Percent Solution Calculator
Calculate percent concentration (w/w, w/v, v/v).
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What it does
The Percent Solution Calculator works out concentration in the three forms laboratories actually use: mass per mass, mass per volume, and volume per volume. Enter the amount of solute and the amount of solution, choose the convention, and it returns the percentage to four decimal places. It runs the other way too: give a target percentage and the volume to prepare, and it returns the mass or volume of solute to measure out, which is the question a protocol usually poses. It is the tool for recipes written in percent rather than molarity, which covers saline, sucrose, agar, ethanol, glycerol, acids and most biological buffers.
How it works
The three conventions differ only in what sits in the numerator and the denominator. Mass percent is the mass of solute divided by the mass of solution, times 100. Mass per volume percent is grams of solute divided by millilitres of solution, times 100. Volume percent is millilitres of solute divided by millilitres of solution, times 100. In every case the denominator is the total solution, not the solvent that was added, so 5 percent w/v means 5 g in a final volume of 100 mL rather than 5 g dissolved in 100 mL of water. Each input is converted to a common base before the division, so grams and milligrams, or millilitres, microlitres and litres, can be used freely, and the unit choices are restricted to the combinations that belong to the selected convention: mass over mass, mass over volume, or volume over volume. A volume cannot be divided by a mass here, because converting between the two needs the density of the solution and the tool does not ask for it.
Worked example
Normal saline is 0.9 percent w/v, that is 0.9 g of sodium chloride per 100 mL of solution, or 9.0 g per litre. Entering 0.9 and 100 returns 0.9000. To prepare 5 percent w/v sodium chloride, weigh 5.00 g and make the volume up to 100 mL, and the tool returns 5.0000 from 5 and 100. For 70 percent v/v ethanol, measure 70 mL of ethanol and add water to a final volume of 100 mL rather than adding 30 mL of water, because ethanol and water do not occupy additive volumes on mixing. Scaling works the same way: 250 mL of 0.9 percent saline needs 0.9 times 250 / 100 = 2.25 g rather than 0.9 g. For a mass based recipe the denominator changes, so 3.5 percent w/w means 3.5 g of salt plus 96.5 g of water to make 100 g of solution in total, which is why a w/w recipe is weighed rather than made up to a mark.
When to use it
Use it to turn a percent recipe into an amount you can weigh or measure, to check what a stated percentage really means before relying on it, and to convert between the conventions when a protocol and a stock bottle disagree. The convention matters more than the arithmetic. Percent w/v is the default in most biological recipes because it is defined against a final volume, which is what a volumetric flask delivers, but the same number read as w/w describes a different solution whenever the density differs from 1 g/mL: 70 percent v/v ethanol is only about 62 percent w/w, because a millilitre of ethanol weighs 0.789 g. Glycerol at 1.26 g/mL and sulfuric acid at 1.84 g/mL widen the gap further, so weight and volume percentages of the same stock are genuinely different numbers rather than two ways of writing one. A result above 100 percent is possible when the solute amount exceeds the solution amount that was entered, which usually means the denominator should have been the solvent plus the solute rather than the solvent alone.
FAQ
- What is the difference between % w/w, % w/v and % v/v?
- They differ in the numerator and the denominator: % w/w is mass of solute over mass of solution, % w/v is grams of solute over millilitres of solution, and % v/v is millilitres of solute over millilitres of solution. In all three the denominator is the finished solution, not the solvent added. Pick the convention that matches how your protocol and your balance or cylinder measure the components.
- Why is 0.9% saline 0.9 g per 100 mL?
- Because % w/v is defined as grams per 100 mL of solution, and 0.9% NaCl is the standard isotonic concentration for cells: 9.0 g per litre, or roughly 154 mM. Weigh 0.9 g, dissolve it, and make the volume up to 100 mL; entering 0.9 and 100 returns 0.9000.
- Can I convert between percent and molarity?
- Not without extra information. Percent is a ratio of masses or volumes, while molarity is moles per litre. To get from % w/v to molarity, divide by the molar mass and scale the volume: 0.9% w/v NaCl is 9.0 g/L divided by 58.44 g/mol, which is 0.154 M. Moving between % w/w and % w/v additionally needs the solution density, which the tool neither asks for nor can infer.
- Does the calculator convert units for me?
- Yes, within a convention. Grams and milligrams are interchangeable for mass, and millilitres, microlitres and litres for volume, so 0.5 g over 100 mL and 500 mg over 0.1 L both return 0.5000 percent w/v. What it will not do is convert mass to volume, because that needs the density of the solution: 70 percent v/v ethanol is about 62 percent w/w since a millilitre of ethanol weighs 0.789 g. The unit choices are therefore restricted to combinations that belong to the selected convention, and a w/w calculation cannot be set up with a volume.