Humans vs Vampires Calculator — Population Crossover Model
Set up the vampire apocalypse: choose how many vampires appear on day one, how many humans each turns per year, and the human population growth rate — then see exactly when (if ever) the bloodsuckers take over.
%/yr
Year when vampire population first equals or exceeds human population
How does this calculator work?
Starting from 1 vampire and 8 billion humans, with each vampire converting 1 person per year and humans growing at 0.9%/yr, vampires outnumber humans in roughly 33 years. Vampire growth is exponential; human growth is slow — exponential always wins eventually. Crossover year = when V(t) ≥ H(t) in the year-by-year simulation.
Formula
How this is calculated
The model runs a discrete year-by-year simulation. Each year, the surviving human population first grows at the user-specified natural rate (currently about 0.9% globally). Then the vampire population converts humans: each vampire turns up to "bite rate" new humans per year, but never more than the humans that remain. Newly bitten humans become vampires immediately, increasing V and decreasing H simultaneously.
Vampire population growth is essentially exponential — at a bite rate of 1, vampire numbers double roughly every year. Human population growth is much slower (less than 1% per year), so the vampires always win eventually unless the bite rate is tiny. The crossover year is when the vampire count first equals or surpasses the human count. With a single starting vampire and 8 billion humans, one bite per year per vampire leads to crossover in roughly 33 years — a neat demonstration of how quickly unchecked exponential growth overtakes a large but linearly growing population.
This is of course a simplified entertainment model — it ignores vampire mortality, immune humans, defensive countermeasures, and real epidemiological dynamics. For a rigorous treatment, the same math underlies SIR (Susceptible-Infected-Recovered) models in epidemiology.
Frequently asked questions
If each vampire bites fewer new victims per year than the human natural growth rate can replace (roughly < 0.009 per vampire per year at 0.9% growth), vampires grow too slowly to ever catch up. In practice, any bite rate below about 0.01 keeps humans permanently ahead.
The doubling time (≈ ln(2) / ln(1 + bite_rate)) tells you how fast the vampire population multiplies. At a bite rate of 1, doubling happens in about 1 year; at 0.1, it takes about 7 years. The gap between human and vampire doubling times determines when crossover occurs.
Yes — the simulation mirrors compartmental population models used in epidemiology (SIR/SIS models). The vampire is the "infected" compartment, humans are "susceptible", and there is no "recovered" compartment (since becoming a vampire is permanent in folklore). Published papers have applied exactly this framework to vampire mythology.
Also known as
TG we-Calculate Editorial Team. (2026). Humans vs Vampires Calculator — Population Crossover Model [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/humans-vs-vampires-calculator
TG we-Calculate Editorial Team. "Humans vs Vampires Calculator — Population Crossover Model." TG we-Calculate. 2026. https://we-calculate.com/calculator/humans-vs-vampires-calculator.
TG we-Calculate Editorial Team, "Humans vs Vampires Calculator — Population Crossover Model," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/humans-vs-vampires-calculator
@misc{wecalculate_humans_vs_vampires_calculator, title = {Humans vs Vampires Calculator — Population Crossover Model}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/humans-vs-vampires-calculator}}, year = {2026}, note = {TG we-Calculate} }
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