and because the diameter ratio sits inside a logarithm, a small absolute error near a ratio of 1 swings the computed VDT considerably. A nodule under 6 mm measured six weeks apart is far shakier ground for this formula than one measured 10 mm at a year's interval.
Can I use this calculator with volume measurements instead of diameters?
Not directly — this instrument expects two linear diameter readings, the numbers a radiologist reports from routine CT review. If a scanner's semi-automated software already outputs volumes for both time points, the doubling time is simpler: VDT = (days × ln 2) / ln(V₂/V₁), with no factor of 3, because the cube conversion has already been done for you.
Does a longer interval between scans give a more reliable result?
Generally, yes. A longer gap lets real growth accumulate well past the noise floor of the measurement itself, so the diameter ratio reflects biology rather than measurement scatter. That is part of why many follow-up protocols space repeat CTs by several months to a year for smaller or slower-growing nodules rather than rescanning every few weeks.
References
- Schwartz M. 1961, Cancer — biomathematical approach to tumor growth (PubMed)
- Gould MK et al. 2013, Chest — ACCP evidence-based guideline on pulmonary nodules (PubMed)
Read this first: This instrument computes a screening figure from population formulas — it is not a diagnosis, and it cannot see the whole picture a clinician can. Use it to inform a conversation, not to replace one.