ChemBench

Dilution Calculator

The universal dilution equation that every chemistry and biology lab uses daily.

Initial molarity (M₁)

Initial volume (V₁)

Final molarity (M₂)

Final volume V₂

What you entered

Initial molarity (M₁): 6Initial volume (V₁): 0.5Final molarity (M₂): 1

1
M₁V₁ = M₂V₂ → V₂ = M₁V₁ ÷ M₂
(6 × 0.5) ÷ 1= 3 L

Result

Final volume V₂: 3

To dilute a 6 M solution to 1 M, you need a final volume of 3 L. Add 2.5 L of solvent to your 0.5 L stock.

Dilution volumes using M1V1 = M2V2

Moles of solute do not change when you add solvent, so concentration times volume stays constant. The result is the final volume you dilute to, not the volume of water to add.

Stock conc.	Stock volume	Target conc.	Final volume	Solvent to add
1 M	100 mL	0.1 M	1,000 mL	900 mL
2 M	50 mL	0.5 M	200 mL	150 mL
12 M	10 mL	1 M	120 mL	110 mL
0.5 M	200 mL	0.1 M	1,000 mL	800 mL
6 M	25 mL	0.5 M	300 mL	275 mL
10 M	5 mL	0.25 M	200 mL	195 mL

When diluting concentrated acid, always add acid to water rather than water to acid: the mixing is strongly exothermic and can boil and spit if done the wrong way round.

Moles are conserved, not concentration

When you add solvent to a solution, the number of moles of solute stays the same — only the concentration drops. M₁V₁ = M₂V₂ works because both sides equal the number of moles: moles = molarity × volume.

Where this formula applies (and where it doesn't)

M₁V₁ = M₂V₂ assumes ideal dilution — it works perfectly for most lab solutions, but breaks down for concentrated acids or solutions where mixing changes total volume significantly (like mixing ethanol and water).

Frequently asked questions

I have 50 mL of 6 M HCl and need 0.5 M — how much water do I add?

M1V1 = M2V2 → 6 × 50 = 0.5 × V2 → V2 = 600 mL total. Add 600 - 50 = 550 mL of water. Always add acid to water, never the reverse.

How is the dilution calculator different from the molarity calculator?

The molarity calculator finds concentration from mass and volume. The dilution calculator finds the new volume (or concentration) when you add solvent to an existing solution. Use molarity first to determine your stock concentration, then dilution to reach a target.

Can I use M1V1 = M2V2 for serial dilutions?

Yes. Apply it sequentially: the output of one dilution becomes the input of the next. A 1:10 dilution done 3 times gives an overall 1:1000 dilution — a common microbiology technique.

Why must I add acid to water and not water to acid?

Adding water to concentrated acid can cause violent, localized boiling because the mixing is exothermic. Adding acid to water distributes the heat over a large volume of water, making it far safer.