qPCR Standard Curve Calculator
Estimate amplification efficiency, slope and R² from serially diluted standards, and back-calculate the copy number of an unknown sample.
6 Cq values parsed
Optional: enter an unknown sample Cq to estimate its copy number.
Efficiency
99.9%
Slope
-3.3243
Intercept
38.29
R²
1.00000
ΔCq per 10-fold dilution
3.32
| Standard (copies) | Cq | Fitted | Residual |
|---|---|---|---|
| 1.000×10^7 | 15.02 | 15.02 | -0.001 |
| 1.000×10^6 | 18.35 | 18.35 | 0.005 |
| 100,000 | 21.66 | 21.67 | -0.010 |
| 10,000 | 25.01 | 24.99 | 0.016 |
| 1,000 | 28.30 | 28.32 | -0.018 |
| 100 | 31.65 | 31.64 | 0.008 |
Learn more
What it does
A qPCR standard curve converts the Cq values of a dilution series into a quantitative relationship between cycle number and template amount. It is the standard way to confirm that a real-time PCR assay amplifies as expected before using it for absolute or relative quantification. The calculator fits a straight line through the standards and reports the slope, intercept, R², amplification efficiency and the observed ΔCq per 10-fold dilution.
How it works
The curve follows Cq = slope × log10(N) + intercept, where N is the template amount in copies. Amplification efficiency is E = 10^(-1/slope) - 1, so E = 1 means 100% efficiency, and the slope for perfect efficiency is -3.32 because a 10-fold dilution should shift Cq by about 3.32 cycles. The reverse relation is slope = -1 / log10(1 + E). To recover an unknown sample amount, the calculator uses template = 10^((Cq - intercept) / slope).
Worked example
With a top standard of 1×10^7 copies, a 10-fold dilution across 6 points, and Cq values of 15.02, 18.35, 21.66, 25.01, 28.30 and 31.65, the fit gives slope -3.3240, intercept 38.29, R² 0.999996, efficiency 99.90% and a ΔCq of 3.32 per 10-fold step. An unknown sample at Cq = 24.80 back-calculates to 1.14×10^4 copies.
When to use it
Use a standard curve when you need absolute quantification, such as reporting target copies per reaction or copies per microlitre of sample. Run it during assay validation to confirm the slope sits near -3.32 and efficiency is within 90–110% before trusting Cq-based results. It is also the right check after changing reagents, a new primer pair, or a different plate, where a shifted slope or low R² flags a pipetting or reaction problem.
FAQ
- How is qPCR amplification efficiency calculated, and what counts as acceptable?
- Efficiency is E = 10^(-1/slope) - 1, expressed as a percentage (E = 1 is 100%). A 100% efficient assay has a slope of about -3.32, because each 10-fold dilution should change Cq by log10(10) = 1 cycle-equivalent, giving ΔCq ≈ 3.32. An efficiency within 90–110% (slope roughly -3.58 to -3.10) is generally considered acceptable for quantification.
- Why is the slope of a qPCR standard curve negative?
- Because Cq decreases as template amount increases: a more concentrated standard needs fewer cycles to cross the threshold. So log10(template) and Cq are inversely related, and the fitted line has a negative slope. The steeper (more negative) the slope, the lower the efficiency; perfect 100% efficiency corresponds to -3.32.
- What R² value is good enough for a standard curve?
- Aim for R² of at least 0.99, with 0.999 or higher preferred for absolute quantification. An R² below about 0.98 means the points scatter from the fitted line, which usually points to pipetting errors across the dilution series, uneven template, or a noisy assay. Treat a low R² as a signal to repeat the standards rather than trust the copy-number output.
- What should ΔCq be for each 10-fold dilution?
- For a perfect 100% efficiency assay, each 10-fold dilution shifts Cq by exactly log10(10) × 3.32 = 3.32 cycles. In practice ΔCq between consecutive 10-fold standards should fall close to 3.3, and a value far from 3.32 (for example 2.5 or 4.5) indicates non-ideal efficiency. The observed ΔCq reported here is the average spacing across your standards.