Poisson distribution
Calculate a probability mass function and evaluate a probability statement.
Mean event count per interval or droplet.
Optional; large values are rendered around the meaningful mass.
A number from 0 to 1.
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 loading from droplet size and concentration, or solve for a target positive rate.
0% is valid; 100% has no finite λ.
Diameter mode assumes spherical droplets; volume mode uses the entered volume directly.
Canonical volume: pL (1 pL = 10⁻¹² L). λ = cells/mL × volume(pL) / 1,000,000,000.
Observed λ from occupancy
Use a measured fraction or enter positive and total droplet counts.
Choose the unit explicitly; 100% has no finite λ.
If p is the positive fraction, P(empty) = 1 − p = e−λ.
Observed λ = −ln(1 − p). Count mode also reports a 95% Wilson interval transformed through this relation.
Co-encapsulation probability
View independent population loading as a joint distribution and four-state overview.
Conditional co-encapsulation
Interpret the result within the positive subpopulation you care about.
All-droplet probabilities
Assumptions: homogeneous concentration, fixed droplet volume, random independent partitioning, and independent Poisson processes. The joint heatmap includes explicit row, column, and corner tail mass.