Serial Dilution Calculator – Free Calculator

Understanding the serial dilution calculator — concept and principle

A serial dilution reduces a concentration step by step, using the same dilution factor each time. It is the standard way to reach very low concentrations accurately, for bacterial plate counts, standard curves, antibody titres and drug-sensitivity tests. This calculator gives the final concentration after k steps, the transfer and diluent volumes for each tube, and the full concentration series.

Each tube is one-tenth of the one before; six steps multiply to 10⁶, so 1000 ends at 0.001.

How it is calculated

Final concentration = C₀ ÷ DFᵏ, where C₀ is the starting concentration, DF the dilution factor per step and k the number of steps.
Transfer volume = V_t ÷ DF, the volume moved from one tube to the next, where V_t is the volume in each tube after mixing.
Diluent per tube = V_t − V_t ÷ DF.
Tube i (i = 1 … k) has concentration C₀ ÷ DFⁱ.

The concentration unit is whatever you enter (cells/mL, µg/mL, M); the volumes are in mL.

The principle

Each step is an ordinary C₁V₁ = C₂V₂ dilution: moving 1 part into a tube so that the total is DF parts divides the concentration by DF. Repeating it multiplies the factors, so k steps give an overall factor of DFᵏ. This is a geometric sequence, which is why each tube in a 10-fold series is one order of magnitude (one log₁₀ unit) lower than the one before. Large overall dilutions are made from several comfortable pipetting volumes instead of one tiny one.

Worked example

Defaults: C₀ = 1000, DF = 10, k = 6 steps, V_t = 10 mL.

Overall factor: 10⁶ = 1,000,000.
Final concentration: 1000 ÷ 1,000,000 = 0.001.
Transfer volume: 10 ÷ 10 = 1 mL; diluent per tube: 10 − 1 = 9 mL.
Series: 100, 10, 1, 0.1, 0.01, 0.001.

Each point is the calculator re-run with only “Steps” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Steps	Final concentration
1.5	31.6227766
3	1
4.5	0.0316227766
6	0.001
7.5	0.0000316228
9	0.000001
12	1e-9

How to read the result

Prepare six tubes with 9 mL of diluent, move 1 mL from the stock into tube 1, mix well, move 1 mL from tube 1 into tube 2, and so on. In plate counting you then choose the dilution whose colonies fall in a countable range and multiply back by its total factor. Twofold series (DF = 2) are common for titres and minimum inhibitory concentrations.

Common mistakes

Not mixing thoroughly before each transfer, which carries errors into every later tube.
Reusing the same pipette tip, so concentrated liquid contaminates the next tube.
Forgetting that every tube except the last loses one transfer volume, so it holds V_t − V_t ÷ DF afterwards.
Counting the stock as step 1, which shifts every concentration by one factor.

Keep in mind: Small errors compound geometrically: a 2% pipetting error in the same direction at every step grows to about 13% after six steps. For quantitative work use calibrated pipettes and check against a reference standard.

Frequently asked questions

How do I make a 1:100 dilution in two steps?

Do two 1:10 steps, each moving 1 part into 9 parts of diluent.

How do I calculate the original concentration from a plate count?

Divide the colony count by the plated volume, then multiply by the total dilution factor of that tube.

Why not dilute 1:1,000,000 in one step?

You would need to pipette a tiny volume into a huge one, which is impractical and inaccurate.

Sources: Harris, D. C., Quantitative Chemical Analysis, W. H. Freeman · Madigan, M. T. et al., Brock Biology of Microorganisms, Pearson

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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