Diluting a Solution Concentration Calculator

Find the concentration after adding water to a salt solution, or the amount of water needed to reach a target concentration, with step-by-step working.

Input

A calculator for the classic word problem of diluting a salt solution with water. Find the concentration after adding water, or the water needed to reach a target concentration.

Original solution mass

Original concentration

Water added

Enter mass in grams and concentration in percent. Concentration must be from 0 to 100.

Result

Concentration after diluting

4 %

Amount of salt

16 g

Total after diluting

400 g

Water added

200 g

How to solve it

Find the salt. 200 g at 8 percent gives 200 times 8 divided by 100, which is 16 g of salt.

Find the new total mass. Add 200 g of water to 200 g to get 400 g.

Find the new concentration. Salt 16 g divided by total 400 g, times 100, equals 4 percent.

How it works

The mass of salt in a solution does not change when you add water. For an a g solution at c percent, the salt equals a times c divided by 100 grams.
Adding w g of water makes the total a plus w grams, so the new concentration is salt divided by the new total, times 100.
To reach a target concentration, work backward from the salt to find the required total, then subtract the original mass to get the water needed.
Adding water always lowers the concentration, so the target must be lower than the starting concentration.

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