Serial dilution calculator
Concentration, transfer and diluent volume for every tube in a dilution series.
Concentration, transfer and diluent volume for every tube in a dilution series.
A serial dilution is a chain of dilutions in which each tube is made from the one before it by the same factor. Ten-fold steps from a 1 M stock give 100 mM, 10 mM, 1 mM and so on; two-fold steps halve the concentration each time. Because every step reuses the previous tube, a series reaches very low concentrations with small, accurate volumes, which a single direct dilution cannot do. Standard curves, titres, MIC plates and cell counts all rely on it.
V is the volume each tube should hold when it is made and f is the fold per step. Every tube receives the same diluent volume, then the transfer volume from the previous tube, and is mixed before the next transfer. After n steps the concentration is the stock divided by fn, and the overall dilution is 1:fn.
Worked example. A 10-fold series of six tubes at 100 µL from a 1000 µM stock: each tube gets 90 µL of diluent and 10 µL from the tube before, so the concentrations run 100, 10, 1, 0.1, 0.01 and 0.001 µM, that is 1 nM in tube 6, an overall dilution of 1:10⁶. Total diluent is 540 µL and only 10 µL of stock is used.
Each tube passes one transfer volume on to the next, so tubes 1 to n−1 end with V − V ÷ f while tube n keeps the full V. In the 10-fold example above, tubes 1–5 finish with 90 µL and tube 6 with 100 µL. If every well must hold the same volume, discard the transfer volume from the last tube. The planner shows the finishing volume of every tube so nothing is a surprise.
Errors compound: a 3 % error on each transfer becomes about 20 % after six steps. Keep transfers at 2 µL or more, preferably 10 µL or more, by choosing a larger tube volume or a smaller fold. Mix each tube fully before transferring, change tips between tubes, and pre-wet the tip for viscous or protein solutions. The planner flags any transfer below 2 µL. For a single dilution from stock to a working concentration, the C₁V₁ = C₂V₂ dilution calculator is the simpler tool.
Put 900 µL of diluent in each tube. Transfer 100 µL of stock into tube 1 and mix; transfer 100 µL from tube 1 into tube 2 and mix; repeat down the row. Each tube is 10× more dilute than the one before, so tube 3 is 1:1000. The planner gives the exact volumes for any fold, tube volume and number of tubes.
A dilution factor of 10 (10-fold, written 1:10) means one part sample in ten parts total, so 1 part sample plus 9 parts diluent. Some people write 1:9 to mean the same mix; check which convention a protocol uses. This planner uses the total-volume convention: a 10-fold step transfers one tenth of the tube volume.
Every tube except the last gives up one transfer volume to the next tube. If each tube starts with V and passes on V ÷ f, it ends with V − V ÷ f while the last tube keeps the whole V. Discard the transfer volume from the last tube if all tubes need to match, or simply plan for it.
Divide the stock by the target and take the logarithm in base f: steps = log(stock ÷ target) ÷ log(f), rounded up. From 1 mM to 1 nM in 10-fold steps needs 6 tubes. Enter a target in the planner and it works this out for you.
Keep every transfer at 2 µL or more with a calibrated pipette, and ideally 10 µL or more. Below that, the error on a single pipetting step is several percent and it compounds down the series. Use a larger tube volume or a smaller fold if the planner flags a small transfer.