A serial dilution reaches very low concentrations by repeating the same small dilution again and again. Instead of trying to pipette 1 µL into 999 mL for a 1:1,000,000 dilution, you dilute 1:10 six times. Each step is easy to pipette accurately, and the series gives you a whole range of concentrations at once – ideal for standard curves, minimum inhibitory concentration tests, ELISA plates and counting bacteria by plating.
Planning the volumes is where mistakes happen. Each tube must end up with enough liquid for every test you will run plus a margin for pipetting losses, and it must also supply the transfer to the next tube. This calculator starts from the volume you need to keep in each tube and works out the transfer volume, the diluent, the starting volume and how much of a more concentrated stock to use for the first tube.
You can specify a constant dilution factor (1:2, 1:10…) or the first and last concentrations, in which case the factor is calculated so the series spans the range in equal logarithmic steps.
How to use the Serial Dilution Calculator
- Method
- Number of solutions (including the starting solution)
- Dilution factor between solutions (1 : D)
- Concentration of the starting solution
- Concentration of the last solution
- Volume taken per use (test)
- Number of uses per solution
- Allow for pipetting losses as
- Percentage error
- Pipette error volume
- Stock solution concentration (0 = start from the starting solution)
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
From the volume per use, the number of uses and the error margin the calculator finds the volume that must remain in each tube. With dilution factor D, transferring V_min ÷ (D − 1) into V_min of diluent gives exactly 1:D and leaves V_min after the next transfer. The table lists every tube; the chart shows the concentrations on a logarithmic scale.
Worked example
Six solutions, 1:10 each, starting at 0.1 M from a 1 M stock. Each solution must supply 3 uses of 1 mL plus 10%, so 3.3 mL must stay in every tube. The transfer volume is 3.3 ÷ (10 − 1) = 0.367 mL, added to 3.3 mL of diluent in each repeat tube. The starting tube needs 3.3 + 0.367 = 3.667 mL, made from 3.667 × 0.1 ÷ 1 = 0.367 mL of stock and 3.3 mL of diluent. The last tube is 0.1 ÷ 10⁵ = 1 × 10⁻⁶ M, and 19.8 mL of diluent is used in total.
Good practice
Change pipette tips between tubes, mix each tube thoroughly before transferring, and work from the most dilute to the most concentrated when using the series. For plating, choose the dilution that gives 30–300 colonies per plate.
Formula
C(n) = C₀ ÷ Dⁿ⁻¹ (tube n, dilution factor D)
D = (C₀ ÷ C_last)¹ ÷ (N − 1)) for a concentration range
Minimum volume V_min = volume per use × uses × (1 + error)
Transfer volume = V_min ÷ (D − 1); diluent per tube = V_min
Stock volume = (V_min + transfer) × C₀ ÷ C_stock
Worked example
Inputs — Method: Dilution factor; Number of solutions (including the starting solution): 6; Dilution factor between solutions (1 : D): 10; Concentration of the starting solution: 0.1 mol/L (M); Volume taken per use (test): 1 mL; Number of uses per solution: 3; Allow for pipetting losses as: Percentage error; Percentage error: 10 %; Stock solution concentration (0 = start from the starting solution): 1 mol/L (M).
Results — Dilution table = # Concentration (M) Total dilution Take (mL) Add diluent (mL) Made (mL) Left (mL)
──────────────────────────────────────────────────────────────────────────────────────────────────
1 0.1 1 0.3667 stock 3.3 3.6667 3.3
2 0.01 10 0.3667 from #1 3.3 3.6667 3.3
3 1 × 10⁻³ 100 0.3667 from #2 3.3 3.6667 3.3
4 1 × 10⁻⁴ 1,000 0.3667 from #3 3.3 3.6667 3.3
5 1 × 10⁻⁵ 10,000 0.3667 from #4 3.3 3.6667 3.3
6 1 × 10⁻⁶ 100,000 0.3667 from #5 3.3 3.6667 3.6667; Concentration of the last solution = 0.000001; Dilution factor per step = 10; Total dilution of the last solution = 100,000 ×; Volume left in each solution = 0.0033; Volume to transfer between solutions = 0.0004.
Key terms
- Dilution factor (D)
- Ratio of the concentration before to after one dilution step.
- Total dilution
- Product of all step dilution factors up to a given tube.
- Diluent
- Liquid used to dilute, such as water, buffer or broth.
- Stock solution
- Concentrated solution used to prepare the first tube.
Frequently asked questions
What is a serial dilution?
A series of dilutions in which each solution is made from the previous one with the same dilution factor.
How do I make a 1:10 serial dilution?
Transfer 1 part of the previous tube into 9 parts of diluent – for example 100 µL into 900 µL – mix well and repeat.
How do I find the concentration after n dilutions?
Divide the starting concentration by the dilution factor raised to the number of steps: 0.1 M after five 1:10 steps is 0.1 ÷ 10⁵ = 10⁻⁶ M.
What is the difference between dilution factor and dilution ratio?
A 1:10 dilution factor means 1 part in 10 parts total (1 + 9). Some labels write 1:9 for the same thing – 1 part plus 9 parts diluent.
How do I calculate CFU/mL from a serial dilution?
Colonies counted ÷ volume plated (mL) × total dilution factor of that tube. 45 colonies from 0.1 mL of a 10⁻⁵ tube = 4.5 × 10⁷ CFU/mL.
Why add a pipetting error margin?
Liquid clings to tips and tube walls; a 5–10% margin makes sure the last test still has enough volume.
What dilution factor should I use for a 2-fold series?
D = 2: transfer a volume equal to the diluent in the tube – the classic doubling dilution used for antibody titres and MIC tests.