Lung Nodule Growth Rate Calculator (volume doubling time from two CT scans)

Understanding the lung nodule growth rate calculator — concept and principle

This calculator works out the volume doubling time (VDT) of a lung nodule from its size on two CT scans and the days between them. Radiologists and chest doctors use doubling time to judge whether a nodule behaves like a cancer, an infection or a harmless lesion.

Diameter → sphere volume: with the default inputs the result is 520 days (doubling time · 400–600).

How it is calculated

VDT (days) = Δt × ln 2 ÷ ln(V₂ ÷ V₁)

Δt is the number of days between scans; V₁ and V₂ are the two volumes.
If you enter diameters, each becomes the volume of a sphere: V = π ÷ 6 × d³.
Volume change (%) = (V₂ ÷ V₁ − 1) × 100.

The principle

Tumours grow roughly exponentially: the volume doubles in a fixed time. Taking logarithms turns the two measurements into a growth rate, and ln 2 divided by that rate gives the doubling time. Because volume rises with the cube of the diameter, a small change in diameter is a large change in volume: a 26% larger diameter doubles the volume. That is why volumetric software is preferred for small nodules.

Worked example

Default inputs: diameters 6.0 mm and 6.5 mm, scans 180 days apart.

V₁ = π ÷ 6 × 6.0³ = 113 mm³; V₂ = π ÷ 6 × 6.5³ = 144 mm³.
Volume change = 143.8 ÷ 113.1 − 1 = 27.1%.
VDT = 180 × 0.693 ÷ ln(1.2714) = 124.8 ÷ 0.2401 = 520 days.
520 is between 400 and 600 → 400–600 days – intermediate.

How to read the result

Where does your result fall?

Most malignant solid nodules double in roughly 20–400 days. Very fast doubling (under about 20 days) usually means infection or inflammation, and solid nodules with a VDT over 600 days are rarely cancer. The British Thoracic Society treats a volume increase of 25% or more as real growth and allows discharge only when a VDT above 600 days is measured by volumetry. Part-solid and ground-glass nodules grow more slowly and follow different rules.

Common mistakes

Trusting diameter changes under 1–2 mm, which are within CT measurement error.
Comparing scans with different slice thickness or reconstruction.
Applying solid-nodule cut-offs to ground-glass nodules.

Keep in mind: This is a calculation aid, not a diagnosis. Nodule management follows guidelines and the judgement of a radiologist and respiratory team.

Frequently asked questions

What doubling time suggests cancer?

Solid lung cancers usually double in about 20–400 days.

Why use volume rather than diameter?

Volume detects growth earlier and is less affected by irregular shape.

Does a stable nodule mean it is benign?

Solid nodules stable for two years are usually benign, but ground-glass nodules may need longer follow-up.

Sources: Callister MEJ et al., "British Thoracic Society guidelines for the investigation and management of pulmonary nodules", Thorax 2015;70(Suppl 2):ii1–ii54

Checked 9 Nov 2026. Exponential volume doubling time VDT = Δt·ln2/ln(V₂/V₁) with spherical volume π/6·d³ (standard); BTS Guidelines for the Investigation and Management of Pulmonary Nodules (Callister MEJ et al., Thorax 2015) — growth defined as a volume increase of 25% or more, discharge only with volumetric VDT over 600 days, as summarised by The Radiology Assistant (“BTS guideline of pulmonary nodules”); 400-day cut-off as a standard value.

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