pH, pOH, H⁺ and OH⁻ Calculator

This calculator converts between pH, pOH, hydrogen-ion concentration (H⁺), and hydroxide-ion concentration (OH⁻) for an aqueous solution at 25 °C. Enter one value in the matching field; it returns the other three, using the ideal dilute-solution relationships and concentrations in mol/L.

Formula

The defining relationships are pH = −log₁₀[H⁺] and pOH = −log₁₀[OH⁻], where the concentration brackets represent molar concentration in mol/L. At 25 °C in dilute water, pH + pOH = 14.00, so [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ (mol/L)². The calculator’s four inputs are independent fields for convenience; use the one matching the value you know. Each output is calculated from its corresponding input, rather than reconciling conflicting entries.

For a pH input, [H⁺] = 10^−pH mol/L; for a pOH input, [OH⁻] = 10^−pOH mol/L. To convert from a concentration, take its negative base-10 logarithm. These formulas assume activity is adequately approximated by concentration, as is often reasonable for dilute solutions. Strictly, pH is defined using hydrogen-ion activity, not simply concentration.

Worked Example

Using the default values, pH = 7, pOH = 7, [H⁺] = 0.0000001 mol/L, and [OH⁻] = 0.0000001 mol/L:

• pH from [H⁺]: −log₁₀(0.0000001) = 7.00.
• pOH from [OH⁻]: −log₁₀(0.0000001) = 7.00.
• [H⁺] from pH: 10⁻⁷ = 0.0000001 mol/L, displayed to three decimal places in mol/L as 0.000.
• [OH⁻] from pOH: 10⁻⁷ = 0.0000001 mol/L, displayed to three decimal places in mol/L as 0.000.

The last two displayed outputs illustrate why fixed decimal places are unsuitable for tiny concentrations: rounding to three decimal places hides the actual nonzero value. Read those results as 1.00 × 10⁻⁷ mol/L; the calculator should display very small values in scientific notation. The pH and pOH outputs remain useful at the selected precision.

Assumptions

• Aqueous solution at 25 °C, where pH + pOH = 14.00 is the conventional approximation.
• Dilute-solution behavior, with activities approximated by concentrations.
• The entered concentration is a positive molar concentration. A concentration of exactly zero has no finite logarithmic pH or pOH.
• This is a conversion calculator, not a model of chemical equilibria, buffer capacity, or the composition of a particular sample.

How to Use the Calculator

Choose the field that corresponds to your known measurement or calculated value. For example, if you know pH 3.20, enter 3.20 in the pH field. The corresponding hydrogen-ion concentration is 10^−3.20 = 6.31 × 10⁻⁴ mol/L. The hydroxide concentration can be found from pOH = 14.00 − 3.20 = 10.80, giving [OH⁻] = 10^−10.80 = 1.58 × 10⁻¹¹ mol/L under the stated assumptions.

For a concentration input, enter mol/L, not mmol/L, µmol/L, or a mass concentration such as mg/L. Convert first: 1 mmol/L = 0.001 mol/L, and 1 µmol/L = 0.000001 mol/L. If you have a mass concentration, you also need the substance’s molar mass to convert it to mol/L. A mass-per-volume value alone is not a hydrogen- or hydroxide-ion concentration.

The input fields are separate because a single known quantity is normally enough to calculate the others. They are not a consistency checker: entering different values in all four fields can produce outputs that do not agree with one another. Enter one known value at a time, and check the returned values against the 25 °C relationship pH + pOH = 14.00 when that approximation applies.

How pH and pOH Relate

pH is a logarithmic measure: a change of one pH unit corresponds to a tenfold change in hydrogen-ion activity. Thus, pH 4 is about ten times more acidic in hydrogen-ion concentration than pH 5 under comparable dilute conditions, and about one hundred times more concentrated than pH 6. The pH scale is not a linear concentration scale.

In water, hydrogen and hydroxide ions are linked by water’s ion-product constant, Kw = [H⁺][OH⁻] ≈ 1.0 × 10⁻¹⁴ at 25 °C. This gives pH + pOH ≈ 14.00 for dilute aqueous solutions. Neutrality at 25 °C means equal hydrogen- and hydroxide-ion activities, commonly represented as pH 7.00. Neutral pH is not always 7 at other temperatures because Kw changes with temperature.

Limits, Measurement, and Common Mistakes

The calculator limits pH and pOH inputs to 0–14 and concentration inputs to 0–1 mol/L as a practical range for this basic aqueous calculation. These are calculator bounds, not universal laws: concentrated solutions and values outside the usual range can occur, but the simple dilute-solution interpretation becomes less reliable. A zero concentration is excluded in practice because log₁₀(0) is undefined; enter a positive value supported by the measurement or model.

• Confusing pH with concentration: pH is dimensionless and logarithmic; [H⁺] is a concentration with units.
• Using the wrong logarithm: these formulas use base 10, not the natural logarithm.
• Mixing up pH and pOH: pH describes hydrogen ions; pOH describes hydroxide ions.
• Over-reading rounded results: retain enough significant figures for concentrations and do not interpret 0.000 as a true zero when the unrounded value is tiny.
• Assuming every solution has pH 0–14: that is a useful introductory range, not an absolute boundary for every concentrated or nonaqueous system.

For an actual sample, a calibrated pH meter reading is the real check; temperature and ionic strength shift pH, and the meter measures activity-related behavior rather than directly validating this ideal concentration conversion. Follow your lab method, the safety data sheet (SDS), and your supervisor for any bench work.

Frequently Asked Questions

How do I calculate pH from H⁺ concentration?
Use pH = −log₁₀[H⁺], with [H⁺] expressed in mol/L. For 1.0 × 10⁻⁴ mol/L, pH is 4.00 under the ideal dilute approximation.

How do I calculate pOH from OH⁻ concentration?
Use pOH = −log₁₀[OH⁻], again with concentration in mol/L. For 1.0 × 10⁻⁵ mol/L, pOH is 5.00.

How do I get pH from pOH?
At 25 °C in dilute water, subtract pOH from 14.00: pH = 14.00 − pOH. For pOH 6.00, the estimated pH is 8.00.

Is pH 7 always neutral?
No. It is the conventional neutral value for dilute water at 25 °C. Because water’s ion-product constant changes with temperature, neutral pH can differ from 7 at other temperatures.

Why does the calculated value differ from my pH meter?
The calculator assumes ideal dilute behavior and uses concentration, while pH is defined in terms of activity. Temperature, ionic strength, calibration, sample handling, and the solution’s chemistry can all contribute to a difference; the meter reading is the practical check for the sample.

Related

• Lowest pKa Calculator: Compare Acid Strength
• Tris Buffer pH Calculation: Henderson–Hasselbalch for Tris and Tris-HCl
• pH Calculator From Concentration: pH = −log[H+]

in ph | pH | - | 7 | 0 | 14
in poh | pOH | - | 7 | 0 | 14
in h | Hydrogen-ion concentration [H+] | mol/L | 0.0000001 | 0 | 1
in oh | Hydroxide-ion concentration [OH-] | mol/L | 0.0000001 | 0 | 1
out phcalc | pH | - | -log10(h) | 2
out pohcalc | pOH | -log10(oh) | 2
out hcalc | Hydrogen-ion concentration [H+] | mol/L | 10 ^ (-ph) | 3
out ohcalc | Hydroxide-ion concentration [OH-] | mol/L | 10 ^ (-poh) | 3