Digital PCR calculator for ddPCR and dPCR data

What it does

It calculates the concentration of one target sequence in the original sample, in copies per µL of the original sample and copies per mL of the original sample, from the positive and accepted partition counts of a digital PCR run, under a declared partition volume, a declared reaction composition and a declared pre-PCR dilution, with every intermediate value shown.

In titer mode the per-mL result is labelled as a vector genome or genome copy titer according to your declarations.

The software's concentration uses a partition volume set by the software. On one platform that value changed between software versions (0.91 nL, then 0.85 nL; Corbisier et al. 2015). So the tool starts from the counts and asks you to declare the volume.

How to use it

1. The run. Enter the instrument and software version, the partition volume with its unit, and the target name. The Published values list shows what others have published; it never fills the field for you.
2. Sample preparations. For each preparation, say whether the sample was diluted before PCR and enter each dilution step as the volume in and the total volume of the step. Then enter the total volume of the reaction after the sample is added, and the volume of sample in it.
3. Partition counts per well. Type each well's positive and accepted partitions, or paste a table and say which column is which. Choose each well's preparation, and tick the wells to include in the mean.
4. Titer mode. For a vector lot, switch titer mode on and answer its three questions.
5. Read the result. It updates as you type. Anything missing or refused is named beside its field, with what to do.

How it works

Each well goes through the same nine steps, in this order, for every preparation.

Quan P-L, Sauzade M, Brouzes E. dPCR: A Technology Review. Sensors 2018;18(4):1271, section 2.1: the ratio of positive partitions k (containing some target sequences) over the total number of partitions n is sufficient to predict the initial concentration of the target sequence in the sample with λ=−ln(1− k/n).

Ligant's mapping: k = positive partitions; n = accepted partitions, read as Quan's "total number of partitions" analysed.

Quan defines λ = m/n for "m molecules" distributed "into n partitions". m copies in n partitions of volume Vd are m ÷ (n × Vd) = lambda ÷ Vd copies per µL.

Addgene's protocol writes the titer as T = (R × C × D × 1000) ÷ V, where "R = Reaction volume (20 µL)", "C = Copies/µL", "D = Dilution factor of virus" and "V = Volume of virus in reaction mix (4 µL)". In that protocol each reaction is 20 µL of master mix plus 5 µL of diluted sample, and 20 µL of it is loaded, so we read R and V as the loaded volume and the sample in it: 20 ÷ 4 = 25 ÷ 5 = 5, the same ratio this tool asks for as total ÷ sample. C is the copies per µL reported by the instrument software, which uses the software's partition volume; this tool computes it from your counts and the partition volume you declare.

Worked example, step by step

Results are shown to 7 significant figures, and lambda to 10, so that you can follow the arithmetic by hand. The number of digits is not the precision of the measurement, which this release does not calculate; the counts beside each result show how many partitions it rests on. Values of 10 million or more are written in scientific notation.

Constants and assumptions

Assumptions

Quan et al. 2018: "Quantification by dPCR assumes that partitions possess identical volumes".

Flags

Flags never block a result. Each is shown with its code:

The calculation is open source. Read the code

Zin EA, Desrosiers M, Ocari T, et al. Impact of DNase digestion on titer measurements of engineered adeno-associated virus serotypes. Mol Ther Methods Clin Dev 2025;33. doi:10.1016/j.omtm.2025.101419

Zin et al. 2025: © 2025 The Authors. Open access under CC BY-NC-ND 4.0 (https://creativecommons.org/licenses/by-nc-nd/4.0/). Quoted in short extracts, unchanged.

Addgene. ddPCR Titration of AAV Vectors (protocol; last reviewed 31 August 2023). https://www.addgene.org/protocols/aav-ddpcr-titration/

Hindson BJ, Ness KD, Masquelier DA, et al. High-Throughput Droplet Digital PCR System for Absolute Quantitation of DNA Copy Number. Anal Chem 2011;83(22):8604–8610. https://pmc.ncbi.nlm.nih.gov/articles/PMC3216358/

Corbisier P, Pinheiro L, Mazoua S, et al. DNA copy number concentration measured by digital and droplet digital quantitative PCR using certified reference materials. Anal Bioanal Chem 2015;407(7):1831–1840. https://pmc.ncbi.nlm.nih.gov/articles/PMC4336415/

Why not a spreadsheet?

A spreadsheet leaves these to memory or habit. Here each is a recorded declaration, beside its field and in every result:

• which volume is "the reaction volume";
• which partition volume applied, on which software version;
• whether positive and accepted counts come from the same well;
• DNase and lysis for a vector titer;
• the direction of a dilution factor (1 µL into 10 µL total is factor 10).

The tool rounds to the digits shown only for display. Every later step uses the unrounded value, held at the computer's full precision of about 16 significant digits, which is a limit of the arithmetic, not of the measurement. Multiplying the shown values by hand can therefore differ from the result in the last digits.

Units are carried and converted on the number you typed, and the same entries always give the same results.

What it does not do

It does not call partitions positive or negative, set a threshold, judge instrument quality, give a confidence interval, carry a default partition volume, or judge whether the partition volume you declare is right for your instrument.

It does not cover reading the positive and accepted partitions and checking the threshold and partition quality in your instrument software, nor any extraction or concentration step before the first dilution you entered.

What the tool cannot detect:

1. Whether the threshold between positive and negative partitions is right, or whether rain, merged partitions or poor partitioning affected the counts.
2. Whether the partition volume you declare is right for your instrument.
3. The uncertainty of the estimate: release 1.0 gives no confidence interval.
4. Whether the volumes typed match what was pipetted, or whether the positive and accepted counts come from the same well.
5. Whether DNase digestion worked: "DNase-treated" records your statement, not a test.
6. Whether capsids were opened completely, or whether a heat step affected some capsids differently.
7. Capsid integrity, and empty against full capsids: a genome titer counts genomes only.
8. Whether a counted amplicon sits on a complete genome; two targets can disagree, and the tool does not know which is right.
9. Primer or probe bias between targets, and inhibitors.
10. Loss of vector on tube walls at high dilution.
11. RNA-genome vectors.
12. Whether target copies were clumped or linked. An aggregate of vector particles, or copies joined on one DNA fragment, sits in one partition and reads as one positive partition, while the calculation assumes copies are spread independently, so the result is low. For AAV, Zin et al. (2025) note that an aggregate can yield "one positive droplet that represents one viral genome instead of registering all AAVs present in the aggregate".
13. Whether all wells and preparations came from the same original sample or aliquot, and whether the lot is what the record says.
14. Any extraction or concentration step before the first dilution you entered. The result is per µL of the material you started diluting from, for example your DNA extract; the tool does not go back through an extraction, whose recovery it cannot know.

Titer mode is for DNA-genome vector lots, such as AAV. It does not cover RNA-genome vectors measured by RT-ddPCR, such as lentiviral lots.

Two targets on one lot are two measurements. Each is reported under its own target name, and the tool does not average or compare them.

ddPCR, Droplet Digital, QX200, QX600 and QuantaSoft are trademarks of Bio-Rad Laboratories, Inc. QIAcuity is a trademark of the QIAGEN Group. Absolute Q and QuantStudio are trademarks of Thermo Fisher Scientific and its subsidiaries. Stilla and naica are trademarks of Stilla Technologies. Other names may be trademarks of their respective owners. All are used here only to identify the instruments, data and sources the calculator refers to. Ligant is not affiliated with, sponsored or endorsed by any of these companies.

How do I calculate copies per µL from positive and negative droplets in ddPCR?

Enter the positive partitions (droplets, on a droplet instrument) and the accepted partitions: every partition your instrument's software counted and used, positive and negative together, so accepted = positive + negative. The tool computes the fraction positive, p = positive ÷ accepted, then lambda = −ln(1 − p), the average number of copies per partition (Quan et al. 2018, section 2.1), and divides by the partition volume you declare to give copies per µL of reaction. It then scales back through your reaction volumes and dilutions to copies per µL of your original sample.

Why can't I just divide the positive partitions by the volume?

A partition can hold more than one copy, and it reads positive whether it holds one copy or three, so counting positive partitions alone undercounts. If copies are spread among the partitions at random, the fraction of negative partitions is e^−lambda, so lambda = −ln(1 − p) recovers the average number of copies per partition. In the worked example, 15,000 positive of 20,000 accepted gives lambda = 1.386, not 0.75.

What is the difference between positive partitions and accepted partitions, and which number do I enter?

Accepted partitions are the partitions your instrument's software counted and used in its analysis, not the number it tried to make. Enter both numbers, from the same well and target. Using the number the instrument tried to make shifts p. Positive partitions cannot be more than accepted partitions; the tool refuses that entry.

What partition volume should I use for my instrument and software version?

The one that applies to your instrument, plate or cartridge, and software version: check your instrument's and software's documentation. Results scale as 1 ÷ partition volume, so this choice changes every result. Published values differ between platforms and, on one platform, between software versions (Corbisier et al. 2015). The tool shows published values with their sources and never chooses one; it uses only the value you enter, and it cannot know the value for your instrument.

Do I enter the total reaction volume or the sample volume, and how do I enter a 1:10 dilution?

Both. Enter the total volume of the reaction after the sample is added, and the volume of sample in it: for 20 µL of master mix plus 5 µL of sample, enter 25 and 5, not 20 and 5, which would make the answer 20 percent low. The volume loaded into the droplet generator or chip is not needed. For a dilution, enter the volume in and the total volume: 1 µL of sample into 10 µL total is a factor of 10. The tool asks for volumes rather than "1:10" because some labs write 1:10 for 1 part sample plus 10 parts diluent, a factor of 11.

How do I convert ddPCR copies per µL to vg/mL for an AAV titer?

This tool starts from the partition counts, not from the copies per µL your software reports, because the software's figure uses a partition volume set by the software. Switch on titer mode and enter the counts, the partition volume, the reaction volumes and your dilutions. The tool multiplies copies per µL of reaction by total ÷ sample volume and by the dilution factor to give copies per µL of your original sample, then by 1,000 for copies per mL, and labels that result by your declarations.

Is vg/mL the same as GC/mL, and does it matter whether I used DNase?

Not as this tool labels them, and it matters. If you declare a DNase step, or another way of removing or blocking free DNA, the result is labelled vector genomes per mL (vg/mL). If you declare no such step, or do not know, it is labelled genome copies per mL (GC/mL), because free DNA in the sample is counted as genome copies. The target is always in the label. A genome titer counts genomes; it says nothing about capsids without genomes.

Why does the tool ask which instrument and software version I used?

The partition volume differs between platforms, and on one platform the value the software uses changed between software versions (0.91 nL, then 0.85 nL; Corbisier et al. 2015). The accepted count is also the software's own result. Recording the instrument and software version lets a reader see which volume and which analysis applied.