How this instrument works
Serial dilution is the practice of diluting a solution repeatedly, by the same factor each time, rather than attempting one enormous dilution in a single step. Each step multiplies the previous concentration by 1/DF, where DF is the dilution factor applied at every step, so after n steps the starting concentration C0 has been divided by DF raised to the power n: Cn = C0 / DF^n.
The reason to dilute in stages rather than all at once is practical accuracy. Diluting a stock solution by a factor of 1,000,000 directly would mean pipetting an almost immeasurably small volume of stock into a huge volume of diluent, and small pipetting errors at that scale become enormous relative errors in the final concentration. Six successive 1:10 dilutions reach that same millionfold reduction through six easily measured, accurately pipetted steps instead, each one a manageable 1:10 transfer.
Serial dilution is the standard method behind microbiology's colony-counting technique, where a bacterial culture too concentrated to count directly is diluted step by step until a plate yields a countable number of colonies, and it underlies preparing calibration standards and titration curves across analytical chemistry and pharmacology, wherever a series of accurately known, evenly spaced concentrations is needed for comparison or a standard curve.
- Enter the concentration of your original, undiluted stock into Starting concentration.
- Enter the dilution factor applied at each individual step into Dilution factor per step — 10 for a 1:10 dilution at every step, 2 for a 1:2 dilution, and so on.
- Enter how many dilution steps you're performing into Number of serial dilutions.
- Read Concentration after n dilutions directly beneath the three fields — it recalculates the instant any of them changes.
- Dilution factor per step must be greater than 1 — a factor of 1 or less wouldn't dilute anything, or would concentrate the solution instead.
Worked example — three tenfold dilutions of a 1,000 unit/mL stock
Enter 1000 into Starting concentration, 10 into Dilution factor per step, and 3 into Number of serial dilutions — a stock solution at 1,000 units per millilitre, diluted 1:10 three separate times in a row. Concentration after n dilutions reads 1.0.
That comes from 1000 / 10^3 = 1000 / 1000 = 1 unit/mL, a thousandfold overall reduction reached through three individually accurate 1:10 transfers rather than one difficult thousandfold dilution attempted in a single step. Along the way, the intermediate concentrations after the first and second steps were 100 and 10 units/mL respectively — each one still simple enough to pipette accurately.
Questions
Why not just dilute the stock all the way in one step?
Because reaching a very large overall dilution factor in a single step means transferring an extremely small volume of stock into a much larger volume of diluent, and small pipetting or measurement errors at that scale translate into large relative errors in the final concentration. Splitting the same overall reduction into several smaller, equal steps keeps every individual transfer within an accurately measurable range.
What's the overall dilution factor across all n steps?
It's DF raised to the power n, not DF multiplied by n. Three successive 1:10 dilutions give an overall factor of 10^3 = 1,000-fold, not 10 x 3 = 30-fold — a distinction worth double-checking, since underestimating the overall factor by treating it as additive rather than exponential is a common serial-dilution mistake.
Does the dilution factor have to be the same at every step?
For this formula, yes — Cn = C0 / DF^n assumes an identical dilution factor applied at each of the n steps, which is what makes it a true 'serial' dilution with a constant geometric ratio between consecutive concentrations. A dilution series using a different factor at each step (a variable-factor series) needs each step's reduction multiplied through individually rather than raised to a single power.
How is this used in microbiology colony counting?
A bacterial culture is typically far too concentrated to count individual colonies directly on a plate, so it's serially diluted — often through a series of 1:10 steps — until a plate from one of the later dilutions yields a countable number of colonies, typically in the range of about 30 to 300. Multiplying that countable colony number back through the known dilution factor at that step recovers the original culture's concentration.
What units does the concentration need to be in?
Any consistent unit works — units per millilitre, molarity, colony-forming units, percent, or any other concentration measure — as long as Starting concentration and the resulting Concentration after n dilutions are read in that same unit. The formula only involves ratios and doesn't depend on which specific concentration unit you're tracking.