PCR Amplification Calculator
How many DNA copies a PCR produces after a given number of cycles at a given efficiency — the mass that makes, and the cycles needed to reach a detectable amount from a few starting molecules.
Each cycle doubles the template at 100% efficiency; real reactions run at 90 to 98%, so the count is starting copies times (1 + efficiency) to the power of cycles.
How the pcr amplification calculator works
Each cycle doubles the template at 100% efficiency; real reactions run at 90 to 98%, so the count is starting copies times (1 + efficiency) to the power of cycles. Thirty cycles at 95% turns ten molecules into 7 billion.
The plateau is not modelled here — reagents run out somewhere past 10¹² copies — which is why quantitative PCR reads the exponential phase and why the cycle-to-threshold row is the useful one.
Formula: copies = N₀ × (1 + E)^n; cycles to target = log(target / N₀) / log(1 + E)
Worked examples
| Inputs | Copies after the cycles | Note |
|---|---|---|
| Ten copies, 30 cycles | 5.024e+9 | about 7 billion |
| Perfect efficiency | 1.074e+10 | over 10 billion |
| A single molecule | 3.994e+11 | detectable |
FAQFrequently asked questions
How much does PCR amplify?
At 95% efficiency, 30 cycles multiply the template by about 500 million; at 100%, by a billion. Ten molecules become nanograms of product.
What is amplification efficiency?
The fraction of template copied each cycle. Ninety to a hundred per cent is a good assay; below 90 the standard curve is unreliable.
Why does the reaction plateau?
Primers, nucleotides and polymerase run out, and product strands re-anneal to each other. Somewhere around 10¹² copies the curve flattens.
What is a Ct value?
The cycle at which fluorescence crosses a threshold. Each tenfold more starting template lowers it by about 3.3 cycles, which is how qPCR quantifies.
Can I amplify a single molecule?
Yes — 40 cycles at good efficiency takes one copy to detectable levels. It is also why contamination is the constant hazard of PCR.
Where these figures come from
- NCBI Bookshelf — Molecular Biology of the Cell — growth kinetics and molecular conventions
- Wellcome Sanger Institute — a leading UK genomics institute
Last checked: September 2026. Formulas are the standard textbook forms; assumptions are stated on each page because they are where these models break.