pH stands for "power of hydrogen" and equals −log₁₀[H⁺]. It measures the hydrogen ion activity in a solution on a scale typically from 0 to 14.

Can pH go below 0 or above 14?

Yes. Concentrated strong acids can have negative pH (e.g., 10 M HCl has pH ≈ −1), and concentrated strong bases can exceed 14.

Why is pH logarithmic?

Because hydrogen ion concentrations span 14 orders of magnitude (from 1 to 10⁻¹⁴ M). A logarithmic scale makes these values practical to work with.

Kw is the ion product of water: Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25°C. It increases with temperature (about 10⁻¹³ at 60°C).

Does temperature affect pH?

Yes. Water's Kw increases with temperature, so neutral pH drops below 7 at higher temperatures. At 37°C (body temperature), neutral pH is about 6.8.

What is the difference between pH and pOH?

pH measures acidity ([H⁺]), while pOH measures basicity ([OH⁻]). They always sum to pKw, which is 14 at 25°C.

Hydrogen Ion Concentration Calculator

Convert between pH, [H⁺], and [OH⁻]. Calculate hydrogen and hydroxide ion concentrations from pH or vice versa.

Common Substances

Input Mode:

pH Value

7.0000

Negative log of hydrogen ion concentration: pH = −log₁₀[H⁺].

pOH

7.0000

pOH = 14 − pH. Measures hydroxide ion activity.

[H⁺] (M)

1.0000e-7

Hydrogen ion concentration in moles per liter.

[OH⁻] (M)

1.0000e-7

Hydroxide ion concentration from Kw = [H⁺][OH⁻] = 10⁻¹⁴.

Solution Nature

Neutral

pH = 7 = neutral.

[H⁺] vs. Pure Water

1.00×

How many times more (or fewer) H⁺ ions compared to pure water.

pH Position on Scale

0 (Acid)7 (Neutral)14 (Base)

pH Scale Reference

pH	[H⁺] (M)	Nature	Example
0	1	Acidic	Battery acid
1	0.1	Acidic	Gastric acid
2	0.01	Acidic	Lemon juice
3	0.001	Acidic	Vinegar
5	1×10⁻⁵	Acidic	Black coffee
7	1×10⁻⁷	Neutral	Pure water
8	1×10⁻⁸	Basic	Sea water
10	1×10⁻¹⁰	Basic	Milk of magnesia
12	1×10⁻¹²	Basic	Soapy water
14	1×10⁻¹⁴	Basic	Drain cleaner

Planning notes, formulas, and examples

About the Hydrogen Ion Concentration Calculator

The hydrogen ion concentration [H⁺] is the master variable that defines the acidity or basicity of every aqueous solution. The pH scale, defined as pH = −log₁₀[H⁺], compresses the enormous range of possible hydrogen ion concentrations (from about 1 M in strong acid to 10⁻¹⁴ M in strong base) into a manageable 0–14 scale that chemists and biologists use daily.

Understanding the relationship between pH, [H⁺], and [OH⁻] is critical in virtually every branch of science. In biochemistry, enzyme activity depends on precise pH; a shift of just 0.1 pH units can alter reaction rates by 25% or more. In environmental science, even small changes in water pH affect aquatic ecosystem health. In medicine, blood pH must be maintained between 7.35 and 7.45, with deviations causing acidosis or alkalosis.

This calculator converts freely between pH, [H⁺], and [OH⁻], using the water autoionization constant Kw = [H⁺][OH⁻] = 10⁻¹⁴ at 25°C. Enter any one value and quickly get all the others, along with a visual pH scale showing where your solution falls and a reference table of common substances.

When This Page Helps

Converting between pH and molar concentrations requires logarithmic calculations that are easy to get wrong, especially with scientific notation. This calculator does it quickly and shows the context of where your solution sits on the acid-base spectrum.

How to Use the Inputs

Select your input mode: pH, [H⁺] concentration, or [OH⁻] concentration.
Enter the known value (pH as a number, concentrations in M).
Or click a preset button for a common substance.
Read pH, pOH, [H⁺], and [OH⁻] from the output cards.
See where the solution falls on the color-coded pH scale.
Compare with common substances in the reference table.

Formula used

pH = −log₁₀[H⁺]. pOH = −log₁₀[OH⁻]. pH + pOH = 14 (at 25°C). [H⁺] = 10^(−pH). [OH⁻] = Kw/[H⁺] = 10⁻¹⁴/[H⁺].

Example Calculation

Result: [H⁺] = 0.01 M, [OH⁻] = 1×10⁻¹² M

[H⁺] = 10^(−2) = 0.01 M. pOH = 14 − 2 = 12. [OH⁻] = 10^(−12) = 1×10⁻¹² M. This is 100,000 times more acidic than pure water.

Tips & Best Practices

Remember: each pH unit represents a 10-fold change in [H⁺] concentration.
Body pH is very tightly regulated — normal blood pH has only a 0.1 unit range (7.35–7.45).
pH measurements are temperature-dependent; always calibrate your pH meter at the measurement temperature.
For very dilute or very concentrated solutions, pH = −log[H⁺] becomes approximate; activity coefficients matter.
In non-aqueous solvents, pH is defined differently and the 0–14 scale does not apply.

The pH Scale in Historical Context

The pH concept was introduced by Danish chemist Søren Sørensen in 1909 while working at the Carlsberg Laboratory in Copenhagen. He needed a convenient way to express hydrogen ion concentrations during enzyme studies. The original definition used the hydrogen electrode; modern pH meters use glass electrodes calibrated against standard buffers.

Biological Significance of [H⁺]

Living systems maintain exquisitely tight pH control. Blood plasma has a pH of 7.35–7.45; deviation by just 0.2 units can be life-threatening. The stomach operates at pH 1.5–3.5 to denature proteins and kill bacteria. Lysosomes maintain pH ~4.5 for acidic hydrolase activity. Each organelle has its own optimal pH, maintained by proton pumps and buffers.

Strong vs. Weak Acid pH Calculations

For strong acids that fully dissociate, [H⁺] equals the acid concentration: 0.01 M HCl has [H⁺] = 0.01 M and pH = 2.0. For weak acids, the calculation requires the Ka equilibrium: [H⁺] = √(Ka × C) for dilute solutions. This calculator works with the final [H⁺] regardless of whether it came from a strong or weak acid.

Sources & Methodology

Last updated: June 1, 2026

Frequently Asked Questions

pH stands for "power of hydrogen" and equals −log₁₀[H⁺]. It measures the hydrogen ion activity in a solution on a scale typically from 0 to 14.