Calculate PCR cycles: final copies after a set number of cycles, cycles needed to reach a target, or starting copies, plus product mass and extension time.

100% gain = perfect doubling each cycle. Or switch to × per cycle, where 2 = doubling.

Product length (mass and extension time)
Double-stranded product length. Adds the product mass and a typical extension time.

Related Calculators

PCR Cycle Formula

The PCR Cycle Calculator estimates the theoretical number of DNA copies produced after a selected number of amplification cycles. Under ideal conditions, the target sequence doubles during each cycle, so the total copy count grows exponentially rather than linearly.

C = I × 2ⁿ
  • C: DNA copies after the selected number of cycles
  • I: initial DNA copies
  • n: number of PCR cycles

The formulas below use the ideal 100% gain (2-fold per cycle) special case. Back-solving also requires the chosen efficiency; at other efficiencies, replace 2 with 1 + E, where E is fractional gain.

n = log₂((C) / (I))
I = (C) / (2ⁿ)

What a PCR Cycle Means

A PCR cycle is one complete round of:

  1. Denaturation – the DNA strands separate.
  2. Annealing – primers bind to the target sequence.
  3. Extension – polymerase synthesizes new DNA strands.

Repeating these steps drives rapid amplification, which is why even a modest increase in cycle count can create a very large change in copy number.

How to Calculate PCR Copy Number

  1. Determine the initial number of DNA copies.
  2. Determine the number of PCR cycles completed.
  3. Apply the amplification formula.
  4. Interpret the result as a constant-efficiency exponential-phase model. Actual reactions may lose efficiency and plateau.

With positive constant efficiency the model is exponential. At zero gain, the amount stays unchanged: a larger target is unreachable and an already-met target needs zero cycles. Fractional cycles and fractional copy equivalents are mathematical interpolation, not partial instrument cycles or physical fractions of a molecule.

Example Calculations

If a reaction starts with 25 copies and runs for 12 cycles, the ideal final copy count is:

C = 25 × 2¹² = 102400

If you want to estimate how many cycles are needed to increase 100 starting copies to 1,000,000 copies, solve for the cycle count:

n = log₂((1000000) / (100)) ≈ 13.29

Since PCR runs in whole cycles, you would need 14 full cycles to exceed one million copies in the ideal doubling model.

Common Cycle Counts and Ideal Amplification

Cycles Ideal Fold Increase Copies from 1 Starting Template
5 32× 32
10 1,024× 1,024
15 32,768× 32,768
20 1,048,576× 1,048,576
25 33,554,432× 33,554,432
30 1,073,741,824× 1,073,741,824
35 34,359,738,368× 34,359,738,368
40 1,099,511,627,776× 1,099,511,627,776

Efficiency Matters in Real PCR

The calculator uses the selected constant gain from 0–100% (1–2 fold per cycle); the examples and table above use ideal doubling. These are bounds for this physical copy-growth model, not acceptance limits for an apparent efficiency fitted from qPCR data. In practice, efficiency varies with primer design, template quality, inhibitors, reagent depletion and plateau effects.

C = I × (1 + E)ⁿ
  • E is fractional gain per cycle: percent gain divided by 100. Fold per cycle equals 1 + E.
  • An efficiency value of 1 corresponds to ideal doubling.
  • Lower efficiency produces fewer copies than the simple doubling model predicts.

Use this constant-efficiency model for teaching and scenario comparison, not a recommended protocol, detection limit or diagnosis. The sensitivity display holds the modeled starting amount and cycle count fixed at efficiencies five percentage points lower and higher, clipped to 0–100%, and reports the actual endpoints. It is not a confidence interval.

How to Interpret the Output

  • Copy mode reports modeled target-copy equivalents. Mass mode assumes the same target amplicon molecular species at both ends; do not substitute total genomic DNA, an entire plasmid, RNA, ssDNA or total extracted sample mass.
  • Optional copy-to-dsDNA mass uses copies × amplicon base pairs × approximately 660 g/mol/bp ÷ 6.02214076×10²³ × 10⁹ to estimate ng. The molecular-weight factor is approximate; the Avogadro constant is exact. This does not measure concentration, purity or actual product yield.
  • High cycle counts can increase total product, but they can also increase nonspecific amplification and late-cycle plateau behavior.
  • This calculator is best for estimating amplification trends, comparing cycle counts, and back-solving for targets.
  • If you need concentration, dilution, or primer preparation values, use a dedicated concentration or dilution calculator alongside this one.

Frequently Asked Questions

Does every PCR cycle exactly double DNA?
No. Exact doubling is the idealized model. Real-world efficiency usually varies across the run.
Why does one extra cycle change the result so much?
PCR amplification is exponential, so each new cycle acts on all copies generated in the previous cycles.
Can this calculator be used backward?
Yes, with the selected efficiency and the other required quantities. Cycle mode finds the minimum nonnegative cycles to meet or exceed the target and verifies the adjacent whole-cycle amounts. A larger target cannot be reached at zero gain.
Is this the same as qPCR quantification?
No. End-point copy estimates are useful for theory and planning, while quantitative PCR relies on fluorescence thresholds and amplification behavior during the run.