Dilution Formula and Dilution Calculator
Dilution Formula and Dilution Calculator
Calculate how many mL of stock solution to take, the final volume or the concentration after dilution. Works for molarity, normality, percent and ppm.
What is dilution?
Dilution lowers the concentration of a solution by adding solvent. The amount of solute stays the same; only the solvent increases. So the number of moles before and after dilution is equal.
Dilution formula
The formula works for any concentration unit, such as M, N, % or ppm, as long as the unit is the same on both sides. Likewise, V1 and V2 must use the same volume unit.
Worked examples
Example 1: 0.1 M HCl from 1 M HCl
You have 1 M HCl and need 100 mL of 0.1 M HCl. How many mL of 1 M HCl do you take?
- M1 × V1 = M2 × V2
- 1 M × V1 = 0.1 M × 100 mL
- V1 = 10 mL
Answer: take 10 mL of 1 M HCl and dilute with distilled water to 100 mL in a volumetric flask.
Example 2: from concentrated sulfuric acid
Concentrated 98% sulfuric acid is about 18.4 M. How many mL do you need for 500 mL of 1 M H2SO4?
- 18.4 M × V1 = 1 M × 500 mL
- V1 = 500 ÷ 18.4 = 27.2 mL
Answer: about 27.2 mL of concentrated acid, added slowly to water, then diluted to 500 mL.
Example 3: 96% ethanol to 70%
How many mL of 96% ethanol do you need to make 100 mL of 70% ethanol?
- 96% × V1 = 70% × 100 mL
- V1 = 7000 ÷ 96 = 72.9 mL
Answer: about 72.9 mL of 96% ethanol, then add water to 100 mL.
Why the solvent added is not always V2 − V1
Volumes are not always additive. Mixing ethanol and water, for example, gives a slightly smaller volume than the sum of the two. The correct method is to take V1 and add solvent up to the mark V2 in a volumetric flask, rather than adding exactly V2 − V1.
Molarity of a concentrated reagent
Concentrated reagent bottles usually state the assay (% w/w) and density. The molarity is M = (% × density × 10) ÷ Mr. For 98% H2SO4, density 1.84 g/mL, Mr 98.08: M = (98 × 1.84 × 10) ÷ 98.08 = 18.4 M. There is a calculator for this in the From concentrated reagent tab on the chemistry calculator page.
Frequently asked questions
Can M1V1 = M2V2 be used with percentages?
Yes, as long as the unit is the same on both sides. For volume percent (% v/v) the result is an approximation, because mixed volumes are not always additive.
Does the formula work for normality?
Yes. N1 × V1 = N2 × V2 works the same way.
What if I mix two solutions of different concentrations?
That is mixing, not dilution. The formula is: M mix = (M1 × V1 + M2 × V2) ÷ (V1 + V2).
What is serial dilution?
Several dilutions in a row, for example 1:10 and then 1:10 again for a total of 1:100. The dilution factors are multiplied.
What equipment gives an accurate dilution?
A volumetric pipette or micropipette for V1 and a volumetric flask for the final volume V2. Measuring cylinders are not accurate enough for standard solutions.
Prepare solutions with analytical-grade reagents
AMI Scientific is one of the official TCI distributors in Indonesia. Reagents with lot CoA & SDS, formal quotations and tax invoices for universities and laboratories.
Other formulas & calculators: molarity, mole, molality, normality, titration, pH, buffer, molar mass, ppm, mole fraction, mass percent, periodic table, chemical MSDS.