Dilution and Molarity Calculator (C1V1 = C2V2)

Making up solutions at the right concentration is one of the most common jobs at the bench, and one of the easiest places to slip a decimal point. This free calculator handles the two calculations labs use most: diluting a stock solution (C1V1 = C2V2) and working out how much solid to weigh out for a solution of a given molarity.

Dilution calculator (C1V1 = C2V2)

How it works

The amount of solute does not change when you dilute, so the stock concentration multiplied by the stock volume equals the final concentration multiplied by the final volume: C1 × V1 = C2 × V2. Rearranged for the volume of stock you need: V1 = (C2 × V2) ÷ C1.

Worked example: to make 100 mL of 10 mM solution from a 1 M stock, V1 = (10 mM × 100 mL) ÷ 1000 mM = 1 mL. Add 1 mL of stock to 99 mL of diluent.

• Both concentrations must be in the same kind of unit: molar (M, mM, µM, nM) or mass per volume (mg/mL, µg/mL, % w/v, where 1% = 10 mg/mL). The calculator converts within each kind for you.
• “Diluent” is whatever the solution is made up in: purified water, PBS or another buffer.
• For very large dilutions (more than about 1 in 1000), a two-step serial dilution is usually more accurate than pipetting a tiny volume of stock.

Molarity calculator: mass to weigh out

The formula is mass (g) = concentration (mol/L) × volume (L) × molecular weight (g/mol). The default example is 500 mL of 150 mM sodium chloride (MW 58.44 g/mol), which needs 4.383 g.

• Use the molecular weight of the exact form you are weighing. Hydrates are heavier: sodium acetate trihydrate is 136.08 g/mol, anhydrous sodium acetate is 82.03 g/mol.
• Dissolve the solid in about 80% of the final volume first, then make up to the mark. Adding the solid to the full volume gives a slightly wrong final volume.
• For solids that are slow to dissolve in water, a small volume of DMSO is often used to make a concentrated stock, which is then diluted with the calculator above.

Good practice

• Write the calculation on the label or in your notebook: what, concentration, solvent, date.
• Use calibrated pipettes and choose one whose range suits the volume (a 1 mL pipette at 20 µL is far less accurate than a 20 µL pipette).
• Filter sterile solutions through a 0.22 µm syringe filter and store aliquots in sterile vials. See our syringe filter guide and aliquoting guide.

Related: PBS and buffer recipes, with a buffer calculator. Supplies used here: WFI water, 0.9% saline, 1× PBS.

This calculator is a convenience tool; always check critical calculations. Union Biolabs products are supplied for laboratory research use only.