Percent to Molarity: Formula and Calculator

This calculator converts a percentage concentration (w/v, w/w, or v/v) into molarity (mol/L) using the density and molar mass of the solute. Enter the percentage, the solute’s molar mass, and the solution’s density (if needed), and you get the molarity in moles per liter. The formula and a step-by-step example are provided below.

Formula

The general formula to convert percent concentration to molarity is:

Molarity (M) = (Percent × Density × 10) / Molar Mass

Where:

• Percent – the concentration expressed as a percentage (e.g., 5% means 5 g per 100 mL for w/v, or 5 g per 100 g for w/w).
• Density – density of the solution in g/mL (for w/v, the density is often taken as 1 g/mL for dilute aqueous solutions).
• Molar Mass – molar mass of the solute in g/mol.
• 10 – conversion factor from 100 mL to 1 L (since 100 mL = 0.1 L, and 1/0.1 = 10).

The formula assumes that the percentage is based on mass/volume (w/v) for the most common case. For w/w or v/v, adjustments are needed as described in the next section.

Worked Example

Using the default values from the calculator: 5% w/v solution of NaCl (molar mass 58.44 g/mol) with a solution density of 1.00 g/mL.

1. Start with the formula: M = (Percent × Density × 10) / Molar Mass
2. Plug in the numbers: M = (5 × 1.00 × 10) / 58.44
3. Multiply: 5 × 1.00 × 10 = 50
4. Divide: 50 / 58.44 = 0.8555…
5. Round to 4 decimal places: 0.8555 mol/L

The calculator gives the same result: 0.8555 M.

Understanding Percent Concentrations

Percent concentration can be expressed in three ways, and the correct interpretation is critical for conversion:

• % w/v (mass/volume) – grams of solute per 100 mL of solution. This is common in biology and chemistry for solutions like saline or glucose.
• % w/w (mass/mass) – grams of solute per 100 g of solution. Used for solids or concentrated acids, e.g., 37% HCl.
• % v/v (volume/volume) – mL of solute per 100 mL of solution. Used for liquid solutes like ethanol.

For w/v, the density factor in the formula is often 1 g/mL for dilute aqueous solutions, but for concentrated solutions, the density must be known. For w/w, you must multiply the percentage by the solution density to get the mass per volume, then apply the molar mass. For v/v, you need the density of the solute to convert volume to mass.

How to Choose the Correct Density

The density of the solution is a key input. For dilute aqueous solutions (less than ~1%), the density is very close to 1.00 g/mL, so many calculations use that approximation. However, for concentrated solutions, the density can differ significantly:

• 37% HCl has a density of about 1.19 g/mL.
• 98% H₂SO₄ has a density of about 1.84 g/mL.
• 70% HNO₃ has a density of about 1.42 g/mL.

Always look up the density of the specific solution you are using, not just the solute. For w/v percentages, the density is not needed if you assume 1 g/mL, but for accurate work, use the actual density.

Common Mistakes and Pitfalls

Several errors are common when converting percent to molarity:

• Using w/w as w/v – For w/w, you must multiply by density to get grams per liter. Example: 37% HCl w/w with density 1.19 g/mL gives 37 g per 100 g, which is 37 × 1.19 = 44.03 g per 100 mL, or 440.3 g/L. Then divide by molar mass (36.46 g/mol) to get ~12.1 M.
• Forgetting the factor of 10 – The 10 comes from converting 100 mL to 1 L. If you use percent as g/100 mL, you need to multiply by 10 to get g/L.
• Using the wrong molar mass – For hydrated salts, use the molar mass of the anhydrous form unless the hydrate is specified. For example, CuSO₄·5H₂O has a different molar mass than CuSO₄.
• Rounding too early – Keep extra digits during intermediate steps, and round only at the final answer.

Limitations of the Formula

The formula works well for solutions where the solute is a solid and the concentration is expressed as w/v or w/w. For v/v solutions, you must know the solute density. Also, the formula assumes ideal behavior – it does not account for volume changes upon mixing, which can be significant for concentrated solutions. For example, mixing ethanol and water results in a volume less than the sum of the parts, so a 50% v/v solution is not exactly 50% w/v. In such cases, the density of the final solution must be measured or looked up.

Frequently Asked Questions

How do I convert 10% w/v to molarity?

For a 10% w/v solution, you have 10 g of solute per 100 mL. Multiply by 10 to get 100 g/L. Then divide by the molar mass. For example, if the solute is NaOH (molar mass 40 g/mol), the molarity is 100/40 = 2.5 M.

What is the molarity of 37% HCl?

37% HCl is w/w. With a density of 1.19 g/mL, you have 37 g HCl per 100 g solution, which is 37 × 1.19 = 44.03 g per 100 mL, or 440.3 g/L. Dividing by the molar mass (36.46 g/mol) gives 12.08 M.

Can I use this calculator for v/v percentages?

Yes, but you must enter the density of the solute, not the solution. The formula then uses the solute density to convert volume to mass. For example, 10% v/v ethanol (density 0.789 g/mL) gives 10 mL ethanol per 100 mL, which is 7.89 g per 100 mL, or 78.9 g/L. Divide by ethanol’s molar mass (46.07 g/mol) to get 1.71 M.

Why do I need the density for w/w but not for w/v?

For w/v, the percentage already gives mass per volume, so you only need to convert to per liter (multiply by 10). For w/w, the percentage gives mass per mass, so you need density to convert mass of solution to volume of solution.

What if my solution is very dilute?

For very dilute solutions (less than 1%), the density is essentially 1 g/mL, and the difference between w/v and w/w is negligible. You can safely use the formula with density = 1.00 g/mL.

Is molarity the same as molality?

No. Molarity is moles of solute per liter of solution, while molality is moles of solute per kilogram of solvent. They are equal only when the solution density is 1 g/mL, which is rare. This calculator gives molarity.

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in p | Percent concentration | % | 5 | 0
in m | Molar mass of solute | g/mol | 58.44 | 0
in d | Density of solution | g/mL | 1.00 | 0
sel type | Concentration type | w/v=1, w/w=2, v/v=3
out molarity | Molarity | mol/L | (p * 10 * d) / (m * 100) | 4