C1V1

Assumptions

Dilution calculator for one step: enter any three of C1, V1, C2, and V2. Use Serial Dilution when the same factor repeats and you need a concentration for every step. The relation is C1 times V1 equals C2 times V2, for the same solute in both solutions. C1 is the stock concentration. V1 is the volume of that stock you pipette. C2 is the concentration after dilution. V2 is the final volume. The diluent volume is V2 minus V1. It is not a second formula.

You choose the unknown. The default unknown is V1, the stock volume, because that is the usual bench question: how much of the concentrated solution goes into the vessel. The other three values, plus the minimum pipette volume, are inputs. Switching the unknown keeps numbers that are still inputs. It does not copy the previous result into the field that just opened.

A dilution on this page means the final concentration is lower than the stock. If C2 is equal to C1, or higher, the page stops and does not invent a negative diluent. Concentrating a solution, or mixing two different solutes, is outside this equation.

How it works

C1 × V1 = C2 × V2

V1 = C2 × V2 ÷ C1

The calculator rearranges that one equation for the unknown. Volumes are converted to litres and concentrations to one base unit before the division. Molar units use mol/L. mmol/L is divided by one thousand, µmol/L by one million, and nmol/L by one billion. Mass units use g/L. One mg/mL is one g/L. One µg/mL is one-thousandth of a g/L, and so is one ng/µL. The result is then scaled back into the unit you selected for the unknown and shown at four significant figures, half away from zero, the same rule as the other solution channels.

Molar concentrations are not converted into mg/mL here. That would need a molecular weight, and this page does not ask for one. If C1 and C2 are different kinds of unit, the message asks you to use the same kind. Empty fields, zero, and negative numbers are rejected in a fixed order: C1, V1, C2, V2, then the minimum pipette volume, skipping whichever one is the unknown.

The WORKING lines quote those converted strings and the rearranged equation. Prep steps quote the same strings: pipette the stock volume, add the diluent, and stop at the final volume and concentration. They do not weigh a solid and they do not draw a plate. Copy result is only the unknown, a number, a space, and its unit. Copy protocol is the longer text, including the working lines.

Pipette minimum

The warning uses the rule already on Serial Dilution. You type the minimum volume your pipette can deliver. The page converts that minimum and the stock volume V1 into litres and marks the result only when V1 is strictly smaller. An equal volume is not marked. There is no hidden cutoff such as a fixed microlitre floor. The diluent is shown either way. The warning is about the stock you pipette, which is the transfer in this single step. If the final volume is made up to the line rather than by pipetting the diluent, judge that step yourself. The amber line reads Below minimum pipette volume.

Worked example

Stock 10 mmol/L, final concentration 1 mmol/L, final volume 1 mL. Minimum pipette volume 50 µL. The unknown is V1, shown in µL.

Result 100.0 µL. Diluent 0.9000 mL. Below minimum pipette volume: no.

1. Pipette 100.0 µL of the stock.
2. Add 0.9000 mL of diluent.
3. The final volume is 1 mL at 1 mmol/L.

• C1 = 10 mmol/L ÷ 1000 = 0.01000 mol/L
• C2 = 1 mmol/L ÷ 1000 = 0.001000 mol/L
• V2 = 1 mL ÷ 1000 = 0.001000 L
• minimum = 50 µL ÷ 1000000 = 0.00005000 L
• V1 = C2 × V2 ÷ C1 = 0.001000 mol/L × 0.001000 L ÷ 0.01000 mol/L = 0.0001000 L
• V1 = 0.0001000 L × 1000000 = 100.0 µL
• diluent = V2 − V1 = 0.001000 L − 0.0001000 L = 0.0009000 L
• diluent = 0.0009000 L × 1000 = 0.9000 mL

Common mistakes

• Using this page for a series. One factor repeated across several tubes belongs on Serial Dilution, which lists every concentration and the transfer for each step.
• Entering the final concentration in the stock field. C1 is the higher concentration. If the numbers are swapped, C2 is not lower than C1 and the page rejects the dilution.
• Mixing mol/L with mg/mL. The two families are not interchangeable without a molecular weight, and this page will not guess one.
• Treating an equal pipette volume as too small. The mark is strict. A stock volume that matches the minimum you typed is allowed.

FAQ

Sources

C1 times V1 equals C2 times V2 is the definition of one dilution of the same solute. This page does not cite a kit protocol and does not add a correction factor. The pipette comparison is the same strict test as Serial Dilution. Open the home index.