This PCR calculator predicts DNA yield across cycles from starting copies and amplification efficiency — and the cycle at which your reaction crosses any target amount.
The exponential phase is glorious and temporary: primers/dNTPs exhaust, polymerase tires, products re-anneal — real reactions plateau (which is why qPCR reads the exponential phase via Ct, not endpoints). Efficiency below ~90% usually indicts primer design, inhibitors (heme, humic acids, ethanol), or annealing temperature — slope of a standard curve converts to efficiency as E = 10^(−1/slope) − 1.
N = N₀ × (1 + E)ᶜ — Exponential Growth with a Polymerase
PCR is the Exponential Growth equation wearing gloves: perfect doubling (E = 1) for 30 cycles multiplies a single molecule a billion-fold. Starting amounts trace back through our DNA Concentration Calculator. Part of our Biology Calculators collection.
Worked Examples (Verified)
- 100 copies, 30 cycles, 100% efficiency (defaults): 100 × 2³⁰ = 1.07 × 10¹¹ copies, crossing the 10⁹ threshold at cycle 23.3 — why Ct values in the low 20s mean “a lot of template”
- Same reaction at 90% efficiency: 2.31 × 10¹⁰ — a 4.7× shortfall from a 10-point efficiency slip; at 80%: 5.5 × 10⁹, a 20× miss. Small per-cycle losses are the entire qPCR accuracy game
- Single-molecule reality: 1 copy × 2³⁵ = 3.4 × 10¹⁰ — digital PCR partitions until this exact arithmetic happens one molecule per well
- Ct differences: 10× more starting template = ~3.32 fewer cycles at perfect efficiency (log₂10) — the conversion every ΔCt analysis silently assumes
Plateau & Practice
- Endpoint gels lie about starting amounts precisely because all reactions converge to the plateau — quantify in the exponential window only.
- Efficiency targets: 90–110% by standard-curve slope (−3.6 to −3.1); >110% usually means inhibition diluting out or primer-dimers fluorescing.
- More cycles ≠ more truth: past ~35–40, artifacts (dimers, concatamers, heteroduplexes) bloom faster than signal.
- Hot-start polymerases and clean template prep move efficiency more than any cycling tweak — chemistry beats choreography.
Related Tools
- DNA Concentration Calculator — copies in, copies out
- Primer Tm Calculator — set annealing with knowledge
- Biology Calculators — the full collection
Frequently Asked Questions
How much DNA does PCR make?
Copies multiply by (1 + efficiency) each cycle: at perfect doubling, 30 cycles = 2³⁰ ≈ 1.07 billion× your starting copies (100 copies → 1.07 × 10¹¹). Real reactions plateau as reagents deplete, which this model — like the exponential phase it describes — deliberately ends before.
What is PCR efficiency and why does it matter?
The fraction of molecules copied per cycle: 100% = perfect doubling. Small deficits compound brutally — 90% efficiency yields 4.7× less product after 30 cycles than 100%; 80% yields 20× less. qPCR quantification stands or falls on knowing it (standard-curve slope: −3.32 = 100%).
How do I interpret a Ct value?
Ct (threshold cycle) is when fluorescence crosses a set line: fewer cycles = more starting template. At 100% efficiency each 3.32 Ct ≈ a 10× difference (1 Ct ≈ 2×). The calculator’s “cycles to target” inverts this: the cycle a given starting copy number reaches a billion copies.
Why not just run 45 cycles for weak samples?
Because the plateau and artifacts wait there: primer-dimers, nonspecific products and reagent exhaustion grow while true signal saturates, and contamination (a single aerosolized molecule amplifies fine) finds its voice. More starting template, better primers, or nested/enrichment strategies beat brute cycles.
What’s the difference between PCR and qPCR math?
None in the growth law — qPCR just watches the exponential phase with fluorescence and reports Ct instead of final yield. RT-qPCR adds a reverse-transcription step (RNA → cDNA) whose own efficiency precedes everything computed here.
Is this PCR calculator free?
Yes — free, instant, no sign-up.