Subcutaneous Tumor Volume Calculator (Caliper Measurement / TGI Tumor Growth Inhibition)

Formula Principles

Subcutaneous xenograft and syngeneic tumor volumes are typically estimated by measuring the long axis L (longest dimension) and short axis W (shortest dimension perpendicular to L) with a caliper, then applying an ellipsoidal approximation.

Modified Ellipsoid Formula (most widely used)

V = (L × W²) / 2

L and W are in mm; V is in mm³ (numerically equivalent to µL). This formula was systematically validated by Tomayko and Reynolds (Cancer Chemother Pharmacol 1989;24(3):148-54, PMID: 2544306): the height of a subcutaneous tumor approximates the short axis W, so the third axis of the prolate spheroid formula is replaced directly by W, simplifying the coefficient from π/6 ≈ 0.524 to 0.5.

Ellipsoid Formula

V = (π/6) × L × W²  ≈  0.5236 × L × W²

The coefficient differs from the modified ellipsoid by 4.7%. Both formulas are widely cited; the same formula must be used consistently within a single study and should be stated in the Methods section.

Tumor Growth Inhibition (TGI)

Tumor Growth Inhibition (TGI) is the primary in vivo efficacy endpoint:

TGI (%) = [1 − ΔT / ΔC] × 100

• ΔT = Tₙ − T₀: difference between final and baseline volume in the treatment group
• ΔC = Cₙ − C₀: difference between final and baseline volume in the control group
• T₀ and C₀ are mean volumes on the day of randomization (before first dosing)

Interpretation: TGI > 100% indicates tumor regression (treatment group volume falls below baseline); 60%–100% indicates strong inhibition; 0%–60% indicates partial inhibition; < 0% indicates the treatment group grew faster than the control.

These ranges describe effect size only, not statistical significance. TGI is a point estimate; whether it is statistically significant depends on within-group variance and group size. A between-group test (typically a t-test or Mann–Whitney U) is required and cannot be inferred from which TGI range the value falls in.

Applicability

Applicable: subcutaneous xenografts in nude, NOD-SCID, or NSG mice; syngeneic subcutaneous tumors such as C57BL/6 × B16 or BALB/c × CT26; tumors with reasonably regular shape where two axes can be measured externally with a caliper.

Not applicable: orthotopic models, which require MRI or bioluminescence imaging; late-stage tumors with highly irregular morphology or extensive necrosis (ellipsoidal approximation error increases substantially); three-dimensional suspension spheroids, which should use the sphere formula V = (4/3)πr³.

Common Errors

1. Swapping L and W: L must be the longest diameter and W the shortest. Because W appears squared, swapping them overestimates volume. For L = 15 mm and W = 10 mm, V = 750 mm³; reversed, V = 1125 mm³—a 50% overestimate.

2. Mixing formulas within the same experiment: The two coefficients differ by 4.7%, introducing an artifactual step in the volume–time curve that reviewers typically notice.

3. Wrong baseline time point for TGI: If T₀/C₀ are taken on the tumor inoculation day rather than the randomization day, and the two groups differ in baseline volume, TGI will be systematically biased.

4. Unit mismatch: Some calipers read in cm; multiply by 10 to convert to mm before entering values, or the computed volume will be off by three orders of magnitude.

Verifiable Examples

The values below are exactly what the tool displays (always two decimal places):

Manual check: L = 15, W = 10 → (15 × 100) / 2 = 750.00 mm³; ellipsoid = (π/6) × 15 × 100 ≈ 785.40 mm³.

TGI example: T₀ = 100, Tₙ = 300, C₀ = 100, Cₙ = 900

ΔT = 300 − 100 = 200
ΔC = 900 − 100 = 800
TGI = (1 − 200/800) × 100 = 75%