← Back to CalculatorsHome
Oncologic Imaging
Demonstration data

Tumour Volume (Ellipsoid)

Estimates tumour volume from three orthogonal diameters using the ellipsoid approximation.

The ellipsoid approximation models a lesion as a regular ellipsoid, giving a quick volume estimate from three orthogonal diameters without dedicated segmentation software. The constant 0.52 is π/6.

🧮 Interactive Calculator

📐 Formula

Volume (mL) = 0.52 × A × B × C (π/6 × A × B × C)

When to Use

  • Estimating volume of a mass, node or cyst from simple caliper measurements.
  • Tracking interval growth and estimating tumour doubling time.
  • When volumetric segmentation is unavailable or impractical.

How It Works

  • Measure three mutually perpendicular diameters A, B and C in centimetres.
  • Multiply the three diameters and scale by π/6 ≈ 0.5236.
  • Result is the ellipsoid volume in millilitres (cm³).
  • For growth kinetics, serial volumes allow calculation of specific growth rate and doubling time.

Interpreting the Result

  • Volume doubling corresponds to a ~26% increase in a single diameter, so small linear changes reflect large volume changes.
  • Short volume-doubling times (weeks) suggest aggressive disease; long times (>400 days) favour benign or indolent processes.
  • Ellipsoid estimates track well with segmented volumes for reasonably regular masses.

Limitations & Pitfalls

  • Overestimates volume for irregular, spiculated or lobulated lesions.
  • Sensitive to measurement error, amplified because errors multiply across three dimensions.
  • Assumes the lesion is solid; cystic or necrotic components are not distinguished.

References

  • Feldman JP, Goldwasser R, Mark S, et al. A mathematical model for tumor volume evaluation using two-dimensions. J Appl Quant Methods. 2009;4(4):455-462.
  • Schwartz M. A biomathematical approach to clinical tumor growth. Cancer. 1961;14:1272-1294.

⚕️ For clinical decision support only. Always verify calculations and apply clinical judgment.