MOI Calculator (Multiplicity of Infection)

Background.

Infect a well at an MOI of 1, one infectious particle for every cell, and the reporter will come up in roughly two cells out of three rather than all of them. Nothing went wrong. Particles land on cells at random, so some cells collect two or three while others collect none, and at an average of one per cell the share left empty is e^−1, or 36.79%.

Multiplicity of infection therefore has two sides. One is bookkeeping: how many infectious units go in, and how much stock that takes. Multiply the MOI by the number of cells present, divide by the titre, and you have the volume to pipette. The same relation runs backwards to give the MOI a known volume actually delivered, or the number of cells to plate so that a fixed volume gives the MOI you want. The other side is the spread. The Poisson distribution turns any MOI into three percentages: cells that receive nothing, cells that receive at least one particle, and cells that receive two or more. Those figures shape an experiment more than the average does. At an MOI of 3 about 5% of cells still escape, while 80% have been hit more than once.

Both inputs behind the arithmetic are easy to get wrong. The cell count should be taken when the virus goes on, not when the cells were plated, because a line that has doubled in between halves the real MOI. The titre must be in infectious units: plaque-forming units, transducing units or infectious units per millilitre. A TCID₅₀ titre needs multiplying by about 0.7 to approximate PFU, and a genome-copy titre, which counts every physical particle, is often hundreds of times higher than the infectious titre and does not belong here at all.

What is moi calculator?

Multiplicity of infection is the number of infectious units added per target cell present at the moment of infection. It is a population average with no unit, so an MOI of 0.5 means half as many infectious particles as cells, not half a particle in every cell. If particles attach independently and at random, the number reaching any one cell follows a Poisson distribution with mean m equal to the MOI: P(k) = e^−m·mᵏ ⁄ k!. Shabram and Aguilar-Cordova made the point in Molecular Therapy that MOI is a statistical probability, and that reading it as a uniform dose implies a homogeneous infected population that does not exist. Epidemiology and population genetics use the term differently, for instance for the number of distinct pathogen lineages in one host; the cell-culture ratio is the meaning here.

How to use this calculator.

1. 01Pick the question: the volume of stock to add, the MOI a known volume achieved, or how many cells to plate for a set volume and MOI.
2. 02Enter the titre in infectious units per mL and note which assay produced it. Multiply a TCID₅₀ titre by 0.7 before entering it, and bear in mind that a titre measured on one cell line may not hold on another.
3. 03Enter the cells present at infection. Counting a spare well just before adding virus beats relying on the seeding number.
4. 04Enter the MOI you want, or the volume you added, and read the three Poisson percentages. If too many cells stay empty, raise the MOI; if multiple hits would spoil the readout, lower it.
5. 05If the volume comes out below about 1 µL, dilute the stock first and enter the diluted titre, since very small volumes are hard to pipette accurately.

The formula.

The bookkeeping is one equation. Infectious units needed are IU = MOI × N, where N is the number of cells, and the volume is V = IU ÷ titre × 1000, the factor of 1000 turning a per-millilitre titre into microlitres. Solving the same relation for the MOI gives titre × V ÷ 1000 ÷ N, and solving for cells gives titre × V ÷ 1000 ÷ MOI. Doubling the cell count doubles the volume; doubling the titre halves it.

The percentages come from assuming every particle attaches independently and every cell is equally likely to receive it. With m particles per cell on average, the fraction of cells receiving exactly k is e^−m·mᵏ ⁄ k!, the form Figliozzi and colleagues used to back-calculate MOI from imaging data. Setting k = 0 gives the empty fraction, e^−m, and its complement 1 − e^−m is the infected fraction. Removing the single-hit term m·e^−m as well leaves the share hit two or more times, 1 − e^−m − m·e^−m. The empty fraction shrinks slowly: from 36.79% at MOI 1 it takes an MOI of 5 to get below 1% (0.67%).

The volume arithmetic holds however the virus spreads; the percentages do not. For a given average, equal susceptibility gives the largest possible infected fraction, so uneven receptor levels or edge effects in a monolayer leave more cells empty than predicted. Spinoculation, polybrene, or a target line different from the one used for titration change how many particles actually attach, which shifts the effective MOI itself.

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.