TCID₅₀ Calculator — Virus Infectious Titer via Reed-Muench Method

Method

TCID₅₀ (50% Tissue Culture Infective Dose) was introduced by Reed and Muench in 1938 (Am J Hyg 27:493-497). It is defined as the virus concentration at which a given inoculum infects exactly 50% of the wells or animals. The endpoint can be any readable binary outcome: cytopathic effect (CPE), fluorescence, death, etc.

Reed-Muench Cumulative Method: Four Steps

Make serial dilutions of the virus stock, inoculate several wells per dilution, and record positive/total wells at each dilution.

Step 1: Cumulative counts

Sum positives starting from the most dilute row upward (toward higher concentration);
Sum negatives starting from the most concentrated row downward (toward higher dilution).

Infection rate% = cumulative positives / (cumulative positives + cumulative negatives) × 100

Step 2: Locate the dilutions bracketing 50%

Find the dilution whose infection rate is just above 50% (call it A, infection rate a%) and the next more dilute step (call it B, infection rate b%).

Step 3: Calculate the Proportionate Distance (PD50)

PD50 = (a - 50) / (a - b)

PD50 ranges from 0 to 1 and represents the relative position of the 50% endpoint between dilutions A and B.

Step 4: Calculate the titer

d50 = log10(dilution_A) - PD50 × log10(dilution factor)

log10(TCID50/mL) = -d50 - log10(inoculum volume_mL)

When inoculating 100 µL (0.1 mL), log10(0.1) = -1, so log10(TCID50/mL) = -d50 + 1.

Worked Example

The following data use 10-fold dilutions, starting at 10⁻¹, 4 wells per dilution, 100 µL inoculum per well:

Dilution    Positive/Total
10⁻¹    4/4
10⁻²    4/4
10⁻³    3/4
10⁻⁴    1/4
10⁻⁵    1/4
10⁻⁶    0/4

Cumulative infection rates by dilution: 100%, 100%, 83.3%, 33.3%, 12.5%, 0%.

The dilutions bracketing 50%: 10⁻³ (83.3%) and 10⁻⁴ (33.3%).

PD50   = (83.3 - 50) / (83.3 - 33.3) = 33.3 / 50 = 0.667
d50    = -3 - 0.667 × 1 = -3.667
log10(TCID50/mL) = 3.667 - log10(0.1) = 3.667 + 1 = 4.667

Result: approximately 4.6 × 10⁴ TCID₅₀/mL.

Limitations

• Dilution intervals must be constant: the calculation assumes each adjacent row differs by the same log₁₀ value (geometric dilution). Skipped dilutions or irregular intervals will produce an incorrect PD50 multiplier.
• Total wells per dilution must be equal: if a contaminated well must be excluded, handle it manually before entering data; the tool does not perform unequal-weight adjustments.
• The series must contain both > 50% and < 50% adjacent dilutions: if all wells are positive or all are negative, interpolation is impossible; widen the dilution range and repeat the experiment.
• This tool gives a statistical estimate, not an exact count: with low replication (≤2 wells per dilution), confidence intervals are wide; do not rely on this method alone for precise quantification — cross-check with a plaque assay (PFU method).

Common Errors

1. Reversing the accumulation direction: positives accumulate from dilute to concentrated, negatives from concentrated to dilute — the directions cannot be swapped. This is the most frequent hand-calculation mistake.
2. Forgetting to correct for inoculum volume: titers for 100 µL versus 200 µL differ by log₁₀2 ≈ 0.3 log units; omitting this correction introduces a systematic error.
3. Forcing interpolation on monotone data: if every dilution has an infection rate > 50% or < 50%, there is no valid A/B pair; no result should be reported.
4. Confusing TCID₅₀ with LD₅₀: the calculation is identical, but LD₅₀ uses animal death as the endpoint; units and interpretation differ entirely — be explicit in any report.