MOI Calculator (Multiplicity of Infection)

Background.

An MOI calculator answers a question with two halves, and most tools only do the first. The first half is stoichiometry: multiplicity of infection is the ratio of infectious units added to cells present, so the volume of stock you need is the MOI times the cell number, divided by the titre. That part is arithmetic and it is exact. The second half is a probability problem, and it is where experiments go wrong. Which cells actually receive a particle is random, so MOI is an average, not a dose. This page solves in three directions — volume to add, MOI achieved, cells to seed — and reports the Poisson split alongside every answer.

The number worth internalising is this one: at an MOI of exactly 1, only 63.2% of cells receive at least one particle, and 36.8% receive nothing at all. That follows from P(0) = e^−MOI, and it is the reason a transduction that looks like it should be complete comes back at two-thirds efficiency. The same distribution says that even at an MOI of 0.5, where the average cell gets half a particle, 9.0% of the whole population — nearly a quarter of the cells that were infected at all — receives two or more. Shabram and Aguilar-Cordova made exactly this complaint in a Molecular Therapy commentary: MOI is misleading because it implies a homogeneous infected cell population, when it is a statistical probability with a Poisson distribution.

The Poisson layer is a model, and its assumptions are worth stating before you rely on it. It supposes that particles distribute independently and at random, that every cell is equally susceptible and equally accessible, that adsorption is effectively synchronous, and that the titre is accurate on the cells you are infecting. Adherent monolayers with edge effects, cell-to-cell variation in receptor expression, and protocols using spinoculation or polybrene all break at least one of those. When they break, the volume arithmetic is still right — you really did add that many units per cell on average — but the percentages are no longer the distribution you get.

The other thing that has to be right is what your titre counts. ATCC defines MOI generically as the ratio of agents to infection targets, which is deliberate, because the numerator changes meaning with the assay that produced it. Plaque-forming units, transducing units, TCID₅₀ and genome copies are four different numbers for the same tube. ATCC derives the TCID₅₀-to-PFU relation from this same Poisson model — at the endpoint P(0) = 0.5, so m = −ln 0.5 ≈ 0.7 — and then adds that the actual number of plaque-forming units should be determined empirically. This calculator does not convert for you: it asks for infectious units and leaves the 0.7 factor as a decision you make deliberately, because burying an estimate inside a result is how a 43% error becomes invisible.

One definitional note. MOI is not defined the same way everywhere. A 2022 review in Frontiers in Epidemiology catalogues at least four incompatible usages across fields, including the number of independent infective events and the number of distinct pathogen lineages in an infection, and states plainly that MOI is not universally defined. This page implements the in-vitro cell-culture ratio — infectious units added per cell present — which is the one a virology or gene-therapy protocol means. Report two significant figures: plaque-assay titres typically carry 30–50% uncertainty, and every number here inherits it.

What is moi calculator?

Multiplicity of infection is the ratio of infectious virus particles added to target cells present at the time of infection. It is dimensionless, and it is an average over the population rather than a quantity any individual cell receives. Because adsorption is a random process, the number of particles landing on any one cell follows a Poisson distribution: P(k) = e^−m·mᵏ/k!, where m is the MOI and k the number of particles. Setting k = 0 gives the fraction of cells that escape infection entirely, e^−m, and its complement 1 − e^−m is the maximum transduction or infection efficiency achievable at that MOI under ideal conditions. The distribution also predicts multiple infection: the fraction receiving two or more particles is 1 − e^−m − m·e^−m, which matters whenever multiple proviral integrations, co-infection or recombination would confound the readout. The numerator of the ratio is only meaningful relative to the titration assay: plaque-forming units count particles that produce a plaque on a permissive monolayer, TCID₅₀ counts by endpoint dilution and is a different number, transducing units are measured by reporter expression on a specific cell line, and genome copies count physical particles whether or not they can infect anything. A titre measured on one cell line does not transfer to another.

How to use this calculator.

1. 01Choose what you are solving for: virus volume, MOI achieved, or cells to seed.
2. 02Enter the titre in infectious units per mL, and make sure you know which unit it is. If it is TCID₅₀, multiply by 0.7 first to approximate PFU — and note that ATCC recommends determining PFU empirically rather than relying on that factor.
3. 03Enter the cell number counted at the moment of infection, not at seeding, if the cells have divided in between.
4. 04Enter the MOI you want, or the volume you actually added.
5. 05Read the volume as the headline answer, but read the Poisson percentages before designing the experiment around it.
6. 06If you need close to complete infection, look at the percent-uninfected figure and raise the MOI accordingly — an MOI of 3 leaves about 5% uninfected, an MOI of 5 about 0.7%.
7. 07If multiple integration would confound your readout, check the percent receiving two or more and lower the MOI instead.
8. 08Report the MOI to two significant figures.

The formula.

The deterministic half is a single ratio. Multiplicity of infection is infectious units divided by cells, so the units you need are the MOI times the cell number, and the volume is those units divided by the titre. Because titres are quoted per millilitre and pipettes are set in microlitres, the calculator multiplies by 1000 at the end. Rearranging the same relation gives the other two modes: dividing delivered units by cells returns the MOI you actually achieved, and dividing delivered units by the MOI returns the cell number that would give it.

The probabilistic half comes from the fact that adsorption is a random, independent process. Under that assumption the number of particles reaching any one cell is Poisson-distributed with mean equal to the MOI: P(k) = e^−m·mᵏ/k!, the form stated by Figliozzi and colleagues, who write it as P{n} = mⁿe^−m/n! and note that P{0} = e^−m. Setting k = 0 gives the uninfected fraction; its complement gives the infected fraction; and subtracting the k = 1 term as well gives the multiply-infected fraction.

Working the default numbers: 5 × 10⁵ cells at an MOI of 0.5 need 2.5 × 10⁵ infectious units, which from a stock at 1 × 10⁸ PFU/mL is 2.5 × 10⁻³ mL, or 2.5 µL. The Poisson layer at m = 0.5 gives e^−0.5 = 0.6065306597, so 60.65% of cells receive nothing, 39.35% receive at least one, and 9.02% receive two or more. Those three figures with the single-hit fraction of 30.33% sum to exactly 100%, which is the check to run if you are computing this by hand.

Dimensionally the arrangement is consistent throughout. MOI is units divided by cells, so it is dimensionless. Units divided by units-per-millilitre gives millilitres, and multiplying by 1000 gives microlitres. The exponent of e is the MOI, which must be dimensionless for the exponential to be defined at all — a useful check that you have not accidentally divided by volume somewhere.

On rounding: every intermediate, including the exponential, is carried at twenty significant digits and rounded once, when the results are returned. There are no bands or thresholds in the arithmetic. The one delicate point is the multiply-infected fraction as the MOI approaches zero, where 1, e^−m and m·e^−m all converge on the same value and their difference is the small quantity of interest; the extra precision protects that subtraction, and the three percentages are additionally clamped into the range 0 to 100 so that no residual rounding error can ever surface as a negative fraction of a population.

The calculator refuses an MOI of zero. In the seed-cells mode that is a genuine division by zero, and in every mode it describes adding no virus at all, which has no answer to give. Zero or negative titres, cell counts and volumes are refused for the same reason.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Figliozzi RW, Chen F, Chi A, Hsia SV (2016). "Using the inverse Poisson distribution to calculate multiplicity of infection and viral replication by a high-throughput fluorescent imaging system." Virologica Sinica. States the distribution used here: "P{n}=m^n e^-m/n!" where m is the MOI, and "P{0}=e^-m"; inverted as m = −ln(1 − P{n>0}). Retrieved 2026-07-29.
2. [2]ATCC, Virology Culture Guide. Independent second authority. Defines MOI as "The ratio of agents (eg, viruses, bacteriophages, bacteria) to infection targets (eg, propagation host)", and derives the TCID₅₀-to-PFU factor from the same Poisson model: "For any titer expressed as TCID50, P(o)=0.5. Thus, e(-m)=0.5 and m= -ln 0.5, which is ≈0.7." Adds that "ATCC recommends that the actual number of PFUs be determined empirically." Retrieved 2026-07-29.
3. [3]Shabram P, Aguilar-Cordova E (2000). "Multiplicity of Infection/Multiplicity of Confusion." Molecular Therapy 2(5):420–421. Commentary: MOI "is misleading because it implies a homogeneous infected cell population, yet it is a statistical probability with a Poisson distribution." Publisher PDF returned HTTP 403 to automated retrieval; abstract and quoted text confirmed via the publisher's indexed record, 2026-07-29.
4. [4]"The many definitions of multiplicity of infection" (2022). Frontiers in Epidemiology. Independent third field: writes the same Poisson kernel as κₘ = e^−λλᵐ/m!, and states that "MOI is not universally defined. Competing definitions vary from verbal ones to those based on concise statistical frameworks." Retrieved 2026-07-29.
5. [5]"Lost in transduction: Critical considerations when using viral vectors" (2022). Frontiers in Cell and Developmental Biology. "The relationship between lentiviral dose, transduction efficiencies, and multiple viral integrations is explained by the Poisson distribution." Argues MOI is problematic for heterogeneous cell populations and that transduction efficiency should be reported. Retrieved 2026-07-29.