Poisson distribution
Calculate a probability mass function and evaluate a probability statement.
Mean event count per interval or droplet.
Leave blank for an automatic range.
Convert occupancy probabilities into expected counts.
The Poisson model assumes independent events at a constant average rate. For droplet assays, λ is the expected number of cells or molecules per droplet.
Theoretical λ in droplets
Estimate λ from droplet diameter and input concentration, or work backwards from a target positive-droplet rate.
Uses the same droplet diameter above.
Volume for a spherical droplet: V(pL) = (π / 6) × diameter³ / 1000
λ = cells/mL × V(pL) / 1,000,000,000
For a target positive fraction p: λ = −ln(1 − p), then cells/mL = λ × 1,000,000,000 / V(pL)
Observed λ from occupancy
Convert measured positive droplet occupancy into λ using the zero-class relation.
Enter a fraction from 0 to 1, or a percent from 0 to 100.
If p is the positive fraction, then P(empty) = 1 − p = e−λ
Observed λ = −ln(1 − p)
Co-encapsulation probability
Calculate independent Poisson probabilities for two populations and multiply them for a joint event.
The joint probability assumes independent encapsulation for population 1 and population 2.