Calculator of Alexandria

Serial dilution calculator

Plan a serial dilution series with the concentration, total dilution and pipetting volumes for every tube.

Any unit: cells/mL, mg/mL, µM… The results use the same unit.

10 for a 1:10 dilution (1 part sample in 10 parts total).

Final concentrationCnC_n
Total dilution (1 in …)
Transfer each step (mL)

Formula

Cn=C0DnC_n = \frac{C_0}{D^n}
How it's derived

The formula

Cn=C0DnC_n = \frac{C_0}{D^n}

C0C_0 is the starting concentration, DD the dilution factor at each step and nn the number of steps. Each transfer moves V/DV/D of sample into V−V/DV - V/D of diluent, where VV is the final volume of each tube.

Where it comes from

A single dilution follows C1V1=C2V2C_1 V_1 = C_2 V_2: the amount of solute doesn’t change, it’s just spread through more liquid. A 1:10 dilution, one part sample in ten parts total, cuts the concentration by 10.

A serial dilution repeats that step, each time starting from the tube before. Each step divides by DD again, so after nn steps the concentration has been divided by DD multiplied by itself nn times, DnD^n.

Why not do it in one go? Getting a 1:1,000,000 dilution in one step would mean pipetting 1 µL into a litre. Six 1:10 steps use easy, accurate volumes instead.

Worked example

A bacterial culture at 10810^8 cells/mL, diluted 1:10 six times into 1 mL tubes:

C6=108106=100 cells/mLC_6 = \frac{10^8}{10^6} = 100\ \text{cells/mL}

Each tube gets 900 µL of diluent, then 100 µL from the tube before. Plating 100 µL from the last tube should give about 10 colonies.

Watch out for

  • Errors compound. A small pipetting error repeats at every step. Mix each tube well and change tips between transfers.
  • Dilution factor vs ratio. “1:10” in biology usually means 1 part in 10 total (factor 10). Some fields write 1:9 for the same thing (1 part to 9 parts diluent). Check which one a protocol means.

Sources

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