Select the appropriate tab (% w/v, % w/w, % v/v, or Dilution), then enter any 2 values to calculate the missing one. This calculator helps you express solution concentration using common percent conventions (weight/volume, weight/weight, and volume/volume) and perform simple dilutions using C1V1 = C2V2.
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Percentage Strength Formula
The following formulas are used to calculate percent concentration. Choose the one that matches the convention you are using (% w/v, % w/w, or % v/v).
\begin{aligned}
\%\, (w/v) &= \frac{m_{\text{solute}}}{V_{\text{solution}}}\times 100 \\
\%\, (w/w) &= \frac{m_{\text{solute}}}{m_{\text{solution}}}\times 100 \\
\%\, (v/v) &= \frac{V_{\text{solute}}}{V_{\text{solution}}}\times 100
\end{aligned}Variables:
- Mass of Solute – The mass of the solute that is dissolved in the solution (commonly expressed in grams for % w/v or % w/w).
- Volume of Solute – The volume of the solute (commonly expressed in milliliters for % v/v).
- Volume of Solution – The total volume of the solution (solute + solvent), commonly expressed in milliliters for % w/v and % v/v.
- Mass of Solution – The total mass of the solution (solute + solvent), commonly expressed in grams for % w/w.
For % w/v, the result represents grams of solute per 100 mL of solution; for % w/w, grams of solute per 100 g of solution; and for % v/v, milliliters of solute per 100 mL of solution.
What is Percentage Strength?
Percentage strength is a way to express solution concentration as a percent using a specified convention. The most common conventions are % w/v (weight per volume), % w/w (weight per weight), and % v/v (volume per volume). For example, 5% w/v means 5 g of solute per 100 mL of solution, while 5% w/w means 5 g of solute per 100 g of solution.
How to Calculate Percentage Strength?
The following steps outline how to calculate the percentage strength of a solution.
- Choose the percent convention you need: % w/v, % w/w, or % v/v.
- Measure the corresponding solute amount (mass for % w/v or % w/w; volume for % v/v).
- Measure the corresponding solution amount (solution volume for % w/v or % v/v; solution mass for % w/w).
- Use the matching formula and multiply by 100 to express the ratio as a percent.
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge (example shown for % w/v).
Mass of Solute (grams) = 5 grams
Volume of Solution (milliliters) = 250 milliliters, so Percentage Strength (% w/v) = (5 Ă· 250) Ă— 100 = 2% w/v.
