MOI Calculator
Enter the number of virus particles and the number of host cells to compute the multiplicity of infection (MOI), the average number of virions per cell.
Input Data
Results
At a glance:Multiplicity of infection (MOI) is the average number of virus particles entering each cell in an infection experiment: MOI = virus particles ÷ host cells. It sets the probability distribution of how many virions a single cell receives — not every cell gets exactly MOI virions. At low MOI most cells are uninfected or receive one; at high MOI many cells receive several. Because virion entry is random, the number per cell follows a Poisson distribution: the fraction of cells receiving exactly k virions is e^(−MOI)·MOI^k ÷ k!, so the fraction receiving zero (uninfected) is e^(−MOI). This is why even at MOI = 1 about 37% of cells are uninfected.
Formula
MOI = virus particles ÷ host cells.
Fraction uninfected (0 virions) = e^(−MOI) (Poisson).
Cells receiving ≥1 virion = 1 − e^(−MOI).
$$MOI = \frac{N_{virus}}{N_{cells}}$$$$f(0) = e^{-MOI}$$$$f(\geq 1) = 1 - e^{-MOI}$$How to Use
- Enter the number of infectious virus particles (or PFU).
- Enter the number of target host cells.
- The tool shows MOI and the fraction of cells likely uninfected at that MOI.
Uninfected-cell fraction (Poisson) at different MOI
| MOI | Fraction uninfected e^(−MOI) | Cells infected ≥1 |
|---|---|---|
| 0.5 | 60.7% | 39.3% |
| 1 | 36.8% | 63.2% |
| 2 | 13.5% | 86.5% |
| 5 | 0.67% | 99.3% |
| 10 | 0.0045% | ≈100% |
Because virion entry is random, the number per cell follows a Poisson distribution; at MOI=1 a third of cells are still uninfected.
Case Studies
Standard MOI = 1 infection
Use 1,000,000 PFU to infect 1,000,000 cells.
MOI = 1,000,000 ÷ 1,000,000 = 1.
Fraction uninfected = e^(−1) ≈ 36.8%, so about 63% of cells receive at least one virion; average is one, but not every cell is infected.
Higher MOI for synchronous infection
Use 10,000,000 PFU for the same 1,000,000 cells.
MOI = 10; fraction uninfected = e^(−10) ≈ 0.0045%, so essentially all cells are infected (most with several virions).
High MOI is common when a uniform, synchronous infection is needed (e.g. virus production).
FAQ
Is MOI the exact virions per cell?
No. MOI is only the average (virus particles ÷ cells). Actual virions per cell vary randomly, following a Poisson distribution. At MOI=1, one-third of cells receive none and some receive two or more — average is one, but distribution is spread.
Why are 37% of cells uninfected at MOI=1?
Because entry is Poisson: the probability a cell gets zero virions is e^(−MOI). At MOI=1, e^(−1) ≈ 0.368, so about 37% of cells receive no virion and are not infected; the remaining 63% get at least one.
How to count virus particles — PFU or total particles?
MOI is usually based on infectious units (PFU, TCID₅₀), not total physical particles, because non-infectious particles cannot establish infection. If you only have total-particle count, convert via the particle-to-PFU ratio (often 10–1000 for some viruses). This calculator uses the number you enter as 'infectious units'.
How to choose MOI for an experiment?
Depends on the goal. Low MOI (0.1–1) is used for plaque assays and isolating clones (single infection per cell); MOI 1–5 for routine gene expression; high MOI (≥10) for synchronous virus production or ensuring every cell is infected. Also consider cell sensitivity and cytopathic effects at high MOI.
What if I only know MOI and want total virus?
Rearrange: virus particles = MOI × cells. Given the cell count and target MOI, multiply to get the required infectious units. For example to infect 2×10⁶ cells at MOI=5, prepare 1×10⁷ PFU.
Related Tools
References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.