pH Calculator: Convert H+ Concentration to pH Value Online

What is a pH value calculator?

A pH value calculator converts hydrogen ion concentration into a pH value. It uses the formula pH = -log10([H+]), where [H+] is the concentration of hydrogen ions in a solution, measured in moles per liter (mol/L). The result places a solution on the pH scale, which normally runs from 0 to 14 and shows whether the solution is acidic, neutral, or basic.

What is pH?

pH stands for "power of hydrogen." It measures how many hydrogen ions are dissolved in a liquid. A hydrogen ion is a single proton, written as H+. A solution with many hydrogen ions is acidic. A solution with few hydrogen ions is basic, also called alkaline. Pure water sits in the middle, at pH 7, and is called neutral.

Hydrogen ion concentration is usually a very small number, such as 0.0001 mol/L or 0.0000001 mol/L. The Danish chemist Søren Sørensen introduced the pH scale in 1909 so chemists could write these small numbers as simple, manageable values instead.

pH formula

The formula for pH is:

pH = -log₁₀[H+]

• pH is the result, usually a number between 0 and 14.
• [H+] is the hydrogen ion concentration, in moles per liter (mol/L).
• log₁₀ is the base-10 logarithm.

The minus sign flips the logarithm, so more hydrogen ions give a lower pH, and fewer hydrogen ions give a higher pH. The relationship always runs in opposite directions: a higher [H+] means a lower pH, and a lower [H+] means a higher pH.

Because the formula is a logarithm, each whole step on the pH scale is a tenfold change in hydrogen ion concentration. A solution at pH 4 has ten times more hydrogen ions than one at pH 5, and one hundred times more than one at pH 6.

How to calculate pH from hydrogen ion concentration

1. Find the hydrogen ion concentration, in mol/L.
2. Take the base-10 logarithm of that number.
3. Multiply the result by -1.

Example 1

A solution has a hydrogen ion concentration of 1 × 10⁻⁴ mol/L.

pH = -log₁₀(1 × 10⁻⁴) = -(-4) = 4.00

The solution is acidic, because its pH is below 7.

Example 2

A solution has a hydrogen ion concentration of 6.3 × 10⁻⁵ mol/L.

pH = -log₁₀(6.3 × 10⁻⁵) ≈ 4.20

This solution is also acidic. It is slightly less acidic than the pH 4.00 solution above, because it has fewer hydrogen ions.

The pH scale: acidic, neutral, and basic

• pH below 7: acidic solution (more hydrogen ions)
• pH equal to 7: neutral solution (pure water at 25°C)
• pH above 7: basic, or alkaline, solution (fewer hydrogen ions)

The scale is usually shown from 0 to 14, though it has no fixed lower or upper limit. Very concentrated acids can fall below 0, and very concentrated bases can rise above 14.

A higher pH number always means a lower hydrogen ion concentration, not a higher one. For example, a solution at pH 4.05 has fewer hydrogen ions, about 8.9 × 10⁻⁵ mol/L, than a solution at pH 4.00, which has 1.0 × 10⁻⁴ mol/L. This matters when checking a pH electrode against a reference buffer. If a meter reads pH 4.05 instead of an expected pH 4.00 buffer, it is registering slightly fewer hydrogen ions than the buffer actually contains, and the electrode may need recalibration.

Frequently asked questions

How do you calculate pH from hydrogen ion concentration?

Take the base-10 logarithm of the hydrogen ion concentration in mol/L, then multiply by -1. For [H+] = 1 × 10⁻⁵ mol/L, pH = -log₁₀(10⁻⁵) = 5.00.

What is the difference between pH and hydrogen ion concentration?

They describe the same property in two forms. [H+] is a concentration, in mol/L. pH is its negative base-10 logarithm. The pH scale turns very small concentration numbers into simple values, roughly between 0 and 14.

Does a higher pH mean more or fewer hydrogen ions?

Fewer. Because of the minus sign in the formula, pH and hydrogen ion concentration move in opposite directions. A higher pH always corresponds to a lower [H+], and a lower pH always corresponds to a higher [H+].

Can pH be negative or higher than 14?

Yes, though it is uncommon. Very concentrated acids can have a pH below 0, and very concentrated bases can have a pH above 14. Most everyday solutions fall between 0 and 14.

What is the pH of pure water?

Pure water has a pH of 7.00 at 25°C, with a hydrogen ion concentration of 1 × 10⁻⁷ mol/L. This is defined as neutral, halfway between acidic and basic on the standard scale.

Does temperature affect the pH calculation?

The formula pH = -log₁₀[H+] does not change with temperature. But the hydrogen ion concentration of neutral water does shift with temperature, so the pH value that counts as neutral moves slightly away from 7.00 at temperatures other than 25°C.