Hydrogen Ion Concentration Calculator
Enter any one value - pH, pOH, hydrogen ion concentration [H+], or hydroxide ion concentration [OH-] - and the calculator fills in all the others instantly. You can also enter a temperature to get the Kw value and true neutral point for that temperature, which shifts away from 7.0 at temperatures other than 25 C. The result panel shows whether the solution is acidic, neutral, or basic, gives both concentrations in scientific notation, and walks you through every step of the math.
Formula
Worked example
For a solution with pH 3.5: [H+] = 10^(-3.5) = 3.162 x 10^(-4) mol/L. At 25 C, pOH = 14 - 3.5 = 10.5, so [OH-] = 10^(-10.5) = 3.162 x 10^(-11) mol/L. The product [H+][OH-] = 3.162e-4 x 3.162e-11 = 1.00 x 10^(-14) = Kw, confirming the result.
What is hydrogen ion concentration?
Hydrogen ion concentration, written [H+], is the molar concentration of protons in an aqueous solution, measured in moles per litre (mol/L). In practice, free protons immediately bond with water molecules to form hydronium ions (H3O+), so [H+] and [H3O+] are used interchangeably. Pure water at 25 C has [H+] = 1.00 x 10^(-7) mol/L, meaning about one in every 556 million water molecules is ionised at any given moment. Acids increase [H+] above that baseline by releasing protons; bases decrease it by absorbing protons or releasing hydroxide ions (OH-) that combine with H+.
The pH scale and the connection to [H+]
The pH scale, introduced by Soren Sorensen in 1909, compresses the enormous range of hydrogen ion concentrations - from around 10 mol/L in concentrated acid to 10^(-14) mol/L in strong alkali - into a tidy 0-14 range using the formula pH = -log10[H+]. Because the scale is logarithmic, a one-unit change in pH represents a tenfold change in [H+]: a pH 3 solution has 100 times more hydrogen ions than a pH 5 solution. The neutral point at 25 C is pH 7, where [H+] = [OH-] = 1.00 x 10^(-7) mol/L. Below 7 the solution is acidic (more H+ than OH-), above 7 it is basic or alkaline. Outside the laboratory, pH values below 0 and above 14 are possible in very concentrated strong acids or bases.
pOH, hydroxide ions, and the Kw relationship
The hydroxide ion concentration [OH-] is linked to [H+] through the water ionisation constant Kw: [H+] x [OH-] = Kw. At 25 C, Kw = 1.00 x 10^(-14), which gives pH + pOH = 14 (where pOH = -log10[OH-]). This means knowing any one of the four quantities - pH, pOH, [H+], or [OH-] - lets you calculate the other three. Kw is not a fixed number: it rises with temperature because higher temperatures drive more water molecules to ionise. At 37 C (body temperature) Kw is about 2.4 x 10^(-14), making the neutral pH roughly 6.81. This calculator accepts a temperature input so you can track how the neutral point and Kw shift.
Why temperature changes the neutral pH
Water ionisation (H2O = H+ + OH-) is an endothermic process, so adding heat (raising temperature) shifts the equilibrium toward products and increases Kw. The neutral point is defined as the pH where [H+] = [OH-], i.e., pH = 0.5 x pKw. At 0 C, pKw is about 14.94 and the neutral pH is 7.47; at 50 C, pKw is about 13.26 and the neutral pH is 6.63; at 100 C, pKw drops to around 12.26 and the neutral pH is 6.13. A glass of warm water at pH 6.8 is not acidic - it is neutral for its temperature. This distinction matters in physiology and in industrial processes where solutions are handled well above 25 C.
Common solutions and their typical pH values
| Solution | Typical pH | Classification |
|---|---|---|
| Battery acid / gastric acid | 0-1 | Strong acid |
| Lemon juice / vinegar | 2-3 | Weak-moderate acid |
| Orange juice / coffee | 4-5 | Weak acid |
| Rainwater / milk | 5.5-6.5 | Slightly acidic |
| Pure water at 25 C | 7.00 | Neutral |
| Blood / seawater | 7.4-8.3 | Slightly basic |
| Baking soda solution | 8-9 | Weak base |
| Soap / toothpaste | 9-10 | Moderate base |
| Household ammonia | 11-12 | Strong base |
| Bleach / drain cleaner | 12-14 | Very strong base |
Approximate pH ranges for familiar substances at 25 C. Exact values depend on concentration, temperature, and purity.
Frequently asked questions
How do I convert pH to hydrogen ion concentration?
Use the formula [H+] = 10^(-pH). For example, pH 6.5 gives [H+] = 10^(-6.5) = 3.162 x 10^(-7) mol/L. On a scientific calculator, enter the pH value, change its sign to get -pH, then press the 10^x key (or type 10^(-pH)). This calculator does it instantly.
How do I find pH from hydrogen ion concentration?
Use the formula pH = -log10([H+]). For example, if [H+] = 5.0 x 10^(-4) mol/L, then pH = -log10(5.0 x 10^(-4)) = -(log10(5.0) + log10(10^(-4))) = -(0.699 - 4) = 3.30. Enter the concentration in the [H+] mode of this calculator to get the result in one step.
What is the difference between pH and pOH?
pH measures the hydrogen ion concentration (-log[H+]) and pOH measures the hydroxide ion concentration (-log[OH-]). They are linked by pH + pOH = pKw. At 25 C, pKw = 14, so pH + pOH = 14. A strongly acidic solution with pH 2 has pOH 12, meaning very few hydroxide ions and lots of hydrogen ions.
Why is pH 7 considered neutral?
At 25 C, the ionisation constant of water Kw = 1.00 x 10^(-14). In pure water, [H+] = [OH-], so [H+]^2 = Kw, giving [H+] = 1.00 x 10^(-7) mol/L and pH = 7.00. This balance point is defined as neutral. At other temperatures, Kw changes and so does the neutral pH. At 37 C (body temperature), neutral pH is about 6.81.
Can pH be negative or above 14?
Yes, though it is uncommon outside laboratory settings. Concentrated hydrochloric acid (>1 mol/L) has a pH below 0, and concentrated sodium hydroxide can have a pH above 14. The 0-14 range is a practical guide for dilute aqueous solutions, not a mathematical limit.
How does temperature affect Kw and pH?
Kw increases with temperature because water ionisation is endothermic (absorbs heat). At 25 C, Kw = 1.00 x 10^(-14). At 37 C it is about 2.4 x 10^(-14). The neutral pH (where [H+] = [OH-]) equals 0.5 x pKw, so it shifts from 7.00 at 25 C to about 6.81 at 37 C. A solution at pH 6.81 and 37 C is perfectly neutral, not acidic.
What does [H+] mean in chemistry?
The square brackets [ ] denote molar concentration in mol/L. [H+] is the molar concentration of hydrogen ions (protons) in solution. Because free protons immediately combine with water to form hydronium ions, [H+] and [H3O+] mean the same thing in aqueous chemistry. A value of [H+] = 1 x 10^(-7) mol/L means there is one ten-millionth of a mole of hydrogen ions per litre of solution.