MOI (Multiplicity of Infection) Calculator

Understanding the MOI (multiplicity of infection) calculator — concept and principle

Multiplicity of infection (MOI) is the ratio of infectious virus particles to target cells in an infection or transduction. This calculator tells you how much virus stock to add to a given number of cells to reach a chosen MOI, and uses the Poisson distribution to estimate what fraction of cells will receive at least one infectious particle. It is used in virology, phage biology and lentiviral or AAV gene delivery.

MOI 5 on 10⁶ cells needs 50 µL of a 10⁸ PFU/mL stock and infects 99.33% of cells.

How it is calculated

Infectious units needed = cells × MOI.
Volume (mL) = cells × MOI ÷ titre (PFU/mL); the calculator multiplies by 1,000 to show µL.
Fraction infected = 1 − e^(−MOI).

Titre can be in plaque-forming units (PFU), transducing units (TU) or infectious units per mL, as long as it measures infectious particles, not total genomes.

The principle

Virus particles land on cells at random. If on average m infectious particles are added per cell, the number a given cell receives follows a Poisson distribution with mean m. The probability of receiving zero is e^(−m), so the probability of receiving one or more is 1 − e^(−m). This explains why MOI 1 infects only about 63% of cells, not 100%: many cells get two or more particles while others get none.

Worked example

Inputs: 1 × 10⁶ cells, MOI = 5, titre = 1 × 10⁸ PFU/mL.
PFU needed: 1 × 10⁶ × 5 = 5 × 10⁶ PFU.
Volume: 5 × 10⁶ ÷ 1 × 10⁸ = 0.05 mL = 50 µL.
Uninfected fraction: e^(−5) = 0.0067, so fraction infected = 99.33%.

Each point is the calculator re-run with only “Virus titre (PFU/mL)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Virus titre (PFU/mL)	Virus volume (µL)
2.5e+07	200
5e+07	100
7.5e+07	66.66666667
1e+08	50
1.25e+08	40
1.5e+08	33.33333333
2e+08	25

How to read the result

Low MOI (well below 1) is used when you want most infected cells to carry a single copy, for example in pooled CRISPR screens, or for multi-cycle virus growth. At MOI 0.3, about 26% of cells are infected and most of those receive just one particle. High MOI (5–10) is used for synchronous single-cycle infections where nearly every cell must be infected. Check the fraction infected against the outcome you need.

Common mistakes

Using physical particle or genome-copy titre (for example vg/mL) as if it were infectious titre.
Counting cells at seeding instead of at the time of infection, after they have divided.
Forgetting the 1,000 factor between mL and µL.
Assuming every cell type is equally susceptible; titres measured on one cell line may not transfer to another.

Keep in mind: The Poisson estimate assumes every cell is equally accessible and susceptible. Real infections vary with cell type, adsorption time and volume, so confirm infection rates experimentally.

Frequently asked questions

Why does MOI 1 not infect every cell?

Particles distribute randomly; with an average of one per cell, e^(−1) ≈ 37% of cells receive none.

How do I dilute stock if the volume is too small to pipette?

Make an intermediate dilution, such as 1:10 in medium, then add ten times the calculated volume.

What fraction gets exactly one particle?

Under the Poisson model, MOI × e^(−MOI); at MOI 5 that is only about 3.4%.

Sources: E. L. Ellis and M. Delbrück, "The growth of bacteriophage", Journal of General Physiology 22, 365–384 (1939) · D. M. Knipe and P. M. Howley (eds), Fields Virology, Lippincott Williams & Wilkins

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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