pH Calculator
Convert between pH, pOH, hydrogen-ion concentration, and hydroxide-ion concentration, or estimate the equilibrium pH of a monoprotic weak acid or weak base at 25 °C.
Solution inputs
Live result
Related quantities
| Quantity | Symbol | Value | Unit |
|---|---|---|---|
| Acidity index | pH | 2.3816 | dimensionless |
| Hydrogen-ion concentration | [H⁺] | 4.1536 × 10⁻³ | mol/L |
| Basicity index | pOH | 11.6184 | dimensionless |
| Hydroxide-ion concentration | [OH⁻] | 2.4076 × 10⁻¹² | mol/L |
How to use this pH calculator
What this calculator does
This calculator translates among four closely related aqueous-solution quantities: pH, hydrogen-ion concentration [H⁺], pOH, and hydroxide-ion concentration [OH⁻]. It can also estimate equilibrium pH for a monoprotic weak acid from its analytical concentration and Kₐ, or for a weak base from concentration and Kᵦ. The calculation assumes a dilute ideal aqueous solution at 25 °C, where Kw is 1.0 × 10 – 14. It is an equation-based estimate, not a substitute for a calibrated pH measurement, and it does not model buffers, salts, multiple dissociation steps, activity coefficients, or temperature-dependent Kw. NIST's discussion of pH metrology and traceable measurement explains why laboratory pH is ultimately an operational measurement rather than only a concentration calculation.
When to use it
Use it to check chemistry homework, convert a measured or specified pH into ion concentrations, estimate the starting pH of a dilute weak-acid or weak-base solution, or compare how concentration and ionization constant change equilibrium acidity. It is also useful for preparing a calculation sheet before laboratory work or for reviewing water-chemistry data, while recognizing that real samples may depart from ideal behavior.
How to calculate
- The calculator opens with a complete demonstration: a 0.100 mol/L weak acid with Kₐ = 1.80 × 10 – 4. Results and a validated example workbook are available immediately.
- Choose Calculate from. Select pH, [H⁺], pOH, [OH⁻], weak acid, or weak base. The labels and required fields update to match the selected method.
- Replace the demonstration values. Use decimal points under the en-US convention. Scientific notation such as
1.8e-4is accepted. Concentrations and ionization constants must be positive; pH and pOH may be any finite number because concentrated idealized solutions can fall outside 0 – 14. - Read the live pH, ion concentrations, pOH, classification, and – when applicable – percent ionization. The table repeats the core quantities in a compact export-ready form.
- Select Download Excel to build a fresh workbook from the current validated model. Select Reset to clear the demonstration and all calculated state; Excel export then remains unavailable until a complete valid input set is entered again.
Input guide
Calculate from is required and selects the mathematical path. Choosing pH expects one finite dimensionless value; increasing it lowers [H⁺][H⁺] expects a positive mol/L value, for example 0.001; entering zero is invalid because its logarithm is undefined. The pOH and Hydroxide-ion concentration [OH⁻] modes work analogously. For Weak acid concentration and Kₐ, Analytical concentration (mol/L) is the initial formal concentration, such as 0.1, and Acid ionization constant Kₐ is a positive equilibrium constant such as 0.00018. Larger Kₐ or larger concentration generally increases [H⁺] and lowers pH. For Weak base concentration and Kᵦ, the same concentration field is paired with Base ionization constant Kᵦ; larger Kᵦ generally raises [OH⁻] and pH. A common mistake is entering pKₐ or pKᵦ where Kₐ or Kᵦ is requested.
Output guide
pH is the negative base-10 logarithm of [H⁺][H⁺] and Hydroxide-ion concentration [OH⁻][OH⁻]. Under the 25 °C assumption, pH + pOH = 14. State classifies pH below 7 as acidic, exactly 7 as neutral within display precision, and above 7 as basic. Percent ionization appears for weak-electrolyte modes and reports the calculated dissociated concentration divided by analytical concentration; a high percentage signals that the weak-electrolyte approximation would be poor, which is why this calculator solves the quadratic equation exactly. These are mathematical estimates based on the selected inputs, not recommendations or measured quality grades.
Worked example
For the startup weak-acid example, C = 0.100 mol/L and Kₐ = 0.000180. With x = [H⁺], the equilibrium relation is Kₐ = x²/(C – x). Solving x² + Kₐx – KₐC = 0 gives x = ( – Kₐ + √(Kₐ² + 4KₐC))/2 = 0.0041539 mol/L. Therefore pH = – log₁₀(0.0041536) = 2.3816. Then pOH = 14 – 2.3816 = 11.6184, [OH⁻] = 10 – 11.6184 = 2.4076 × 10 – 12 mol/L, and percent ionization is 0.0041536/0.100 × 100 = 4.1536%.
Understanding the model
The familiar relation pH = – log₁₀[H⁺][H⁺]. The positive quadratic root is retained. The same structure applies to a weak base, but x represents [OH⁻]. An instructional treatment of weak-acid pH calculations with the quadratic equation shows why the exact root is preferable when ionization is not negligible.
pH is logarithmic: changing pH by one unit corresponds to a tenfold change in hydrogen-ion activity under comparable conditions. In environmental work, pH affects chemical speciation and biological processes; the U.S. EPA's pH overview for aquatic systems explains several causal pathways and biological consequences. Use measured, temperature-appropriate, matrix-specific data whenever a decision depends on actual water, food, clinical, or industrial conditions.