Calculators · Radiology · Formula

Tumour volume doubling time

Also called VDT, TVDT, Schwartz formula, nodule doubling time

Time for a nodule or tumour to double in volume from two measurements (Schwartz exponential-growth formula).

Measurement entered

Fill 4 more fields to see the result.

Formula and scoring

VDT = t × ln 2 ÷ ln(V2/V1). With diameters (sphere): VDT = t × ln 2 ÷ [3 × ln(D2/D1)].

Exam and ward pearls

  • A 26% increase in diameter = one volume doubling (1.26³ ≈ 2).
  • Ground-glass adenocarcinomas grow slowly — median VDT 1,059 days in one series of 49 growing nodules — so short-term stability does not exclude them.

When not to rely on it

  • Small diameter errors become large volume errors (cubed); use volumetric software with the same CT technique where possible.

Source

  1. Schwartz M. A biomathematical approach to clinical tumor growth. Cancer. 1961;14:1272-94. doi:10.1002/1097-0142(196111/12)14:6<1272::aid-cncr2820140618>3.0.co;2-h · PMID 13909709
  2. Oki T, Iizuka S, Otsuki Y, Nakamura T. Diagnostic utility of tumor volume doubling time in ciliated muconodular papillary tumor/bronchiolar adenoma mimicking invasive mucinous adenocarcinoma. Radiol Case Rep. 2026;21(8):3408-12 (modified Schwartz formula). doi:10.1016/j.radcr.2026.04.061 · PMID 42232149
  3. He Y, Che S, Xie J, et al. Relationships between growth rate and Ki-67 and immune indices in ground-glass nodule-featured lung adenocarcinoma. BMC Cancer. 2025;25(1):686. doi:10.1186/s12885-025-14078-z · PMID 40887608

Formula and cut-offs checked against these sources on 8 Nov 2026. Educational tool for clinicians; it does not replace clinical judgement.

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