Calculate qPCR amplification efficiency from the slope of a standard curve (E = 10^(−1/slope) − 1), with a quality assessment.
Standard Curve Slope
The slope of the linear regression line from your qPCR standard curve (Ct on the y-axis, log₁₀ of the dilution on the x-axis). A perfect 100% efficient reaction has a slope of −3.32.
Example standard curves
Amplification Efficiency
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Enter the standard curve slope above to compute amplification efficiency.
Fold Amplification per Cycle
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How many times the template amount multiplies with each PCR cycle (1 + E).
Assay Quality
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The accepted range for a well-optimized qPCR assay is 90–110% efficiency.
Scenario Comparison
This curve
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Ideal (slope −3.32)
100.1%
2.001x per cycle — the theoretical maximum doubling rate.
Amplification efficiency tells you how faithfully your qPCR assay doubles template DNA each cycle — and it's the single most important quality check before trusting any quantification result from that assay.
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Walk-through
How to Use This Calculator
3 steps▸
1
Run your standard curve
Amplify a dilution series (e.g. 5 points, 10x or 5x apart) of a known template and record the Ct value at each dilution. Plot Ct on the y-axis against log₁₀(dilution) on the x-axis and fit a linear regression line — most qPCR instrument software does this automatically.
2
Enter the slope
Take the slope of that regression line and enter it above. The slope is always negative, since Ct decreases as template concentration increases. A perfectly 100% efficient reaction (exact doubling every cycle) has a slope of −3.32.
3
Check efficiency and quality
The calculator converts the slope into an amplification efficiency percentage, a fold-per-cycle multiplier, and a quality verdict. Efficiency between 90% and 110% is generally accepted as a well-optimized assay; outside that range, revisit primer design, template purity, or reaction conditions before trusting quantification results.
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Reference
Formula & Methodology
1 formula▸
Amplification efficiency from slope
E = 10^(−1 / slope) − 1
E is the fractional amplification efficiency (0 = no amplification, 1 = perfect doubling). Multiply by 100 for percentage efficiency. The slope comes from a linear regression of Ct (cycle threshold) against log₁₀(dilution factor) across a dilution series of the same template. Fold change per cycle is 1 + E — at 100% efficiency, fold = 2 (the template doubles every cycle).
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Glossary
Key Terms Explained
7 terms▸
qPCR ↗Quantitative (real-time) polymerase chain reaction — a PCR variant that measures the amount of amplified DNA after each cycle using a fluorescent reporter, allowing the starting template amount to be quantified.
Amplification efficiency ↗The fraction of template molecules that are successfully copied each PCR cycle, expressed as E (0 to 1+) or as a percentage. 100% efficiency means every template molecule is copied exactly once per cycle, doubling the total amount.
Standard curve ↗A plot of Ct values against the log of a known template dilution series, used to derive amplification efficiency (from the slope) and quantify unknown samples (from the y-intercept).
Slope ↗The gradient of the linear regression line fit to a qPCR standard curve (Ct vs. log₁₀ dilution). A slope of exactly −3.32 corresponds to 100% efficiency; steeper (more negative) slopes indicate lower efficiency, shallower slopes indicate higher apparent efficiency.
Ct (cycle threshold) ↗The PCR cycle number at which the fluorescent signal crosses a fixed detection threshold above background. Lower Ct values indicate a higher starting amount of template.
Real-time PCR ↗Another name for qPCR — amplification and fluorescence detection happen simultaneously in real time, cycle by cycle, rather than being measured only at the end of the reaction.
Log dilution ↗The base-10 logarithm of a sample's dilution factor relative to an undiluted stock, used as the x-axis of a qPCR standard curve so that serial dilutions (e.g. 1:10, 1:100, 1:1000) plot as evenly spaced points.
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Scenarios
Real-World Examples
3 worked examples▸
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Well-optimized assay
Standard curve slope of −3.32 (the theoretical ideal)
Slope -3.32
E = 10^(−1/−3.32) − 1 ≈ 1.001, or 100.1% efficiency — essentially exact doubling each cycle (2.001x fold per cycle). This sits squarely in the accepted 90–110% range, so quantification results from this assay can be trusted without further optimization.
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Fold-per-cycle check
Same ideal slope, focused on the doubling rate
Slope -3.32
Fold per cycle = 1 + E ≈ 2.001x. After 10 cycles, template increases roughly 2.001^10 ≈ 1,027-fold — very close to the theoretical 1,024-fold (2^10) of a perfectly doubling reaction.
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Under-optimized assay
Standard curve slope of −3.6 (steeper than ideal)
Slope -3.6
E = 10^(−1/−3.6) − 1 ≈ 0.896, or 89.6% efficiency — just below the 90% quality cutoff, flagged as "Re-optimize." A steeper-than-ideal slope like this usually points to inhibitors in the template, suboptimal primer design, or pipetting inconsistency in the dilution series.
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Reference
Cite This Calculator
APA & MLA▸
Use either format to cite this calculator in a paper, report, or resource list.
Amplification efficiency tells you how faithfully your qPCR assay doubles template DNA each cycle — and it's the single most important quality check before trusting any quantification result from that assay. This calculator converts the slope of a standard curve into an efficiency percentage, a fold-per-cycle multiplier, and a pass/fail quality verdict.
How the qPCR Efficiency Calculator works
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The calculator implements the standard relationship between a qPCR standard curve's slope and amplification efficiency: E = 10^(−1/slope) − 1. This formula falls directly out of the exponential amplification model — after n cycles, template amount grows by a factor of (1 + E)^n, and Ct is proportional to −log₁₀ of the starting amount divided by log₁₀(1 + E). Rearranging for a linear Ct-vs-log(dilution) fit gives the slope-to-efficiency conversion used here. A slope of exactly −3.32 (which is −1/log₁₀(2)) corresponds to E = 1, i.e. exact doubling — 100% efficiency.
Inputs and what they mean
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The only input is the slope of your standard curve's linear regression (Ct on the y-axis, log₁₀ of the dilution factor on the x-axis). This slope is produced automatically by most real-time PCR instrument software once you enter a dilution series and its Ct values — you don't need to fit the regression by hand. The slope is always negative because Ct falls as template concentration rises. Typical real-world slopes for a working assay fall between about −3.1 and −3.6, corresponding to roughly 90–110% efficiency.
Limits and edge cases
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Efficiency calculated this way assumes your dilution series spans a range where PCR kinetics stay linear — reactions that are wildly over- or under-diluted, saturate the detection reaction, or include pipetting errors can distort the slope independent of true assay efficiency. Efficiency above 110% often indicates pipetting inaccuracy in the dilution series or co-amplification of non-specific products rather than a genuinely "super-efficient" reaction. A slope of exactly zero is undefined for this formula (division by zero) and signals a failed or flat standard curve — re-run the dilution series rather than trusting any efficiency number from it.
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Questions
Frequently Asked Questions
6 questions▸
What is the formula for qPCR efficiency?+
E = 10^(−1/slope) − 1, where slope is the gradient of the linear regression fit to Ct values plotted against log₁₀(dilution) across a standard curve dilution series. Multiply E by 100 to express it as a percentage.
What slope corresponds to the ideal 100% efficiency?+
A slope of −3.32 corresponds to exactly 100% efficiency — the template doubles precisely once every cycle. This value comes from −1/log₁₀(2).
What's a good efficiency range for a qPCR assay?+
90% to 110% efficiency is the generally accepted range for a well-optimized assay, corresponding to standard curve slopes of roughly −3.1 to −3.6. Efficiency outside this range suggests the assay needs troubleshooting before its quantification results can be trusted.
What does fold per cycle mean?+
Fold per cycle is 1 + E — the multiplier applied to the template amount with every PCR cycle. At 100% efficiency, fold per cycle is 2.0 (exact doubling); at 90% efficiency it's 1.9, and at 110% it's 2.1.
What units does this calculator use?+
The slope input is unitless (it's the gradient of Ct, which has no units, against log₁₀ of a dilution factor, which is also unitless). The efficiency output is a percentage, and fold per cycle is a dimensionless multiplier.
Why is my qPCR efficiency too low or too high?+
Low efficiency (below 90%) is usually caused by PCR inhibitors carried over in the template, suboptimal primer or probe design, degraded template, or an annealing temperature that's too high. Efficiency above 110% often points to pipetting error in the dilution series, primer-dimer formation, or non-specific amplification products inflating the signal. Re-running the standard curve with fresh dilutions and re-optimizing primer concentrations or annealing temperature is the standard fix.
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