How to use
- Choose how you want to enter the curve. Enter a slope is for when you already have the slope of your standard curve; Fit a standard curve is for when you only have concentrations and Ct values, and it works out the regression and the graph as well.
- Enter a slope needs one number. The slope is negative.
- Fit a standard curve takes concentration and Ct pairs in the table. You can copy two columns out of a spreadsheet and paste them in, and rows can be added or removed. Enter concentrations as they are — the log is taken for you.
- The efficiency (%) appears large, with the per-cycle amplification factor beneath it. In standard curve mode the slope, intercept, R², point count and graph appear alongside.
- The dilution factor is optional. It plays no part in the calculation and only feeds a note telling you what the Ct gap between steps should be.
Exponents can be entered with e — for example, 1.5×10⁻⁵ is entered as 1.5e-5.
Formula and practical notes
A qPCR standard curve is what you get by diluting a sample of known concentration step by step, measuring the Ct of each, and fitting a line between log₁₀(concentration) and Ct.
- Standard curve
- Ct = slope × log₁₀(concentration) + intercept
A higher concentration gives a lower Ct, so the slope is negative.
Where the efficiency comes from
Suppose the product grows by a fixed factor F each cycle. At the point where fluorescence reaches the threshold, this holds:
- starting amount × F^Ct = constant
Taking logs of both sides and rearranging gives the relation between the slope and F.
- Slope
- slope = − 1 ÷ log₁₀(F)
- Amplification factor
- F = 10^(−1÷slope)
F is the per-cycle amplification factor. A perfect doubling means F = 2, and the slope is then −1 ÷ log₁₀2 = −3.3219.
Efficiency is the proportion gained in one cycle, so it is F minus one.
- Efficiency
- E(%) = ( 10^(−1÷slope) − 1 ) × 100
F = 2 gives an efficiency of 100%. That is why the theoretical maximum is 100% and not 200% — DNA is double-stranded, so a cycle can at best double it.
What the intercept means
The intercept is the Ct where log₁₀(concentration) is zero, that is, the Ct at a concentration of one. Absolute quantification reads that number. It is why this calculator offers no option to force the intercept through zero, unlike the standard curve calculator.
The dilution factor and the slope
The ideal slope of −3.3219 does not depend on the dilution factor. The slope answers ‘how many cycles does Ct move when the concentration changes ten-fold’, which is the same whatever factor you diluted by.
What the dilution factor changes is the Ct gap between steps.
- Ct gap per step
- log₂(dilution factor)
A 10-fold dilution gives 3.32 cycles, a 2-fold one gives 1.00. It is a figure to check your data against by eye.
Practical notes
- A positive slope means the axes are the wrong way round. Ct belongs on the y axis and log(concentration) on the x axis. This calculator refuses a positive slope and shows only the sign-flipped value for reference. It withholds the answer because a swapped axis is a likely reading of the input, not a certain one.
- 90–110% is a commonly quoted reference range, not a pass mark. This calculator reports the value; it does not judge it. The acceptable range is set by the assay and your laboratory procedure.
- An efficiency above 100% is usually inhibition. Nothing has genuinely more than doubled — inhibitors in the more concentrated standards push their Ct later than expected, which flattens the slope. Try dropping the most concentrated standard and fitting again.
- Do not include points from outside the range of the curve. Too concentrated brings inhibition; too dilute brings stochastic variation.
- A high R² does not mean the efficiency is right. R² only says how closely the points follow a line. Inhibition that affects every point evenly gives a beautiful line with the wrong slope.
- Rows with a concentration of zero or below are left out of the calculation, because the log cannot be taken. How many were dropped is shown on screen.