Chemical Solution Mixer

What this calculator does

You have a bottle of something strong and you need a weaker working solution. Give it the strength of the stock, the strength you want, and how much finished solution you need. It tells you how much stock to measure out and how much solvent goes with it.

The dilution equation

C₁ × V₁ = C₂ × V₂

• C₁: concentration of the stock you are starting from
• V₁: volume of stock to measure out, which is what you are solving for
• C₂: concentration you want
• V₂: final volume you want

Rearranged, that is V₁ = (C₂ × V₂) ÷ C₁.

The concentration units cancel out, so percent works here exactly as well as molarity does. The one rule is that both concentrations use the same unit. Feeding a percent stock against a molar target produces a number that means nothing at all.

Worked example: 10% from a full-strength stock

You need 500 mL at 10%, and the bottle on the shelf is 100%.

• V₁ = (10 × 500) ÷ 100 = 50 mL of stock
• Solvent = 500 − 50 = 450 mL
• Which is 1 part stock to 9 parts solvent, written 1:9

Which percent, though?

“10%” is three different things depending on who wrote the label:

• % w/v is grams of solute per 100 mL of solution. Most lab reagents are quoted this way.
• % v/v is millilitres per 100 mL. Alcohols and liquid acids.
• % w/w is grams per 100 g of solution. Concentrated acids, syrups, brines.

The arithmetic is identical for all three. The answer only means what you think it means if the stock and the target are quoted the same way. Concentrated sulfuric acid sold as 98% is w/w, and reading it as v/v will leave you short.

Add to the mark, not by the jugful

The result gives you a solvent volume because it is a useful sanity check, but that is not quite how to mix an accurate solution. Volumes are not perfectly additive. Fifty millilitres of ethanol poured into fifty of water gives about 96 mL, not 100. For anything that has to be right, measure the stock into a volumetric flask and top up to the final volume line. For bleach, cleaning solutions and fertiliser, pouring in the solvent volume is fine.

Going the other way

This page only dilutes. If you need to work out how much solid to weigh for a molar solution, that is the molar concentration calculator instead.

Safety note: always add acid to water, never water to concentrated acid. Diluting a concentrated acid releases a lot of heat, and pouring water onto acid can flash it back out of the vessel.