How this calculator works
The step count excludes the starting tube, labelled step 0. Each next tube receives one transfer plus fresh diluent. A uniform prepared volume leaves enough liquid in every intermediate tube after its outgoing transfer. The final tube has extra liquid because it has no outgoing transfer. A master stock can be diluted to prepare step 0. Reserve allowance increases available working volume; it does not model concentration uncertainty, independent pipetting error or evaporation.
Formula
Ck = C0/D^k. For a range, D = (C0/Cend)^(1/steps). With retained usable volume R, transfer = R/(D - 1), prepared volume = R + transfer, and fresh diluent per step = R.
Worked example
Starting at 1 mol/L, three tenfold steps end at 0.001 mol/L. If each tube must retain 1 mL with zero reserve, prepare 1.111111 mL per tube, transferring 0.111111 mL into 1 mL diluent. Two tenfold steps end at 0.01 mol/L.
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Frequently asked questions
Why prepare more than the volume I use?
Intermediate tubes must supply the next transfer and still retain the required amount for their own uses.
Does step zero count as a dilution?
No. It is the starting solution; three dilution steps produce steps 1, 2 and 3.
Does reserve percentage predict concentration error?
No. It is extra working-volume allowance. A statistical uncertainty calculation needs a separate measurement model.