pH Calculator
Calculate the pH and pOH of a solution from its hydrogen ion (H⁺) or hydroxide ion (OH⁻) concentration. Enter the molar concentration and an optional temperature to get pH, pOH and pKw.
Find pH and pOH from Ion Concentration
pH Formula
Where:
- \([\mathrm{H^+}]\) — hydrogen (hydronium) ion concentration in mol/L
- \([\mathrm{OH^-}]\) — hydroxide ion concentration in mol/L
- \(\mathrm{p}K_w\) — ion product constant of water \((-\log_{10}K_w)\)
- \(T\) — temperature in °C
The pH is the negative base-10 logarithm of the hydrogen ion concentration. Because \(\mathrm{pH} + \mathrm{pOH} = \mathrm{p}K_w\), knowing either ion concentration and the temperature fixes both values.
pH – Calculation Example
Example: a solution has a hydrogen ion concentration of \(0.0001\) mol/L (\(10^{-4}\) mol/L) at 25 °C.
\[ \mathrm{pH} = -\log_{10}(10^{-4}) = 4.000 \]
\[ \mathrm{p}K_w = 14.94 - 0.04209 \times 25 + 0.0001711 \times 25^2 \approx 13.995 \]
\[ \mathrm{pOH} = 13.995 - 4.000 = 9.995 \]
Result: pH = 4.000, pOH = 9.995, pKw ≈ 13.995. The solution is acidic (pH < 7).
How to Use the pH Calculator
- In the Known Ion dropdown, select whether you measured the hydrogen ion (H⁺ / H₃O⁺) or the hydroxide ion (OH⁻).
- Enter the Ion Concentration value, e.g. 0.0001.
- Pick the matching Unit (mol/L, mmol/L, µmol/L or nmol/L) — the calculator converts it to mol/L automatically.
- Optionally set the Temperature and its unit (°C or °F). If left empty, 25 °C is assumed, giving pKw ≈ 14.00.
- Read the results: pH, pOH, pKw at This Temperature, and whether the solution is acidic, basic or neutral.
What Is pH and What Does the Result Mean?
pH measures how acidic or basic (alkaline) an aqueous solution is. It is defined as the negative logarithm of the hydrogen ion activity; for dilute solutions, the concentration \([\mathrm{H^+}]\) is an excellent approximation. Because the scale is logarithmic, each whole pH unit represents a tenfold change in acidity: a solution of pH 3 has ten times more H⁺ ions than one of pH 4, and a hundred times more than pH 5.
The pOH is the mirror image of pH: it expresses the hydroxide ion concentration the same way. The two are linked through the ion product of water, \(K_w = [\mathrm{H^+}][\mathrm{OH^-}]\), so \(\mathrm{pH} + \mathrm{pOH} = \mathrm{p}K_w\). At 25 °C, \(\mathrm{p}K_w \approx 14\), which is why pH 7 is called neutral at room temperature: \([\mathrm{H^+}] = [\mathrm{OH^-}] = 10^{-7}\) mol/L.
Interpreting the result: pH below 7 means the solution is acidic, pH above 7 means it is basic, and pH exactly 7 means neutral — but only at that temperature. The pKw of water changes with temperature (about 14.94 at 0 °C, 13.26 at 60 °C), so pure water is neutral at pH ≈ 6.14 near 100 °C, not pH 7. That is why the calculator asks for temperature and reports the pKw it used.
Assumptions, Limitations and Practical Tips
- Concentration vs. activity: the calculator uses molar concentrations. In concentrated solutions (above roughly 0.1 mol/L of dissolved salts), ionic interactions make the true pH differ from the value computed here; a pH meter measures activity directly.
- Temperature model: the empirical pKw formula is accurate from 0 to 60 °C and still reasonable up to 100 °C. Values above 60 °C are approximate.
- Strong vs. weak electrolytes: entering an analytical (total) concentration assumes the ion is fully dissociated. For weak acids and bases, or for buffered mixtures, first determine the equilibrium concentration — our Acetate Buffer Composition calculator can help with buffer systems.
- Unit shortcuts: 0.0001 mol/L can be entered as 100 µmol/L or 0.1 mmol/L — pick whichever unit you have and the conversion is handled for you.
- Dilution problems: if your concentration comes from diluting a stock solution, use the C1V1 = C2V2 dilution calculator first, then feed the result here.
- Spectrophotometry: if you determine concentrations from absorbance measurements, the Beer–Lambert Law calculator pairs well with this tool.
Quick Reference: pH of Common Substances
| Substance | Approximate pH |
|---|---|
| Gastric acid | 1–2 |
| Lemon juice | 2–3 |
| Black coffee | 5 |
| Pure water (25 °C) | 7 |
| Seawater | 8 |
| Baking soda solution | 9 |
| Household ammonia | 11–12 |
| Drain cleaner (NaOH) | 13–14 |
These are typical ranges at room temperature; actual values depend on concentration and purity.
Frequently Asked Questions
How do I calculate pH by hand without a calculator?
Take the hydrogen ion concentration in mol/L and find the negative base-10 logarithm: \( \mathrm{pH} = -\log_{10}[\mathrm{H^+}] \). For powers of ten this is easy: \( 10^{-3} \) mol/L gives pH 3, \( 10^{-9} \) mol/L gives pH 9. For other values, write the number in scientific notation and use \( \log(ab) = \log a + \log b \). For example, \( 5 \times 10^{-4} \) mol/L gives \( \mathrm{pH} = 4 - \log 5 \approx 3.30 \).
Can pH be negative or higher than 14?
Yes. The 0–14 range is just what typical dilute solutions cover, not a hard limit. A 10 mol/L strong acid has \( \mathrm{pH} = -\log_{10}(10) = -1 \), and a 10 mol/L strong base exceeds pH 15. Very acidic mine runoff and concentrated battery acid have negative pH values. Note, however, that at such high concentrations activity effects make the concentration-based calculation less accurate than a direct measurement.
How do I convert a pH value back to a concentration?
Invert the definition: \( [\mathrm{H^+}] = 10^{-\mathrm{pH}} \) mol/L. A pH of 5.5 corresponds to \( 10^{-5.5} \approx 3.2 \times 10^{-6} \) mol/L, or about 3.2 µmol/L. For hydroxide, use \( [\mathrm{OH^-}] = 10^{-\mathrm{pOH}} \) with \( \mathrm{pOH} = \mathrm{p}K_w - \mathrm{pH} \). This is useful when checking whether an answer or a meter reading is plausible.
What is a 'good' or normal pH value?
It depends entirely on context. Drinking water is typically regulated around pH 6.5–8.5, healthy blood is tightly held near pH 7.4, and soil for most crops lies between 6 and 7.5. There is no universally good pH — an acid pickling bath and an alkaline cleaning solution are both 'correct' at very different values. If you are checking a health-related value such as blood or urine pH, consult a medical professional rather than self-diagnosing from a number.
Why is my calculated pH different from what my pH meter shows?
The two measure slightly different things. This calculator uses the molar concentration, while a meter responds to the hydrogen ion activity, which differs in solutions with appreciable salt content (above roughly 0.1 mol/L). Meter calibration error, electrode drift, and temperature compensation also cause deviations. For dilute solutions of strong acids and bases, the calculated and measured values should agree within a few hundredths of a pH unit.
Can I enter the concentration of my acid or base solution directly?
Only for strong, fully dissociated electrolytes — for example, a 0.01 mol/L HCl solution really does contain 0.01 mol/L of H⁺. A weak acid like acetic acid only partially dissociates, so a 0.01 mol/L solution has far less H⁺ than 0.01 mol/L and the true pH is higher. For weak acids and bases you must first compute the equilibrium concentration using the acid's \( K_a \) (or the base's \( K_b \)), then enter that value here.
Does H⁺ or H₃O⁺ matter — which one should I use?
Either — they are used interchangeably in this context. Free protons do not exist alone in water; they bond to water molecules forming hydronium (H₃O⁺). Chemists write both \( [\mathrm{H^+}] \) and \( [\mathrm{H_3O^+}] \) to mean the same quantity, and the pH formula gives identical results. Simply enter the molar concentration of whichever form your data or textbook reports.