# qPCR delta delta Ct (ΔΔCt) calculator

> qPCR fold change calculator: ΔCt, ΔΔCt and 2^−ΔΔCt (Livak, comparative Ct method) from Ct values with replicates, or the Pfaffl ratio. Chart and CSV. Free.

URL: https://www.labcanvas.com/tools/qpcr-calculator

Relative gene expression by the delta delta Ct method (Livak, also called the comparative Ct method) is fold change = 2^−ΔΔCt, where ΔCt = Ct(target) − Ct(reference gene) and ΔΔCt = ΔCt(sample) − ΔCt(control). Paste your Ct values (one row per well, replicates included), choose the control sample, and the calculator gives ΔCt, ΔΔCt, fold change with its SD range, the Pfaffl ratio if efficiencies differ from 100 %, a chart and a CSV.

## Quick answer

- **What it does:** Calculates ΔCt, ΔΔCt and fold change (2^−ΔΔCt, Livak) from qPCR Ct values with replicates, plus the Pfaffl ratio when efficiencies differ from 100 %.
- **Formula:** ΔCt = Ct(target) − Ct(reference); ΔΔCt = mean ΔCt(sample) − mean ΔCt(control); fold change = 2^−ΔΔCt.
- **Example:** Mean ΔCt 6.80 in treated and 9.93 in control cells gives ΔΔCt = −3.13, so fold change = 2^3.13 = 8.77 (8.8-fold higher expression).

Free, in the browser, no account needed. Updated 2026-11-08.

## Features

- Replicates averaged per sample, with SD
- Several target genes at once
- Livak \(2^{-\Delta\Delta\mathrm{Ct}}\) and Pfaffl efficiency correction
- Paste directly from Excel or the instrument export
- Bar chart (PNG/SVG) and CSV table

## How to use it

1. **Enter Ct values**: One row per well: sample, gene, target Ct and reference-gene Ct. Paste from a spreadsheet or type them in.
2. **Choose the control**: Select the calibrator sample (for example untreated or wild type) and, if known, the primer efficiencies.
3. **Read and export**: See \(\Delta\mathrm{Ct}\), \(\Delta\Delta\mathrm{Ct}\) and fold change per sample and gene, then download the table and the chart.

## At a glance

| | |
| --- | --- |
| Input | Ct values pasted from Excel or the instrument export; several target genes |
| Methods | Livak \(2^{-\Delta\Delta\mathrm{Ct}}\) and the Pfaffl efficiency-corrected ratio |
| Replicates | Averaged per sample, with SD and the fold-change range |
| Output | Bar chart (PNG, SVG) and CSV |
| Assumption | Livak assumes about 100 % efficiency for both assays |

## How it works

$$\begin{aligned} \Delta\mathrm{Ct} &= \mathrm{Ct}_\mathrm{target} - \mathrm{Ct}_\mathrm{reference} \\ \Delta\Delta\mathrm{Ct} &= \text{mean } \Delta\mathrm{Ct}_\mathrm{sample} \\ &\quad {}- \text{mean } \Delta\mathrm{Ct}_\mathrm{control} \\ \text{Fold change} &= 2^{-\Delta\Delta\mathrm{Ct}} \\ &\quad \text{(range } 2^{-(\Delta\Delta\mathrm{Ct} \pm \mathrm{SD})}\text{)} \end{aligned}$$

$$\text{Pfaffl ratio} = \frac{E_\mathrm{target}^{\,\Delta\mathrm{Ct}_\mathrm{target}(\mathrm{control} - \mathrm{sample})}}{E_\mathrm{ref}^{\,\Delta\mathrm{Ct}_\mathrm{ref}(\mathrm{control} - \mathrm{sample})}}$$

\(\Delta\mathrm{Ct}\) is calculated per well and averaged per sample, and its standard deviation gives the asymmetric fold-change range. The Livak method assumes both assays have about 100 % efficiency (\(E = 2\)); if a standard curve gives other efficiencies, enter them to add the Pfaffl ratio, with \(E = 1 + \text{efficiency}/100\).

## Worked example: fold change by the 2^−ΔΔCt method

A target gene in untreated (control) and treated cells, GAPDH as the reference, three wells each.

| Sample | Target Ct | GAPDH Ct | \(\Delta\mathrm{Ct}\) |
| --- | --- | --- | --- |
| Control | 28.0 | 18.1 | 9.9 |
| Control | 28.3 | 18.2 | 10.1 |
| Control | 28.1 | 18.3 | 9.8 |
| Treated | 25.1 | 18.2 | 6.9 |
| Treated | 24.9 | 18.1 | 6.8 |
| Treated | 25.0 | 18.3 | 6.7 |

- **\(\mathbf{\Delta Ct}\) per well**, target minus reference: control 9.9, 10.1 and 9.8 (mean 9.93); treated 6.9, 6.8 and 6.7 (mean 6.80, SD 0.10).
- \(\mathbf{\Delta\Delta Ct} = \text{mean } \Delta\mathrm{Ct}\text{ treated}\) \({}- \text{mean } \Delta\mathrm{Ct}\text{ control}\) \(= 6.80 - 9.93 = -3.13\).
- **Fold change** \(= 2^{-\Delta\Delta\mathrm{Ct}} = 2^{3.13} = \mathbf{8.77}\): the target is expressed about 8.8 times more in treated cells.
- **Range** from the treated SD: \(2^{-(-3.13 + 0.10)}\) to \(2^{-(-3.13 - 0.10)}\) = **8.19 to 9.40**. The range is not symmetric around 8.77 because the scale is exponential.

In a spreadsheet: \(\Delta\mathrm{Ct} = \text{target} - \text{reference}\) in each row, average per sample, subtract the control average, then =2^(−ΔΔCt). The control’s own fold change is 1 by definition.

## Questions

### How do I calculate fold change from Ct values?

Subtract the reference gene Ct from the target Ct in each well (\(\Delta\mathrm{Ct}\)), average per sample, subtract the control’s average \(\Delta\mathrm{Ct}\) (\(\Delta\Delta\mathrm{Ct}\)), and raise 2 to minus that number: \(\text{fold change} = 2^{-\Delta\Delta\mathrm{Ct}}\). A \(\Delta\Delta\mathrm{Ct}\) of −3 means \(2^3 = 8\) times more expression than the control; +1 means half.

### How do I show qPCR fold change in a graph?

Plot fold change (control = 1) on a log2 axis, or plot \(\Delta\Delta\mathrm{Ct}\) directly, so increases and decreases are drawn symmetrically. Show the range from the \(\Delta\mathrm{Ct}\) SD as error bars and state the number of biological replicates.

### How do you calculate fold change from Ct values?

Subtract the reference-gene Ct from the target Ct for each sample (\(\Delta\mathrm{Ct}\)), subtract the control’s \(\Delta\mathrm{Ct}\) (\(\Delta\Delta\mathrm{Ct}\)), and raise 2 to the power of \(-\Delta\Delta\mathrm{Ct}\).

### What does \(2^{-\Delta\Delta\mathrm{Ct}}\) mean?

It is the fold change in expression of the target gene in a sample compared with the control, after normalising both to the reference gene. At 100 % efficiency each PCR cycle doubles the product, so a \(\Delta\Delta\mathrm{Ct}\) of −1 means 2-fold more expression, −3 means 8-fold more, and +1 means half as much.

### How do I handle technical replicates?

Average the Ct values of technical replicates (repeat wells of the same cDNA) before calculating \(\Delta\mathrm{Ct}\). Here, enter each well as a row with the same sample name: the calculator averages them, and because each row holds both Ct values, the mean \(\Delta\mathrm{Ct}\) equals the mean target Ct minus the mean reference Ct. If you also have biological replicates, average each one’s technical wells first and enter one row per biological replicate, so the SD shows biological variation.

### How do I calculate \(\Delta\Delta\mathrm{Ct}\) and fold change in Excel?

With the target Ct in column B and the reference Ct in column C (one row per sample, technical replicates averaged with AVERAGE), enter =B2-C2 in D2 for \(\Delta\mathrm{Ct}\), =D2-$D$2 in E2 for \(\Delta\Delta\mathrm{Ct}\) when row 2 is the control, and =POWER(2,-E2) in F2 for the fold change, then fill the formulas down.

### What is the comparative Ct method?

Another name for the \(\Delta\Delta\mathrm{Ct}\) method of Livak and Schmittgen (2001): expression is compared between samples through differences in Ct, normalised to a reference gene, without a standard curve. It assumes both assays amplify with about 100 % efficiency; if they do not, use the Pfaffl ratio.

### What is a good reference (housekeeping) gene?

One whose expression does not change between your conditions, such as GAPDH, ACTB, 18S rRNA or B2M, validated for your samples. Using the geometric mean of two or three reference genes is more robust.

### When should I use the Pfaffl method?

When the target and reference assays have different amplification efficiencies (outside about 90–110 %), measured with a standard curve. With equal 100 % efficiencies it gives the same result as \(2^{-\Delta\Delta\mathrm{Ct}}\).

### Should statistics be done on fold change or \(\Delta\mathrm{Ct}\)?

On \(\Delta\mathrm{Ct}\) (or \(\Delta\Delta\mathrm{Ct}\)) values, which are approximately normally distributed; fold changes are log-normal. Report fold change for readability.

### What does a fold change below 1 mean?

Lower expression than the control: 0.5 is half the control level (a 2-fold decrease).