Molarity Calculator for Solutions, Dilutions and Buffers

How to use the molarity calculator

1. Molarity: type a formula (NaCl) or a name (Tris, disodium EDTA), pick what to solve for and fill in the other two values. The molar mass is split element by element.
2. Dilution: enter three of C₁, V₁, C₂ and V₂. Units may differ on each side, and 10x stocks work as they are.
3. Serial: give the start, the dilution factor, the number of tubes and the volume per tube or per transfer.
4. Recipe: list each reagent, its final concentration and whether you weigh it or pipette a stock. Type your bottle's hydrate if it differs, then print the prep sheet.
5. Buffer: pick the buffer, pH, concentration, volume and temperature, then mix two forms or titrate one.

Molarity, molality, normality and the formulas

Molarity (M) is moles of solute per litre of solution, so the mass to weigh is m = c × V × M, with M the molar mass in g/mol. Molality is moles per kilogram of solvent; bench recipes are almost always molar. Normality counts reacting equivalents per litre: 1 M H₂SO₄ is 2 N in acid-base work. This tool works in molarity and mass concentration.

The molar mass sums each atomic weight times its count, using the IUPAC abridged standard atomic weights (CIAAW 2024): NaCl is 22.990 + 35.45 = 58.44 g/mol. Percent w/v is grams per 100 mL, so 0.9% NaCl is 9 g/L, or 154 mM.

A dilution keeps the solute fixed: C₁V₁ = C₂V₂, plus V₂ − V₁ of diluent. In a serial dilution with factor DF, tube k holds C₀ ÷ DFᵏ and each transfer is T = V ÷ DF. Buffers follow pH = pKa + log([A⁻] ÷ [HA]), with the pKa corrected for temperature and ionic strength.

Five worked examples

1. The hydrate trap: 250 mL of 0.1 M copper sulfate

The blue crystals are CuSO₄·5H₂O, 249.68 g/mol, against 159.60 g/mol for anhydrous CuSO₄. The right amount is 0.1 × 0.250 × 249.68 = 6.242 g. Weigh the anhydrous figure, 3.990 g, of crystals and you get 0.0639 M, 36% short.

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2. 50x TAE down to 1x

For 500 mL of 1x, V₁ = 1 × 500 mL ÷ 50 = 10 mL of stock plus 490 mL of water. No molar mass is needed.

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3. Plating a culture in six 10-fold steps

To bring 1 × 10⁹ CFU/mL down to 1 × 10³ CFU/mL (about 100 colonies from 100 µL), move 100 µL into 900 µL six times. That uses 5.4 mL of diluent, and tube 6 holds 10⁻⁶ of the start.

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4. A five-reagent lysis buffer

For 500 mL of 50 mM Tris, 150 mM NaCl, 5 mM MgCl₂ (hexahydrate on the shelf), 1 mM EDTA (from 0.5 M) and 10% v/v glycerol: 3.028 g Tris base, 4.383 g NaCl, 0.5082 g MgCl₂·6H₂O (2.135 × the anhydrous 0.2380 g), 1 mL EDTA stock, 50 mL glycerol, then water to 500 mL.

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5. 0.1 M potassium phosphate at pH 7.4

The ionic strength, 0.26 M, lowers the working pKa₂ from 7.20 to 6.77, so 81.1% of the phosphate is dibasic: 14.13 g K₂HPO₄ and 2.571 g KH₂PO₄ per litre. The published table (Sambrook) mixes 80.2 mL of 1 M K₂HPO₄ with 19.8 mL of 1 M KH₂PO₄, or 13.97 g and 2.694 g. The textbook equation with pKa 7.20 gives 61.4%.

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Making a buffer that hits its pH

• Pick a pKa within 1 unit of your pH. Further out the buffer is weak; the tool warns and names closer buffers.
• Ionic strength moves the pKa. Tables give pKa at zero ionic strength. The tool starts from the reviewed values of Goldberg, Kishore and Lennen (J. Phys. Chem. Ref. Data, 2002) and applies their extended Debye-Hückel correction. Textbook mode skips it for homework.
• Temperature moves it too. The Tris pKa is 8.072 at 25 °C and 8.710 at 4 °C, so Tris set to pH 8.0 on the bench reads about 0.64 higher in the cold room. Enter your working temperature.
• Finish on a pH meter. Mixing two forms gets close; weighing one form and adding NaOH or HCl suits HEPES and Tris. Check the pH before making up to volume.

Reading the result and common mistakes

• The wrong hydrate. Match the label to the formula. MgCl₂ is sold as the hexahydrate (203.30 g/mol); EDTA stocks use disodium EDTA dihydrate (372.24 g/mol), not the free acid (292.24 g/mol), which is what plain EDTA gives, with a warning.
• Solution volume, not water volume. Dissolve in less and fill to the mark.
• Ratio wording. 1:10 here means 1 part in 10 total; some protocols write 1:9 or 1 + 9 for the same step.
• Dead volume. Make about 10% more diluent and stock than the table lists.
• Rounding. Amounts show 4 significant figures and molar masses 0.01 g/mol; the maths keeps full precision. Older atomic-weight tables can shift the last digit (CuSO₄·5H₂O is 249.68 here, 249.69 on PubChem).
• Sodium phosphate and citrate. Sodium binds to these ions, so published tables use a little less of the sodium salt than the tool (up to about 4 mL less Na₂HPO₄ per 100 mL). Expect a small adjustment on the meter.

Open a problem from a link

Each tab keeps its inputs in the address bar, so a link reopens the exact problem:

Embed the Molarity Calculator on your website

Teachers, bloggers and course sites can add this tool to any web page for free. Paste the code below into an HTML or embed block (WordPress, Google Sites, Canvas, Moodle, Blogger, Wix). It loads the same tool you see above, without our menus or ads. Please keep the credit line under the frame. Sizes, a live preview and step-by-step guides for each platform are on the calculator widget page.

Frequently asked questions

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