A little help goes a long way. Find a tool/

Science & Physics

Dilution Calculator

Free dilution calculator (C1V1 = C2V2): enter any three of stock concentration, stock volume, target concentration and final volume to get the missing value, plus the dilution factor. Runs in your browser.

YOUR WORKSPACEFree to use. No sign-up.
—
Enter exactly three values, leave the unknown blank, then press Solve.

Deep dive guides

A LITTLE CONTEXT · 4 MIN READDilution Math: How C1V1 = C2V2 Actually Works

How dilution calculator works

Dilution always follows one equation: C1V1 = C2V2, where C1 is the stock concentration, V1 is how much stock you take, C2 is the target concentration, and V2 is the final volume after topping up with solvent. The product "concentration × volume" is the amount of solute, and dilution never changes it — you only add solvent. That single conservation fact is why any three of the four numbers determine the fourth.

Enter any three of the four fields and leave the unknown blank. The tool solves C1V1 = C2V2 for the missing quantity and shows the dilution factor — how many times stronger the stock is than the working solution (equivalently, the ratio V2/V1). A 10 M stock brought down to 0.5 M is a 20× dilution, so you take one part stock and add 19 parts solvent.

Concentrations can be molar, mg/mL, percent, or any other unit, and volumes can be litres, millilitres or microlitres — the math is unit-agnostic as long as the two concentrations share a unit and the two volumes share a unit. The output also reads as a recipe: measure V1 of stock, then dilute to a final volume V2 (not dilute by adding V2 of solvent — the volumes are not always additive to better than a few percent).

Frequently asked questions

What does C1V1 = C2V2 mean?
It says the amount of solute is unchanged by dilution: stock concentration times stock volume equals final concentration times final volume. Since dilution only adds solvent, C1V1 (the moles or mass of solute you pipette) must equal C2V2 (the same solute, now spread through the larger volume). Knowing any three of the four values gives you the fourth.
How do I make 500 mL of 0.5 M solution from a 10 M stock?
V1 = C2V2/C1 = (0.5 × 500)/10 = 25 mL. Measure 25 mL of the 10 M stock, dispense it into a flask or volumetric flask, and add solvent up to the 500 mL mark. The tool shows the same numbers: stock volume 25 mL, final volume 500 mL, dilution factor 20×.
Do C1 and C2 need the same units?
Yes — and V1 and V2 need the same units as each other. The equation is a ratio relationship, so the units cancel as long as each pair is consistent. You cannot mix a molar stock with a mg/mL target without converting first; convert one of them so both concentrations share a unit, then solve.
What is a dilution factor?
The dilution factor is the ratio of stock concentration to final concentration (C1/C2), which equals the ratio of final volume to stock volume (V2/V1). A 20× dilution means one part stock in twenty parts final solution — nineteen parts solvent added per part stock. Serial dilutions multiply: two 10× steps in a row are a 100× dilution overall.
Is "dilute to 500 mL" the same as "add 500 mL of solvent"?
No, and the distinction matters at higher concentrations. "Dilute to" means bring the total volume up to the mark in a volumetric flask, accounting for the volume the solute itself occupies. Adding exactly V2 of solvent instead can overshoot the final volume slightly because volumes are not always strictly additive. Use volumetric glassware and fill to the mark.