Serial Dilution Calculator
The chain: each tube stocks the next, factors multiply, and tube seven of a 1:10 rack reads a millionfold thinner than the bottle.
Serial Dilution Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Each step assumed perfect — real chains accumulate pipette error
- Ladder card prints the first eight tubes plus the last
In short: 1 mol/L stock, 1:10 steps, seven tubes: tube 1 is 0.100000 mol/L, tube 3 is 0.001000 mol/L, tube 7 is 1.000e-7 mol/L — and the whole rack is one 10,000,000× dilution wearing seven small pipettings. The plate-count world lives here: each tenfold step is one log of thinning, and the last tube’s colonies are countable because the arithmetic says so.
Formula
C(i) = C0/DF^i · total DF = DF^T · each step: 1 part in DF
A serial dilution repeats one small step: tube i sees the stock divided by the step factor i times. Because each tube stocks the next, the factors compound — seven 10× steps are one 10,000,000× dilution. Chaining small, pipette-sized steps beats one heroic jump because each step stays inside the pipette’s honest accuracy; errors compound too, but far more gently than a 10,000,000× single pour ever could.
Worked Example
- Enter the stock concentration.
- Enter the per-step factor (1:2, 1:5, 1:10…).
- Enter how many tubes the chain runs.
- Read the last tube, the ladder, and the total factor.
Defaults: 1 mol/L, 1:10, 7 tubes → tube 7 = 1.000e-7 mol/L; total 10,000,000×. A 1:2 chain, ten tubes: tube 10 = 0.000977 mol/L.
Strengths & Limits Of This Model
Where this engine is strong
- Total factor computed, not hand-multiplied
- Honest exponential rendering below the print threshold
Where it stops
- No per-step error propagation
- No plate-count back-calculation
Practical Use Cases
Plate counts
log steps to countable colonies
Assay standards
a calibration ladder from one stock
MIC panels
twofold chains in microtitre rows
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Serial Dilution Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Why chain small steps instead of one big dilution?
Accuracy is per-pipette-move, and a single 10,000,000× jump asks one move to be heroic across three decades of volume — no pipette is honest there. Seven 1:10 moves each stay inside the instrument’s comfort zone; their errors multiply too, but seven modest errors beat one enormous guess.
Why do microbiologists love 1:10 exactly?
Because a tenfold step is one logarithm: counting colonies from tube 4 of a 1:10 chain multiplies by 10,000 and the log book stays decimal. The whole plate-count method — dilute, plate, count, multiply back — is this ladder with agar at the bottom.
What does DF = 1 mean, honestly?
A rack of identical tubes: every step pours the solution onto itself and nothing thins. The page prints the honest result rather than pretending a chain of ones is a dilution — the ladder card reads the same concentration all the way down, and that is the correct answer.
How far can a chain usefully run?
The arithmetic is unlimited; the bench is not. Each step adds a small relative error, and by a dozen steps the accumulated pipetting error rivals the concentration itself. The ladder card shows the first tubes plus the last; beyond that, the total-factor card speaks for the rack.
What is the difference between a dilution factor and a ratio?
The ratio 1:10 and the factor 10× are the same step said two ways — one part stock in ten parts total, which is a tenfold thinning. Beware the convention trap: some protocols write 1:9 to mean the same thing (one part plus nine parts water). This page’s factor is always C-before divided by C-after, per step.
Can the chain climb back up?
No more than a single dilution can — each step divides, so the ladder only descends. To reconcentrate you leave the dilution world entirely: evaporate, reweigh, or remake from stock. The one-way door is the price of conservation of moles.
How does tube concentration relate to colony counts?
If tube 7 of a 1:10 chain holds 1.000e-7 of the original cell density, then a plate from 0.1 mL of tube 7 carries the cells of 0.00000001 mL of the original culture — count the colonies, divide by that volume, and the original density falls out. The ladder is a microscope for numbers too big to see.
Where does this show up outside microbiology?
Everywhere concentrations must fall gently: calibration ladders for spectrophotometers, drug MIC panels in twofold steps, antibody titres, flavour ladders in food labs. Anywhere a single jump would be dishonest and a ladder of small honest steps will do — which is to say, most of wet science.