# pH Calculator

By Julia Żuławińska
Last updated: May 29, 2020

With this pH calculator, you can determine the pH of a solution in a few ways. It can convert pH to H+, as well as calculate pH from the ionization constant and concentration. pH is an essential factor in chemistry, medicine, and daily life. Read the text below to find out what is the pH scale and the pH formula. In the end, we will also explain how to calculate pH, with an easy step-by-step solution.

Our calculator may ask you for the concentration of the solution. If you don't know it, you can calculate it using our concentration calculator. You can also use the solution dilution calculator in order to calculate the concentration of ions in a diluted solution.

## pH scale

The pH scale (pH) is a numeric scale which is used to define how acidic or basic an aqueous solution is. It commonly ranges between 0 and 14, but can go beyond these values if sufficiently acidic/basic. pH is logarithmically and inversely related to the concentration of hydrogen ions in a solution. The pH to H+ formula that represents this relation is:

pH = -log([H+])

The solution is acidic if its pH is less than 7. If the pH is higher than that number, the solution is basic, as known as alkaline. Solutions with a pH equal to 7 are neutral.

Apart from the mathematical way of determining pH, you can also use pH indicators. The most universal pH test is the litmus paper. It changes its color according to the pH of a solution in which it was dipped. These colors often inspire colorful pH scales: The ph in our bodies is close to neutral. For example, the pH of blood should be around 7.4. The only exception is the stomach, where stomach acids can even reach a pH of 1.

## Definitions of an acid and a base

There are three different theories that define what an acid and base is:

• According to the Arrhenius theory, in an aqueous solution, an acid is a substance able to donate hydrogen ions, while a base donates hydroxide ions;
• Brønsted–Lowry theory says that an acid can donate protons, while a base can accept them; and
• Lewis theory states that an acid is something that can accept electron pairs. Analogously, a base donates electron pairs.

The higher is the concentration of hydrogen ions from acid molecules, the lower the pH of the solution, and, consequently, the higher its acidity. The reverse is true for hydroxide ions and bases; the higher the concentration of hydroxide ions from base molecules, the higher the pH of the solution and, consequently, the higher its basicity.

We can describe the reaction of an acid, HA, in water:

HA ⇌ H⁺ + A⁻,

with the acid ionization constant:

Ka = [A⁻][H⁺]/[HA]

A similar chemical reaction between base BOH and water looks like this:

BOH ⇌ OH⁻ + B⁺

The next equation gives the base ionization constant for the above formula:

Kb = [OH⁻][B⁺]/[BOH]

If you want to know more about chemical equilibrium constants, check out the equilibrium constant calculator.

## How to find pH - pH formula

pH is defined as the negative of the base-ten logarithm of the molar concentration of hydrogen ions present in the solution. The unit for the concentration of hydrogen ions is moles per liter. To determine pH, you can use this pH to H⁺ formula:

pH = -log([H⁺])

If you already know pH, but want to calculate the concentration of ions, use this transformed pH equation:

[H+] = 10-pH

There also exists a pOH scale - which is less popular than the pH scale. pOH is the negative of the logarithm of the hydroxide ion concentration:

pOH = -log([OH⁻]), or [OH-] = 10-pOH

pH and pOH are related to one another by this pOH and pH equation:

pH + pOH = 14

## How to calculate pH? - step by step solution

1. Let’s assume that the concentration of hydrogen ions is equal to 0.0001 mol/l.
2. Calculate pH by using pH to H+ formula:

pH = -log(0.0001) = 4

1. Now, you can also easily determine pOH and a concentration of hydroxide ions:

pOH = 14 - 4 = 10

[OH-] = 10-10 = 0.0000000001

Of course, you don't have to perform all of these calculations by hand! Choose the option to determine pH with ion concentration in the calculator and type any of these four values! Then, watch it do all the work for you!

1. Alternatively, you can find a chemical from the lists (of acids or bases). Let's say you want to know how to find the pH of formic acid - HCOOH. Its Ka is 0.00018.
2. Choose the concentration of the chemical. Let’s assume that it's equal to 0.1 mol/l.
3. In order to find a concentration of H+ ions you have to...:

HCOOH = HCOO- + H+

Ka = [H+]*[HCOO-]/[HCOOH]

where

Ka = x2/(c - x), where

• c is the molar concentration of the solution
• x is equal to molar concentration of H+

For 0.1 M HCOOH:

[H+] = 0.004154

pH = -log([H+]) = -log(0.004154) = 2.38

Now you know how to calculate pH using pH equations. If you find these calculations time-consuming feel free to use our pH calculator. Select your chemical and its concentration and watch it do all the work for you. When you're finished, check out the titration calculator!

Julia Żuławińska
To calculate the pH of a buffer, go to the buffer pH calculator!
I want calculate the pH from..
concentration of an acid
Acid:
hydrochloric acid - HCl
Concentration
M
Result
pH
[H⁺]
M
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