PCR Amplification Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/6/2026
The number of copies after PCR amplification is calculated with final copies = initial copies × 2^(number of cycles), assuming 100% efficiency at each cycle. A single initial copy amplified over 30 cycles theoretically yields more than one billion copies (2³⁰ ≈ 1.07 billion).
Explanation
PCR (polymerase chain reaction) is a molecular biology technique that exponentially amplifies a targeted DNA sequence: at each thermal cycle, the amount of target sequence theoretically doubles, since each DNA strand serves as a template to synthesize a new complementary strand. This exponential (rather than linear) growth is what makes PCR extraordinarily sensitive: even a tiny amount of starting DNA can be amplified, over a few dozen cycles, up to a detectable and analyzable quantity. This calculator applies the theoretical assumption of perfect duplication efficiency (100% at each cycle), the standard assumption taught for this introductory calculation. In practice, the actual efficiency generally declines toward the end of the reaction (often after 25 to 30 cycles), as reagents are depleted and the amplified products begin to interfere with one another — a phenomenon called the plateau effect, which explains why increasing the number of cycles indefinitely does not keep doubling the yield beyond a certain point in practice.
Example: 1 initial copy amplified over 30 cycles
Inputs
Initial copies: 1. Number of cycles: 30.
Calculation
Final copies = 1 × 2³⁰ = 1,073,741,824.
Result
Theoretically, more than one billion copies are obtained after 30 cycles.
Frequently asked questions
Why does the number of copies double at each cycle?
Because each PCR cycle includes three steps (denaturation, primer annealing, extension) that allow an enzyme (DNA polymerase) to synthesize a new complementary DNA strand from each existing strand. Each DNA molecule present at the start of a cycle therefore yields two molecules by the end of that cycle, hence the growth as a power of 2.
Is the real efficiency actually 100% at every cycle?
Rarely across the whole reaction: the actual efficiency generally declines after a certain number of cycles (often 25 to 30), as reagents (primers, nucleotides, enzyme) are depleted, a phenomenon called the plateau effect. This calculator therefore gives a maximum theoretical estimate, useful for understanding the principle of exponential amplification, but the real yield toward the end of the reaction is generally lower than this theoretical figure.
Why are 25 to 35 cycles generally used, not more?
Because exponential amplification quickly becomes sufficient for detection (a few dozen cycles are enough to multiply the initial quantity by more than a billion), and continuing beyond that point no longer brings a significant benefit once the plateau effect is reached, while increasing the risk of artifacts and non-specific products.