Serial dilution calculator

A serial dilution repeats the same dilution several times, each tube made from the one before. If each step dilutes by a factor f, the concentration after n steps is C₁ ÷ fⁿ, and the total dilution factor is fⁿ. Five tenfold steps from a 1 M stock give 1 ÷ 10⁵ = 0.00001 M. This serial dilution calculator is the Serial dilution mode of our Dilution Calculator: it gives the concentration of every tube, the total dilution factor and how much solvent goes in each tube.

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Dilution Calculator

Use C1V1 = C2V2 to plan dilutions and serial dilutions

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How to use the serial dilution calculator

1. Open the Dilution Calculator. Under Calculate, choose Serial dilution.
2. Type the Stock concentration, the Dilution factor per step (10 for tenfold, 2 for twofold) and the Number of steps, from 1 to 50.
3. Optionally type the Volume moved each step to get the solvent needed in each tube.
4. Read the final tube's concentration, the total dilution factor and the concentration of each tube, listed for up to eight tubes.
5. The graph plots the concentration on a log scale, where every step is the same size drop.

Serial dilution formula

For one step, moving a volume V into enough solvent to make f times as much gives a dilution factor f, so the solvent in each tube is V × (f − 1). A tenfold step with 1 mL moved needs 9 mL of solvent. The dilution calculator guide covers single dilutions with C₁V₁ = C₂V₂.

Worked examples you can check in the calculator

Example 1: a twofold dilution series

Start with a 2.0 M stock, halve the concentration at each of 6 steps, and move 5 mL each time. Each tube gets 5 × (2 − 1) = 5 mL of solvent.

The total dilution factor is 2⁶ = 64, and the last tube is 2.0 ÷ 64 = 0.03125 M. Twofold series like this are used to make a range of concentrations for a calibration curve.

Example 2: a tenfold series

With a 0.5 mol/dm³ stock and three tenfold steps, the tubes are 0.05, 0.005 and 0.0005 mol/dm³, a total dilution of 10³ = 1000. With 1 cm³ moved each time, each tube needs 9 cm³ of water. Reaching the same concentration in one step would mean adding 1 cm³ to 999 cm³ of water, which is much harder to measure accurately.

Example 3: counting bacteria

Microbiologists dilute a culture in tenfold steps, spread a small volume of a diluted tube on a plate, and count the colonies. If 0.1 mL from the 10⁶ dilution grows 45 colonies, the original culture had 45 ÷ 0.1 × 10⁶ = 4.5 × 10⁸ cells per mL. The dilution factor scales the count back up to the original.

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Dilution series in A-level Biology: required practical 3

In AQA's A-level Biology specification, required practical 3 is the production of a dilution series of a solute to produce a calibration curve with which to identify the water potential of plant tissue. Most schools make this series by diluting the stock directly to each concentration, rather than by a serial dilution, so each tube is a separate C₁V₁ = C₂V₂ calculation you can check in the calculator above. For 10 cm³ of each solution from a 1.0 mol/dm³ sucrose stock:

1. Cut equal-sized pieces of the plant tissue, such as potato, blot them dry and weigh each one.
2. Put one piece in each concentration and leave them all for the same time at the same temperature.
3. Blot and reweigh each piece, and work out the percentage change in mass: (final mass − initial mass) ÷ initial mass × 100.
4. Plot percentage change in mass against concentration and draw a line of best fit.

Where the line crosses zero change in mass, there is no net osmosis, so the tissue has the same water potential as a solution of that concentration. If the pieces gained 6.0% in 0.2 mol/dm³ and lost 4.0% in 0.4 mol/dm³, a straight line between those points crosses zero at 0.2 + 0.2 × 6.0 ÷ (6.0 + 4.0) = 0.32 mol/dm³. The specification suggests finding the water potential from this intercept: look up the water potential of a 0.32 mol/dm³ sucrose solution and that is the water potential of the tissue.

Common mistakes

• Adding the dilution factors. Three tenfold steps give 10 × 10 × 10 = 1000, not 30.
• Wrong solvent volume. For a factor f, add (f − 1) times the volume moved, not f times.
• Confusing a 1 : 10 ratio with a factor of 10. 1 part to 10 parts of water is a factor of 11; 1 part in 10 total is a factor of 10.
• Not mixing each tube before taking the next sample, so the dilution isn't even.
• Reusing the same pipette tip, which carries stronger solution into the next tube.

Read next

Chemistry · Moles and quantitiesDilution calculator: C1V1 = C2V2 and serial dilutionsSolve C1V1 = C2V2 for any value, find how much water to add, and plan a serial dilution, with worked examples you can check in the calculator.