PCR Yield Calculator: Copies and Nanograms After n Cycles

How it works

N = N₀ × (1 + E)ⁿ, capped at the plateau; N₀ from mass = ng × Nₐ ÷ (template bp × 660 × 10⁹); mass = N × amplicon bp × 660 g/mol ÷ Nₐ; cycles for a target = ⌈log(N_target ÷ N₀) ÷ log(1 + E)⌉; primer ceiling = [primer] × volume × Nₐ; dNTP ceiling = 4 × [dNTP] × volume × Nₐ ÷ (2 × bp)

In the exponential phase each cycle multiplies the target by (1 + E), where E is the amplification efficiency: 100% is a perfect doubling, and well-optimised reactions run at about 90–100%. Thirty cycles at 100% would multiply the template about a billion times (2³⁰ ≈ 1.07 × 10⁹). Real reactions stop growing exponentially when product builds up: polymerase becomes limiting, product strands re-anneal instead of binding primers, and pyrophosphate and duplex DNA inhibit the enzyme. Training material for forensic labs puts the start of the plateau at about 0.3–1 pmol of product, which for a 500 bp amplicon is roughly 100–330 ng; growth slows from there, so near that amount the real yield can fall below the exponential estimate. The calculator caps the yield at the lowest of three ceilings: an empirical plateau concentration (40 ng/µL by default, under More options), the primers (each product duplex consumes one forward and one reverse primer) and the dNTPs (two nucleotides per base pair). It shows the cycle a band becomes visible on a gel, the cycle the plateau begins, a ±5-point efficiency check and the full cycle table. Switch to Cycles for a target to find how many cycles give a set amount, or enter the template as a mass (plasmid or genomic DNA) instead of copies. The model is a simple exponential with a hard ceiling; in practice efficiency falls gradually over the last few cycles before the plateau, so treat cycle numbers near it as approximate.

Worked example

1,000 copies of a 500 bp target at 95% efficiency in 25 µL. One amplicon weighs 500 × 660 ÷ 6.022 × 10²³ = 5.48 × 10⁻¹⁰ ng (0.548 ag). After 30 cycles: 1,000 × 1.95³⁰ = 5.02 × 10¹¹ copies, or 275.3 ng (11.01 ng/µL, 33.37 nM). The plateau ceiling is 40 ng/µL × 25 µL = 1 µg (1.82 × 10¹² copies), below the primer (6.02 × 10¹²) and dNTP (1.20 × 10¹³) ceilings, so the reaction is still exponential. A 10 ng band appears at cycle 26 and the plateau begins around cycle 32. At 90% or 100% efficiency the same run would give 126.3 ng or 588.4 ng.

Sources: NIJ forensic DNA amplification training: the plateau effect (0.3–1 pmol of product) · Omni Calculator – DNA copy number (660 g/mol per bp, N = i × 2ⁿ) · Calculator Academy – PCR cycle calculator (C = I × (1 + E)ⁿ, solve for cycles) · Gene-Quantification: causes of the PCR plateau (Kainz 2000)

Frequently asked questions