Pharmaceutics · Microbiology

Serial Dilution Calculator

Plan simple, serial and stepwise dilutions of a drug stock — volumes to pipette, diluent, every tube's concentration and a printable lab record.

Preparation

Preparation name / drug (optional)

Printed on the lab result card and used to name a saved calculation.

Try a worked example

How the factor is entered

Dilution factor is X in 1:X — 1 part of solution in X parts total. 10 means 1:10, so each tube is C_new = C_start × 1/10 (× 0.1). The textbook form C_final = C_initial × dilution factor uses the fraction 1/X. X must be greater than 1.

Serial dilution

The same dilution factor in every tube.

Initial stock concentration (C₁)

Stock volume available (optional)

Checked against the stock the first tube needs.

Number of steps (tubes)

A whole number, 1–20.

Dilution factor per step (X in 1:X)

fold

Enter X of 1:X — e.g. 10 for 1:10 (× 0.1).

Final volume in each tube

Desired final concentration (optional)

Reports the tube that reaches it. Your inputs are never changed.

Laboratory calculation card

Enter the stock concentration, number of steps, dilution factor and the volume in each tube.

C₁V₁ = C₂V₂ → V₁ = C₂ × V₂ ÷ C₁; diluent = V₂ − V₁

C_new = C_start × 1/X (dilution factor written 1:X)

Volume taken = Final volume ÷ X; diluent = Final volume − Volume taken

Overall factor = X₁ × X₂ × … × Xₙ; C_final = C₁ ÷ overall factor

Keep full volume. If every tube must still hold its final volume after the next tube has taken its share, each tube is made up to V + (volume the next tube takes). That depends on the next tube, so the volumes are worked out backwards from the last tube: made-up volumeᵢ = Vᵢ + made-up volumeᵢ₊₁ ÷ Xᵢ₊₁.

Worked example. Amoxicillin 10 mg/mL, 1:10 × 5 tubes of 10 mL: each tube takes 10 mL ÷ 10 = 1.00 mL and 9.00 mL of diluent. The concentrations are 1, 0.1, 0.01, 0.001 mg/mL and 0.1 µg/mL; the overall factor is 10⁵ = 100,000. With “keep full volume” on, T1 is made up to 11.1 mL (1.11 mL of stock + 10.0 mL diluent) so that it still holds 10.0 mL after T2 takes its 1.11 mL.

Worked example: doubling dilutions of an antibiotic for an MIC practical

For a broth-dilution practical you have an ampicillin stock of 1000 µg/mL and need five doubling (1:2) dilutions, each tube made up to 4 mL. What goes into each tube, and what concentration does the last tube hold? (Illustrative values.)

Mode: Serial dilution
Stock concentration, C₁: 1000 µg/mL
Number of steps: 5
Dilution factor per step: 2 (1:2)
Final volume in each tube: 4 mL
Keep full volume: Off

Volume taken per tube
Volume taken = final volume ÷ X = 4 mL ÷ 2 = 2.00 mL
Diluent per tube
Diluent = 4 mL − 2.00 mL = 2.00 mL
Concentration tube by tube
T1 = 1000 × 1/2 = 500 µg/mL T2 = 250, T3 = 125, T4 = 62.5 µg/mL T5 = 62.5 × 1/2 = 31.25 µg/mL
Overall factor and final concentration
Overall factor = 2⁵ = 32 C_final = 1000 ÷ 32 = 31.25 µg/mL
Materials
Stock required = T1 volume taken = 2.00 mL Total diluent = 5 × 2.00 mL = 10.0 mL

Put 2.00 mL of diluent in each of five tubes, transfer 2.00 mL along the series, and T5 holds 31.25 µg/mL (overall 1:32).

The calculator's summary reads: stock required 2.00 mL, total diluent 10.0 mL, overall dilution factor 1:32, final concentration 31.25 µg/mL. Because each tube gives 2.00 mL to the next, T1–T4 are left with 2.00 mL and T5 with 4.00 mL; switch on "keep full volume" if every tube must end at 4 mL.

Common mistakes

Reading 1:10 as 1 part plus 10 parts. Here 1:X means 1 part in X parts in total (1 mL + 9 mL for 1:10); some older texts write that as 1:9, so check your manual's convention before pipetting.

Adding the step factors instead of multiplying them: five 1:10 steps give 1:100,000, not 1:50.

Using the same tip down the series, or transferring before the tube is mixed. Carry-over and unmixed layers make every later tube wrong, because each tube is made from the one before.

Forgetting that each tube gives up a transfer. Without keep-full, every tube except the last ends with less than the stated final volume.

Mixing mass and molar units: µg/mL and mM cannot be compared without the molecular weight, so the target must be entered in the same family as the stock.

Assumptions and limitations

Pipetting errors compound along the series: if each transfer is 1% off, the last of six tubes can be about 6% off. Prefer fewer, larger steps when only the final concentration matters.

The calculation assumes the diluent contains none of the drug and that the transferred volume and diluent add to the stated final volume.

It describes concentration only. Adsorption to plastic, degradation and solubility limits at the top of the series are not modelled.

Guide: Dilution and Concentration CalculationsThe concept in full, with practice questions.Dilution Calculator (C₁V₁ = C₂V₂)A single-step dilution when the stock volume is easy to measure.Calibration Curve CalculatorFit the standards from a dilution series and read off an unknown.Colony Counter & CFU CalculatorTurn a colony count on a plate from a dilution series back into CFU/mL.

References

Stockton SJ. Stoklosa and Ansel's Pharmaceutical Calculations. 16th ed. Philadelphia: Wolters Kluwer; 2021.
Sinko PJ, editor. Martin's Physical Pharmacy and Pharmaceutical Sciences. 8th ed. Philadelphia: Wolters Kluwer; 2023.

Common questions

Yes, in this calculator. 1:10 means 1 part of solution in 10 parts total (1 mL stock + 9 mL diluent), so the concentration becomes one tenth. Some older texts write 1:9 for 1 part + 9 parts — check which convention your manual uses before you pipette.

When the single-step stock volume would be too small to pipette accurately (below about 10 µL on a typical micropipette), or when you need every intermediate concentration — for example the doubling dilutions of an MIC plate or the points of a standard curve.

Because nothing is taken out of it. Every other tube gives up a transfer to the next tube. Turn on "keep full volume" if every tube must end with the same volume — the calculator then makes each tube up a little larger.

Not without the molecular weight. Mass concentrations (mg/mL, g/L, µg/mL, % w/v) convert among themselves, and molar ones (M, mM, µM) convert among themselves. To cross over, first convert with mM = (mg/mL ÷ MW in g/mol) × 1000.

Pipetting errors compound. If each step is within 1 %, six steps can be about 6 % off in the last tube. Use calibrated pipettes, a fresh tip for each transfer, and mix every tube before taking from it.

About serial dilution

A serial dilution makes a large dilution as a chain of small, equal ones: each tube takes a fixed volume from the tube before it. Ten-fold steps turn a 10 mg/mL amoxicillin stock into 0.1 µg/mL in five tubes, without ever pipetting a volume too small to measure.

Single step or serial?

Single step (C₁V₁ = C₂V₂) when the stock volume is comfortably pipettable — usually 10 µL or more

Serial when the overall dilution is large (1:1,000 and beyond) or you need every intermediate concentration

MIC plates, bacterial counts (CFU) and standard curves for assays all use serial dilutions

Errors compound down a series

A 1 % pipetting error in each of 6 steps can put the last tube about 6 % off — calibrate and use the right pipette

Use a fresh tip for every transfer: a drop carried over from a concentrated tube skews every tube after it

Mix each tube thoroughly before taking from it — an unmixed tube gives a wrong transfer, not just a wrong tube

Prepared by the PharmaWallah student team. Verify results with your textbook or instructor. Report an error · Editorial policy