Dilution Calculator (C₁V₁ = C₂V₂)

Work out how much stock solution to take, or what concentration you will end up with, using C₁V₁ = C₂V₂. Enter any three of stock concentration, volume of stock, final concentration and final volume, and this calculator returns the fourth — then tells you exactly how much solvent to add and how to p...

C₁V₁ = C₂V₂

Three values entered — solving for volume of stock to take.

solved: 50.0000 mL

COMMON DILUTIONS

TAKE THIS MUCH STOCK

50.00 mL

ADD SOLVENT

450.0 mL

DILUTION FACTOR

10.00 ×

SOLUTE MOVED

0.0500 mol

Stock C₁

1.0000 M

Stock volume V₁

50.0000 mL

Final C₂

0.1000 M

Final volume V₂

500.000 mL

Ratio stock:final

1 : 10.00

Stock as % of final

10.000 %

HOW TO PREPARE IT

1

Measure 50.00 mL of the 1.000 stock solution.

2

Put it into a vessel that will hold at least 500.00 mL.

3

Add solvent until the total reaches exactly 500.00 mL — about 450.0 mL, though the mark is what counts, not the amount added.

4

Mix thoroughly. The result is 0.1000, a 10.00× dilution.

THE TRANSFER

THE SOLUTE NEVER CHANGES — ONLY THE VOLUME IT IS SPREAD THROUGHTAKE THIS MUCH STOCK0.0500 L1.000MAKE UP TO0.500 L0.100+ solventthe same 10 dots move across · each is 0.00500 molsame count, larger volume, lower concentration

Why C₁V₁ = C₂V₂ works. Adding solvent does not create or destroy any solute, so the amount of solute is identical on both sides — 0.0500 mol here. Since amount is concentration times volume, C₁V₁ and C₂V₂ are two ways of writing that same unchanged quantity, which is why the equation holds whatever units you use, as long as you are consistent on both sides.

REPEATING THIS DILUTION — EACH STEP DIVIDES BY 10step 10.10000step 20.01000step 30.00100step 40.00010step 51.00e-5step 61.00e-6after 6 steps the concentration is 1.0000e-6 of the original

Repeating a dilution multiplies the effect. Six rounds of this 10.00× step would leave a concentration 1.0000e-6 of where you started — which is how laboratories reach very low concentrations accurately, rather than trying to measure a tiny volume in one go.

HOW BIG A DILUTION IS THAT?

Half strength1:21:5 dilution1:51:10 serial step1:10Two 1:10 steps10²Antibody working10³Bacterial plating10⁶YOURS10.00 ×logarithmic · range adjusts to always include your value

Live simulation · updates as you type

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HOW TO USE

  1. 1

    Enter any three of the four boxes — stock concentration C₁, volume of stock to take V₁, final concentration C₂, and final volume V₂. Known values get a solid black border; the one you leave blank is outlined in gold and fills in automatically.

  2. 2

    Pick units beside each field. Concentration in molar down to nanomolar, or in percent w/v and grams per litre — the units cancel on both sides, so any consistent pair works. Volumes in litres, millilitres, microlitres or decilitres.

  3. 3

    Read the answer, then the three figures beside it: how much solvent to add, the dilution factor, and the amount of solute being moved. The solvent figure is the one you need at the bench.

  4. 4

    Follow the four preparation steps. Note step three in particular — make the solution up to the final volume rather than adding that volume of solvent, because the mark is what defines the concentration.

THE FORMULAS

Dilution equationC₁V₁ = C₂V₂
Volume of stockV₁ = C₂V₂ / C₁
Final volumeV₂ = C₁V₁ / C₂
Final concentrationC₂ = C₁V₁ / V₂
Solvent to addV₂ − V₁
Dilution factorDF = C₁/C₂ = V₂/V₁
Serial dilutionCₙ = C₀ / DFⁿ
What is conservedn = C₁V₁ = C₂V₂

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Last updated: July 29, 2026 · Formula verified · Eagle-eyed accuracy for every calculation.