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Percent Solution Calculator

Calculate the solute needed for a percent solution by weight per volume (% w/v), volume per volume (% v/v) or weight per weight (% w/w).

Formula

% w/v:msolute=%×Vfinal (mL)100\%\ \mathrm{w/v}:\quad m_{\text{solute}} = \dfrac{\%\times V_{\text{final}}\,(\mathrm{mL})}{100}
% v/v:Vsolute=%×Vfinal100\%\ \mathrm{v/v}:\quad V_{\text{solute}} = \dfrac{\%\times V_{\text{final}}}{100}
% w/w:msolute=%×mtotal100\%\ \mathrm{w/w}:\quad m_{\text{solute}} = \dfrac{\%\times m_{\text{total}}}{100}
% w/v\%\ \mathrm{w/v}
grams of solute per 100 mL of solution
% v/v\%\ \mathrm{v/v}
millilitres of solute per 100 mL of solution
% w/w\%\ \mathrm{w/w}
grams of solute per 100 g of solution

How it works

A percent solution states the amount of solute in 100 parts of the finished solution. The three conventions differ in whether each part is measured by mass or by volume, which is why the type must always be stated.

For w/v and v/v the solution is made up to the final volume. For w/w the solute and solvent are both weighed, so the solvent mass is the total minus the solute.

Worked example

Prepare 500 mL of 0.9% w/v sodium chloride.

  1. grams = 0.9 × 500 mL / 100 = 4.5 g.

Dissolve 4.5 g of NaCl and make the volume up to 500 mL.

These are the values the calculator opens with, so you can check its output against this example.

Assumptions

  • % w/v treats 1 mL of solution as the reference volume and does not depend on the solution's density.
  • For v/v, the solute volume is measured before mixing. Volumes of different liquids do not add exactly.

Common mistakes

  • Leaving the type unstated. A 10% w/v and a 10% w/w solution of the same solute are different solutions.
  • For v/v, adding the solute to the full final volume of solvent instead of making the mixture up to volume.
  • Treating % w/v as a true percentage. It is a concentration in g per 100 mL and can exceed 100 for very soluble solutes.

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