Von Bertalanffy Growth Calculator
Length at a given age under the von Bertalanffy growth model used in fisheries and zoology — and the age at which an animal reaches a chosen length.
Many animals grow fast when young and approach a maximum size asymptotically: L(t) = L∞ (1 − e^(−K (t − t₀))).
How the von bertalanffy growth calculator works
Many animals grow fast when young and approach a maximum size asymptotically: L(t) = L∞ (1 − e^(−K (t − t₀))). L∞ is the asymptotic length, K how quickly it is approached (per year) and t₀ the theoretical age at zero length, usually slightly negative. Invert it for the age at a length: t = t₀ − ln(1 − L ÷ L∞) ÷ K. Parameters for hundreds of species are published in FishBase.
Formula: L(t) = L∞ (1 − e^(−K(t − t₀))); t(L) = t₀ − ln(1 − L ÷ L∞) ÷ K
Worked examples
| Inputs | Length at that age | Note |
|---|---|---|
| L∞ 100, K 0.3, t₀ −0.5, age 3 | 65 cm | 65.0 cm; 80 cm at 4.9 years |
| A slow-growing shark: L∞ 300, K 0.05, age 10 | 135.4 cm | 135 cm |
| A fast tropical fish: L∞ 20, K 1.2, age 1 | 14.7 cm | 14.7 cm |
FAQFrequently asked questions
What do L∞, K and t₀ mean?
L∞ is the size the average animal would reach if it lived forever; K sets how fast it gets there (0.1 is slow, a shark or sturgeon; 1 or more is fast, a small tropical fish); t₀ corrects for the fact that growth in the egg and larva does not follow the curve.
Where do I get parameters?
FishBase lists von Bertalanffy parameters for most commercially and scientifically important fish; papers on reptiles, molluscs and mammals use the same form. Values vary between populations and sexes.
Why does growth slow with age?
The model assumes anabolism scales with surface area and catabolism with volume, so net growth falls as the animal gets bigger. It fits most fish well; mammals with determinate growth are better described by other curves.
Can I use weight instead of length?
Weight follows the cube of the length version: W(t) = W∞ (1 − e^(−K(t − t₀)))³. Convert length to weight with the species’ length–weight relationship.
Where these figures come from
- NCBI Bookshelf — Molecular Biology of the Cell — growth kinetics and molecular conventions
- CSIRO — Australia's national science agency
Last checked: September 2026. Formulas are the standard textbook forms; assumptions are stated on each page because they are where these models break.