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PCR, qPCR & Molecular Biology

qPCR ΔCq, ΔΔCq and Efficiency-Adjusted Ratio Workbench

Retain target and reference Cq records for one sample or a sample–calibrator comparison, then apply an explicitly selected equal-doubling or entered-efficiency relative-quantity convention.

Biology · experimental measurements

Separate raw Cq differences, the Livak 2^−ΔΔCq convention and a Pfaffl-style efficiency-adjusted ratio while keeping reference stability, assay comparability and biological interpretation outside the arithmetic.

Private calculations in your browser · explicit inputs and model boundaries
Example preview · Single ΔCqEntered sample Cq records
Target24.8 Cq
Reference21.1 Cq
-24.8024.8

The two bars are the entered threshold-cycle records. Their signed target-minus-reference difference is reported separately.

  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
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Calculation result

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Understand the relationship

The reasoning behind the result

ΔCq is a within-sample subtraction

ΔCq = Cqtarget − Cqreference

Its sign follows the entered target-minus-reference order.

A one-sample ΔCq does not by itself describe change from a calibrator.

ΔΔCq adds a calibrator comparison

ΔΔCq = ΔCqsample − ΔCqcalibrator

Under equal doubling, relative quantity is 2^−ΔΔCq.

The calculation assumes the target and reference comparisons belong to a compatible design.

Distinct efficiencies change the base

ratio = Atarget^ΔCq,target / Areference^ΔCq,reference

The entered percentages become amplification factors A=1+η.

Efficiency adjustment does not validate the source estimates or repair an unstable reference.

Follow the numbers

Reconcile a sample and calibrator

  1. Subtract reference Cq from target Cq inside the sample.
  2. Repeat the same subtraction for the calibrator.
  3. Subtract the two ΔCq values in the displayed order.
  4. Apply either the declared equal-doubling base or the two entered amplification factors.

The relative ratio is conditional on the selected assays, samples, preprocessing and normalization model.

Quick guide

How to use this calculator

  1. Enter Cq values produced under an externally justified preprocessing and threshold procedure.
  2. Choose equal doubling only when that model is intended; otherwise enter externally obtained assay efficiencies.
  3. Interpret ratios only after checking reference stability, assay specificity, replicate handling and experimental design.

Calculation method

Calculation and interpretation

Separate raw Cq differences, the Livak 2^−ΔΔCq convention and a Pfaffl-style efficiency-adjusted ratio while keeping reference stability, assay comparability and biological interpretation outside the arithmetic.

ΔCq = Cqtarget−Cqreference; ΔΔCq = ΔCqsample−ΔCqcalibrator; Livak ratio = 2^−ΔΔCq; efficiency-adjusted ratio = Atarget^(Cqtarget,cal−Cqtarget,sample) / Areference^(Cqreference,cal−Cqreference,sample).

Worked example

Reconcile a sample and calibrator

The relative ratio is conditional on the selected assays, samples, preprocessing and normalization model.

ΔCq = Cqtarget−Cqreference; ΔΔCq = ΔCqsample−ΔCqcalibrator; Livak ratio = 2^−ΔΔCq; efficiency-adjusted ratio = Atarget^(Cqtarget,cal−Cqtarget,sample) / Areference^(Cqreference,cal−Cqreference,sample).

Supported inputs

Precision and limits

Entered Cq records

Baseline, threshold, replicate aggregation, missing wells and censoring are not inferred.

Reference stability is external

The workbench does not decide whether a reference gene or assay is stable or appropriate.

No significance test

A fold ratio is not a confidence interval, p-value, effect-size uncertainty or biological conclusion.

Efficiency evidence is external

Entered efficiencies must come from an appropriate assay-specific method; the workbench does not estimate them here.

No clinical interpretation

The arithmetic does not diagnose, stage, predict or recommend treatment.

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