Serial dilution calculator

qPCR efficiency

After measuring a dilution series, paste the known template quantities and their Cq (Ct) values to fit a standard curve. Keep quantities in one unit or relative scale. Enter each replicate on its own row; every entered well receives equal weight. The example is illustrative data, not an assay validation.

The fit uses Cq = m × log₁₀(quantity) + b. Efficiency is 100 × (10^(−1/m) − 1) percent; a slope of −3.32 gives approximately 100.1%, or 2.001-fold per cycle. A tenfold decrease in quantity raises Cq by about 3.32 at that slope. If you already have the slope, choose Known slope.

The table shows each well’s residual (measured minus fitted Cq). R² describes the fit of these entered wells; it does not establish specificity, detection limits or assay validity. An apparent efficiency above 100% does not demonstrate more than doubling per cycle. No wells are automatically excluded. Missing or “undetermined” Cq values are rejected; do not substitute zero. The 0–100 Cq input range is a calculator limit, not an assay acceptance range.

Save the report to retain every input, the fit and its assumptions. Wells CSV includes the measured and fitted values; Curve SVG saves the plot. For template quantities from a DNA mass and length, use the DNA copy-number worksheet.

Method sources: Bio-Rad iCycler iQ manual, page 120 for the efficiency relationship; Applied Biosystems standard-curve documentation for Cq versus log quantity and the reported fit. Checked October 1, 2026.

Plan a serial dilution, one tube at a time

In a serial dilution, each new solution is prepared from the preceding dilution. With a constant per-step dilution factor F, the concentration in tube n is Cₙ = C₀ / Fⁿ. A tenfold step combines one part sample with nine parts diluent, giving ten parts mixed solution. It does not mean one part sample plus ten parts diluent.

Enter the starting stock concentration, per-step factor and number of diluted tubes. Choose Mixed volume for the amount before transferring onward, or Volume left for the minimum you need in every tube afterward. The original stock is not counted as a tube. The calculator supports 1–24 steps and displays the sample source, transfer, diluent, concentration, final discard and retained volume for each one. It assumes the same dilution factor and mixed volume throughout the series.

Worked example: six tenfold steps

Start with 100 µM stock, choose a factor of 10, six diluted tubes and a mixed volume of 1 mL per tube. Each step transfers 100 µL of the preceding solution into 900 µL of diluent. The tube concentrations are 10, 1, 0.1, 0.01, 0.001 and 0.0001 µM. The final tube has a one-million-fold dilution relative to the original stock.

Only the first tube takes an aliquot from the original stock, so this plan needs 100 µL of original stock. Across all six tubes it uses 5.4 mL of diluent. Each onward transfer comes from a freshly mixed preceding tube, not from the original stock again.

Mixed volume is not retained volume

After mixing, each tube in the example contains 1 mL. Transferring 100 µL onward leaves 900 µL in tubes 1–5. Tube 6 keeps its full 1 mL because it supplies no further tube. Removing a well-mixed aliquot changes the amount remaining, not its concentration.

If you need equal retained volumes, choose Equalize. The plan then explicitly discards 100 µL from the last tube too, leaving 900 µL in all six. That option does not change concentrations or add a seventh dilution. It is a planning choice, not an instruction to discard material from an existing experiment.

Start with the volume you need left

For a twofold series with 100 µL left in each tube, choose Volume left, enter 100 µL and select Equalize. Each step combines 100 µL from the previous solution with 100 µL of diluent. Mix the resulting 200 µL before transferring 100 µL onward; the last tube has an explicit 100 µL discard. All tubes then retain 100 µL.

For a factor F and retained volume R, the transfer is R / (F − 1) and the mixed volume is R × F / (F − 1). This follows from subtracting one transfer from the mixed volume. Keep full leaves extra solution in the last tube. With only one tube and no discard, nothing transfers onward, so the mixed volume simply equals the volume you need left. The downloaded table includes the discard and retained amount separately.

Assumptions and practical limits

The calculation assumes complete mixing, additive volumes, no solute loss and no chemical reaction. It does not estimate pipetting uncertainty or evaporation. Small transfers may be difficult to measure with your equipment; the tool flags a calculated transfer below 1 µL. You can increase the mixed volume while retaining the same factor and concentrations.

The concentration unit stays consistent throughout the table. Choose a molar or mass-per-volume unit that describes your stock. For one stock-to-target calculation, use the single-step dilution calculator. To prepare that stock from a solid, use the molarity calculator and the correct compound formula or molar mass.

Serial dilution is illustrated in OpenStax Microbiology's discussion of microbial growth. This page applies the volume and concentration arithmetic only; it does not infer cell counts or select culture conditions. Save calculation records the inputs and assumptions. Table CSV contains the displayed tube plan, including units and retained volumes.

Starting with a measured cell suspension? The hemocytometer worksheet calculates concentration from large-square counts and records live/dead counts before you plan a dilution. Plate counts from two time points give a bacterial culture's doubling time.