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# DNA Copy Number Calculator

Formula for the DNA/RNA copy numberHow to use the DNA copy number calculator — ExampleFormula for the gene copy number per PCR cycleImproving PCR amplificationFAQs

Welcome to the DNA copy number calculator!

You can use this calculator for your PCR runs to convert nanograms (ng) of DNA to its copy number. You can also use the calculator the other way around to determine the DNA stock solution for a specific DNA or RNA copy number per microliter.

In this tool, you can choose between double or single-stranded DNA or single-stranded RNA. Jump right into the calculation or keep reading to:

• Learn the calculator's formula;

• Go through a step-by-step-example;

• Understand, how to calculate you stock sample dilution;

• Learn how to calculate the copy number per PCR cycle; and

• Get an overview about what factors influence the copy number and your PCR results 🧬.

## Formula for the DNA/RNA copy number

Specific DNA sequences get copied when performing PCRs, depending on different parameters. The number of copies made per specific volume is essential to correctly set up our sample for subsequent analyses such as DNA-sequencing assays.

Use this base formula from the DNA copy number calculator to calculate RNA or DNA in nanograms (ng) to its copy number:

$\small \text{DNA copies/µL} = \frac{C_{\rm DNA}\times N_{\rm A}}{l\times {\rm ng}\times w_{\rm bp}}$

where:

• $C_{\rm DNA}$DNA concentration, in ng/µL (see our DNA concentration calculator);
• $N_{\rm A}$Avogadro's constant$6.022\times10^{23}$ (see our Avogadro's number calculator);
• $l$Length of the template, in base pairs (bp);
• $\rm ng$Conversion factor to nanograms$1\times10^9$; and
• $w_{\rm bp}$Average weight of a base or base pair, in daltons (Da).

In our DNA copy number calculator, you can choose between single-stranded DNA and RNA nucleotides (ssDNA/ssRNA) and double-stranded DNA base pairs (dsDNA) for the average base weight. The calculator uses the following values:

• ssDNA — $330$ Da;
• ssRNA — $340$ Da; and
• dsDNA – $660$ Da.

Let's look at some examples next to understand how to use this formula and the calculator to determine the gene copy number🧪!

## How to use the DNA copy number calculator — Example

### 1. Calculate the copy number

Let's say we measured a stock sample DNA concentration $C_{\rm DNA}$ of 150 ng/µL. The total template length $l$ is 4,700,000 base pairs. Since we have double-stranded DNA, we will choose the standard base-weight $w_{\rm bp}$ of 660 daltons.

We now want to know how many copies of the genome are in 1 µl of this stock:

\!\small \begin{align*} N_{\rm DNA} &= \frac{150 \times 6.022 \times 10^{23}}{4,\!700,\!000 \times 1 \times 10^9 \times 660} \\[1em] &= \frac{9.033 \times 10^{26}}{3.103 \times 10^{19}} \\[1em] &= 29,\!110,\!538 \ \text{copies/µL} \\[.4em] &= 2.91 \times 10^7 \ \text{copies/µL} \end{align*}

where:

• $N_{\rm DNA}$ — Number of copies per microliter;
• $6.022\times 10^{23}$ — Avogadro's constant; and
• $1\times 10^9$ — is the conversion factor to nanograms.

### 2. Calculate stock dilution

Now let's assume that we need a total pipette volume of 10 µL with a final concentration of 2,000,000 copies/µL. With the previous result, you now only need to divide the calculated concentration by the desired concentration and multiply with the desired total pipette volume:

$\footnotesize\frac{2,\!000,\!000\ \text{copies/µL}}{2.911\times10^7\ \text{copies/µL}} \times 10\ \text{µL}\\[.5em] = 0.68\ \text{µL}$

So you would need to pipette $0.68\ \text{µL}$ of the stock solution with $10 - 0.676 = 9.32\ \text{µL}$ of water.

## Formula for the gene copy number per PCR cycle

If you know the copy numbers needed for a subsequent analysis, you might want to determine, how many cycles your PCR needs to run.

In our calculator, you can determine the copy number after a given number of PCR cycles or how many PCR cycles you will need to reach a specific copy number by simply opening the DNA copies per PCR cycle section.

The calculator estimates the number of DNA or RNA copies after a certain amount of PCR cycles with the following easy formula:

$N_{\rm DNA} = i \times {2^n}$

where:

• $N_{\rm DNA}$ — Number of DNA copies after $n$ cycles;
• $i$ — Initial number of DNA copies; and
• $n$ — Number of PCR cycles.

If you want to know, for example, the number of copies after 10 PCR cycles with an initial number of $1.4\times10^5$ DNA copies/µl:

$\small N_{\rm DNA} = 1.4\times{10^5} \times {2^{10}} \\[1em] N_{\rm DNA} = {14.336\times{10^7}} \text{copies/µl}$

## Improving PCR amplification

If you are unhappy with your PCR results, check the following points and verify that you followed all instructions for your chosen PCR kit correctly.

1. The recommended amount of DNA template is 25 to 100 ng per 100-µL reaction volume.

2. Our annealing temperature calculator will be a great help for adjusting your cycler-parameters correctly.

3. Verify that your primers are designed specifically or unspecifically enough and work correctly. Verify the functionality of all other PCR components (nucleotides, buffers, polymerase).

4. Make sure your template DNA does not contain too much DNA (nonspecific amplification) or too little DNA (low yields).

5. Investigate for inhibitors such as bile salts, heme from blood samples, urea from urine samples, viral transport medium, heparin, and formalin, among others.

FAQs

### How is copy number calculated?

Use this formula to calculate the DNA copy number:

DNA copies/µL = (DNA concentration [ng/µL] × Avogadro's constant) / (length of the template [bp] × conversion factor to nanograms × weight of base (pair) [Da])

where:

• The conversion factor to nanograms is 1×10⁹.
• The average weight of a base or base pair is:
• 660 for dsDNA,
• 330 for ssDNA, and
• 340 for ssRNA.

### How many copies after 40 cycles of PCR?

2.8×1046 copies/µL if we assume an initial number of 1.4×105 DNA copies/µL in the stock solution. Use the following equation to verify the result:

N = i × (2n)

where:

• N — Number of DNA copies after n cycles;
• i — Initial number of DNA copies; and
• n — Number of PCR cycles.

For our example:

N = 1.4×105 × (240) = 2.8×1046 copies/µL

### Does each cycle increase the DNA copy number in PCR?

Yes, PCR amplifies the DNA between the two added primers exponentially, with the number of DNA copies doubling after each cycle so that after n cycles, you have 2n copies. However, when reagents in the PCR sample become limiting, the amplification reaches a plateau.

### What are copy number variations (cnv)?

Copy number variations (cnv) are a natural occurrence in which a specific DNA segment's copy number varies among individuals' genomes. They play an essential role in evolution, contribute to population diversity, and development of certain diseases.

We can detect these variations in the repetition of genome sequences with sequencing methods such as NGS.