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qPCR Regression

qPCR standard curve calculator (efficiency, R², unknowns)

Build a standard curve from Quantity (copy number or concentration) and Ct, calculate slope, intercept, R², and PCR efficiency (%). Back-calculate unknown quantities with residual plots, 95% bands, step logs, CSV/LaTeX, and share URLs.

All calculations run in your browser; data is not sent. Use for research/education.

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How to use (3 steps)

  1. Paste standard points (Quantity, Ct) or load a CSV file. Rows with the same Quantity are treated as replicates.
  2. Choose a regression method (OLS/WLS) and options such as 95% bands. Enter unknown Ct values if you have them.
  3. Click Calculate to see the standard curve, efficiency, QC checks, unknown estimates, and step log. Share URLs keep the same settings.

Recommended order

  1. First, build a standard curve (this calculator)
  2. Next, review PCR efficiency (%)Jump to efficiency
  3. If needed, calculate relative expression (ΔCt / ΔΔCt)ΔCt / ΔΔCt

Go deeper

Data input and options

Defaults are examples. Selecting a preset replaces standard/unknown data and settings. For your own data, paste and click Calculate (or Reset). Jump to results

WLS weighting tips

WLS fits with point-wise weights. 1/Q and 1/Q² increase the influence of low-quantity points. Use the w column to set weights per point.

Results (summary)

PCR efficiency (%)

Calculated from slope m as Efficiency = (10^(-1/m) - 1) × 100. The range shown is a guide.

Results will appear here.

Ranges are guides. For research/education, review standard points and residuals together.

Quality checks (guide)

Concentration levels (mean ± SD)

Quantity log10Q n Ct_mean Ct_SD

Standard points (fit rows)

Advanced columns (weight / yhat / residual / leverage / cooksD) can be toggled.

Quantity log10Q Ct weight yhat residual leverage cooksD

Unknown samples (Ct → Quantity)

Sample Ct log10Q_hat Quantity_hat DF Quantity_corrected

Standard curve and residuals

Standard curve (Ct vs log10(Quantity))
Charts are not supported in this browser. See the tables for results.
Hover points to see details.
Residual vs predicted Ct
Charts are not supported in this browser. See the tables for results.
Hover points to see details.

Calculation steps (How it’s calculated)

    Notes for educators

    How to use this calculator effectively

    This calculator is designed to make scenario checks fast. Use a repeatable workflow: baseline first, one variable change at a time, then compare output direction and magnitude.

    How it works

    Run your first scenario with defaults. Then, change exactly one assumption and observe which result changes most. That is the fastest way to identify sensitivity and explain what drives the outcome.

    When to use

    Use this page when you need practical planning support, side-by-side alternatives, or a clean baseline for further discussion.

    Common mistakes to avoid

    Worked example

    Prepare a base case and one alternative case, then compare outputs and validate the direction, scale, and interpretation with the same assumptions across both cases.

    See also

    FAQ

    What is a qPCR standard curve?

    A curve that relates standard quantity (copy number or concentration) to Ct by fitting Ct vs log10(quantity). It helps check linearity (R²) and amplification efficiency.

    How many standard points are required?

    At least two points are required to fit a line. For linearity and outlier checks, 4–6 points are recommended.

    How is PCR efficiency (%) calculated?

    From slope m: Efficiency = (10^(-1/m) - 1) × 100. The displayed range is a guide.

    What does a slope around -3.32 indicate?

    For a 10× dilution series, a slope near -3.32 corresponds to an apparent efficiency of about 100% (ideal guide).

    Can efficiency exceed 100%?

    Because it is inferred from the slope, apparent values over 100% can occur due to dilution error or inhibition. Treat it as a guide and check residuals and standard points.

    Does the share URL include data?

    Only settings (methods and band options) are saved. Standard and unknown data are not included.

    What unit should I use for Quantity?

    Any unit is fine (copy number, ng, concentration). Quantity must be positive for log10.

    References (notes)

    Guides shown on this calculator are general references. For research/education, consult primary sources as needed.

    Comments

    Share questions or improvements (comments load after you click the button).