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PCR, qPCR & Molecular Biology

qPCR Standard-Curve Fit and Quantity Workbench

Fit Cq against entered log10 quantities, expose slope, intercept, residuals and R², derive the slope-based amplification factor, and optionally invert one Cq under that exact calibration.

Biology · experimental measurements

Keep calibration data, assay efficiency and an unknown-sample quantity estimate in one auditable ledger without turning a fitted curve into assay validation, detection-limit evidence or a universal quality grade.

Private calculations in your browser · explicit inputs and model boundaries
Example preview · Five standardsEntered qPCR standard curve
028.03316.1424.1532.1610^2: 2, 32.110^3: 3, 28.810^4: 4, 25.4710^5: 5, 22.210^6: 6, 18.84Entered log10 quantityCq

Points are the entered standards and the line is their least-squares Cq fit. The axes retain the visitor-declared log10 quantity basis.

  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
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Standards: label, log10 quantity, Cq
1 row
Row 1

Empty rows are ignored until edited. Keep commas and tabs out of individual entries; use the paste view for comma- or tab-separated records.

Calculation result

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Understand the relationship

The reasoning behind the result

The regression retains the calibration scale

Cq = a + b log10(Q)

The intercept and slope belong to the entered assay, run and quantity unit.

If x is log10 copies, the inverse is copies; if x is log10 concentration, the inverse remains that concentration unit.

Slope encodes an exponential factor

A = 10^(−1/b)

A negative slope is required for larger entered starting quantities to cross threshold earlier.

Efficiency is A−1; 100% corresponds to an amplification factor of two under this model.

Fit statistics are not validation

R² and residuals describe these points but do not establish specificity, inhibition, limit of detection, uncertainty or reference-material traceability.

Replicates, controls, dynamic range and raw-data handling remain experimental and reporting responsibilities.

Follow the numbers

Fit a declared standard curve

  1. Treat each entered log10 quantity as x and Cq as y.
  2. Fit the least-squares slope and intercept.
  3. Calculate each fitted Cq and residual.
  4. Convert the negative slope into an amplification factor.
  5. When requested, invert the fitted line at the entered unknown Cq.

The estimate inherits the standards' unit, run and calibration assumptions.

Quick guide

How to use this calculator

  1. Enter at least three standards using the exact log10 quantity basis reported for the run.
  2. Inspect every fitted Cq and residual rather than relying on a single efficiency percentage.
  3. Use the inverse estimate only within a validated calibration, matrix, dynamic range and reporting procedure.

Calculation method

Calculation and interpretation

Keep calibration data, assay efficiency and an unknown-sample quantity estimate in one auditable ledger without turning a fitted curve into assay validation, detection-limit evidence or a universal quality grade.

Cq = intercept + slope·log10(Q); amplification factor A = 10^(−1/slope), efficiency = (A−1)×100%; fitted log10(Qunknown) = (Cqunknown−intercept)/slope.

Worked example

Fit a declared standard curve

The estimate inherits the standards' unit, run and calibration assumptions.

Cq = intercept + slope·log10(Q); amplification factor A = 10^(−1/slope), efficiency = (A−1)×100%; fitted log10(Qunknown) = (Cqunknown−intercept)/slope.

Supported inputs

Precision and limits

Entered log10 quantities

The workbench does not infer whether the x-axis represents copies, mass, concentration or another calibrated amount.

Negative slope required

A nonnegative fitted slope is inconsistent with the displayed increasing-quantity qPCR convention and is rejected.

No automatic range grade

No universal slope, efficiency or R² acceptance band is applied.

No LOD or LOQ

Detection probability, quantification uncertainty, matrix effects and replicate precision require additional evidence.

No raw-curve analysis

Baseline, threshold, melt curve, fluorescence kinetics and individual-well exclusions are not inferred.

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