PCR Amplification Calculator
1000 template copies amplified for 30 cycles at 95 % efficiency give about 502387000000 copies, before the reaction plateaus.
502386939855.418
Full answer, then cut to fewer decimals (not rounded):
- 502386939855.418
- 502386939855.41
- 502386939855.4
- Fold amplification (1 + E)ⁿ
- 502386939.9
- Ideal (100 %) copies N₀2ⁿ
- 1073741824000
- Cycles to reach the target
- 20.68718617
- qPCR standard-curve slope for this E
- -3.447864361
Step-by-step solution
- N = N₀(1 + E)ⁿ = 1000 × 1.95^30 = 502386939900
- Slope = −1 ÷ log₁₀(1 + E) = -3.447864361 (−3.32 at 100 %)
PCR Amplification Formula
N = N₀(1 + E)ⁿ
E efficiency (1 = perfect doubling); qPCR slope = −1/log₁₀(1 + E)
Worked Example
1000 starting copies amplified for 30 cycles at 95 % efficiency:
- N = N₀(1 + E)ⁿ = 1000 × 1.95^30 = 502386939900
- Slope = −1 ÷ log₁₀(1 + E) = -3.447864361 (−3.32 at 100 %)
Ideal (100 %) copies N₀2ⁿ: 1073741824000 · Cycles to reach the target: 20.68718617 · qPCR standard-curve slope for this E: -3.447864361
GATE tip
A difference of 1 Ct is a twofold difference in starting template at 100 % efficiency, 3.32 Ct a tenfold one: the basis of ΔΔCt relative quantification.
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Frequently asked questions
Why does PCR plateau?
Primers and nucleotides run low, polymerase activity falls and products re-anneal, so real reactions stop growing exponentially after roughly 30–35 cycles.
How is efficiency measured?
From a dilution series in qPCR: slope −3.32 means 100 %; acceptable efficiency is 90–110 % (slope −3.6 to −3.1).
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). PCR Amplification Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/pcr-amplification-calculator/
IEEE
Scientific Converters, "PCR Amplification Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/pcr-amplification-calculator/