How to Find the Concentration When You're Given the pH

By Michael Judge
Acids have a low pH.

Scientists use pH to measure how acidic or basic water is. A low pH value means water is acidic and a high value means it's basic (sometimes called alkaline). In acidic water, there is an increased concentration of positively charged hydrogen atoms (H+). This concentration determines the pH value. Specifically, the pH is equal to the base 10 logarithm of the H+ concentration, multiplied by -1. If you know the pH of a water solution, you can use this formula in reverse to calculate the H+ concentration in that solution.

Enter into the calculator the pH value for which you intend to calculate the H+ concentration. For example, if the pH of your solution is 5, enter 5 into the calculator. pH values will almost always be between 0 and 14, so your number should be within this range.

Multiply the value you just entered by -1. This is the first step toward calculating the concentration of H+ in the solution, based on the equation pH = (-1) log [H+], where "log" is short for base 10 logarithm and the square brackets around H+ stand for "concentration." Multiplying the pH by -1 puts this equation in the form log[H+] = - pH. In the example, you would multiply 5 by -1 to get -5.

Take the base 10 antilogarithm (or "anti-log") of the value you just calculated. You can take the anti-log by using the 10^x key on the calculator. By doing this, you are changing the pH equation into the form anti-log (log[H+]) = anti-log (- pH). The two reverse operations (anti-log and log) on the left-hand side cancel each other out, leaving [H+] = anti-log (- pH). So the value you calculate in this step is the concentration of H+ in the solution. The units of this concentration are molarity, or moles H+ per liter of solution. The example with a pH of 5 would therefore have an H+ concentration equal to anti-log (-5) which equals 0.00001 moles/liter. (properties of anti-logs from ref 3)


Some scientists prefer to use the formula H3O+ instead of H+, to show that the positive hydrogen atom typically combines with a neutral water molecule (H2O) to form H3O+, known as the hydronium ion.

About the Author

Michael Judge has been writing for over a decade and has been published in "The Globe and Mail" (Canada's national newspaper) and the U.K. magazine "New Scientist." He holds a Master of Science from the University of Waterloo. Michael has worked for an aerospace firm where he was in charge of rocket propellant formulation and is now a college instructor.