Quick answer
pH = −log₁₀[H⁺] and pH + pOH = 14 at 25 °C. A hydrogen-ion concentration of 0.001 M gives pH 3, pOH 11 and [OH⁻] = 10⁻¹¹ M.
Choose whether you start from [H⁺], [OH⁻], pH or pOH and enter the value. The calculator returns all four.
Related tools: Molar Mass Calculator: Molar mass and mass percent composition of a chemical formula. Mole Calculator: Convert between mass, moles and number of particles. Percent Yield Calculator: Percent yield of a reaction.
How to use the pH Calculator
- Choose start from: From [H⁺] (mol/L), From [OH⁻] (mol/L) and From pH.
- Enter value.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Start from | Choose one: From [H⁺] (mol/L); From [OH⁻] (mol/L); From pH | Starts at From [H⁺] (mol/L) |
| Value | A number | — |
Formula and method
Formula
pH = −log₁₀[H⁺]; pH + pOH = 14
IEEE-754 double precision; shown to the decimals indicated.
Assumes 25 °C, where K_w = 10⁻¹⁴; ideal solutions.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Start from = From [H⁺] (mol/L); Value = 0.001.
| Result | Value |
|---|---|
| pH | 3 |
| pOH | 11 |
| [H⁺] | 1.0000e-3 M |
| [OH⁻] | 1.0000e-11 M |
Example 2
Inputs: Start from = From [OH⁻] (mol/L); Value = 0.0001.
| Result | Value |
|---|---|
| pH | 10 |
| pOH | 4 |
| [H⁺] | 1.0000e-10 M |
| [OH⁻] | 1.0000e-4 M |
Example 3
Inputs: Start from = From pH; Value = 4.5.
| Result | Value |
|---|---|
| pH | 4.5 |
| pOH | 9.5 |
| [H⁺] | 3.1623e-5 M |
| [OH⁻] | 3.1623e-10 M |
The first line is the headline result (pH). Below it the pH Calculator lists pOH, [H⁺] and [OH⁻], which describe the same case from other angles. IEEE-754 double precision; shown to the decimals indicated.
Worked example
−log₁₀(0.001) = 3. Then pOH = 14 − 3 = 11 and [OH⁻] = 10⁻¹¹ M. Each pH unit is a factor of 10 in hydrogen-ion concentration, so pH 3 is 100 times more acidic than pH 5.
Typical values
Lemon juice is about 2, pure water 7, blood 7.4 and bleach 12.5. Concentrations must be positive, and pH values outside 0 to 14 are possible for very strong acids or bases. The sum of 14 applies at 25 °C.
How the result changes with value
Holding every other input at the first worked example, this table changes only value. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Value | pH | pOH | [H⁺] |
|---|---|---|---|
| 0.0005 | 3.301 | 10.699 | 5.0000e-4 M |
| 0.001 | 3 | 11 | 1.0000e-3 M |
| 0.002 | 2.699 | 11.301 | 2.0000e-3 M |
| 0.004 | 2.3979 | 11.6021 | 4.0000e-3 M |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Value: entering "0" shows "Concentration must be greater than zero." beside that field and no result.
Choosing between the pH Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Molar Mass Calculator](/science/molar-mass-calculator/) | chemical formula | Molar mass |
| [Mole Calculator](/science/mole/) | start from and molar mass | Amount |
| [Percent Yield Calculator](/science/percent-yield/) | actual yield and theoretical yield | Percent yield |
| [Electron Configuration Calculator](/science/electron-configuration/) | element and charge | Electron configuration of H |
| [Dilution Calculator](/science/dilution-ratio/) | solve for | Final volume V₂ |
Background: chemistry calculations
Most basic chemistry calculations chain three relations: moles n = mass ÷ molar mass, molarity M = n ÷ volume in litres, and dilution C₁V₁ = C₂V₂. Keep units consistent: grams with g/mol, litres with mol/L.
Molar masses come from standard atomic weights, which differ slightly between tables and with the isotopic make-up of a real sample.
Assumptions and limitations
- Concentrations must be positive; pH between 0 and 14 is typical
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for value to confirm this.
Frequently asked questions
What is neutral pH?
Pure water at 25 °C has pH 7, where [H⁺] = [OH⁻] = 10⁻⁷ M; neutral pH shifts slightly with temperature.
Is pH 3 acidic?
Yes. pH 3 is acidic, with [H⁺] = 10⁻³ M, 10,000 times more acidic than neutral water.
How do I find [H⁺] from pH?
10 to the power of −pH.
What does the pH Calculator calculate?
pH, pOH and ion concentrations at 25 °C. It returns pH, pOH, [H⁺] and [OH⁻].
What formula does the pH Calculator use?
pH = −log₁₀[H⁺]; pH + pOH = 14. Assumes 25 °C, where K_w = 10⁻¹⁴; ideal solutions.
What do I need to enter in the pH Calculator?
You enter Start from and Value.
How is the result rounded or limited?
IEEE-754 double precision; shown to the decimals indicated. Concentrations must be positive; pH between 0 and 14 is typical.
What does the “Start from” option change?
It sets how the pH is worked out. The choices are From [H⁺] (mol/L), From [OH⁻] (mol/L) and From pH.
What is an example of a pH result?
With start from From [H⁺] (mol/L) and value 0.001, the pH is 3.
Where does the method come from?
The method follows: IUPAC definition of pH (concentration approximation).
Related calculators
- Molar Mass Calculator — Molar mass and mass percent composition of a chemical formula.
- Mole Calculator — Convert between mass, moles and number of particles.
- Percent Yield Calculator — Percent yield of a reaction.
- Electron Configuration Calculator — Ground-state electron configuration of an element or monatomic ion, with noble-gas shorthand and unpaired electrons.
- Molarity Calculator — Concentration of a solution from solute mass, molar mass and volume.
Sources
- IUPAC definition of pH (concentration approximation)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.