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Short answer: for a strong monoprotic acid that dissociates completely, the hydrogen ion concentration equals the molarity, so pH = −log10(molarity). A 0.01 M solution of hydrochloric acid has a pH of 2.00; a 0.1 M solution has a pH of 1.00. For a strong base you take the negative log of the hydroxide concentration to get pOH, then subtract from 14 (at 25 °C).
The pH formula
The U.S. EPA defines pH as the negative logarithm of the hydrogen ion (H+) concentration, in mol/L, in an aqueous solution: pH = −log10[H+]. The scale usually runs from 0 to 14, with 7 neutral, below 7 acidic and above 7 basic. Because the scale is logarithmic, each one-unit change in pH is a tenfold change in hydrogen ion concentration (EPA CADDIS, pH, https://www.epa.gov/caddis/ph; USGS Water Science School, pH and Water, https://www.usgs.gov/special-topics/water-science-school/science/ph-and-water; both checked 2026-10-29).
Molarity is moles of solute per litre of solution. If you need to get there from grams, see converting moles to molarity, the worked molarity and solution calculations for the lab, and NaOH molarity. For the difference between the two quantities that are often confused, see moles vs molarity.
Assumptions behind the shortcut
- The acid or base is strong and dissociates completely, so [H+] (or [OH−]) equals the molarity multiplied by the number of H+ or OH− each formula unit releases.
- Concentration stands in for activity. EPA notes that a pH meter responds to hydrogen ion activity, not concentration, so a calculated value and a meter reading will not match exactly, especially in concentrated solutions.
- The relationship pH + pOH = 14 holds at 25 °C (Purdue University General Chemistry Help, “Calculating pH and pOH”, checked 2026-10-29).
- This page covers strong acids and bases. Weak acids and bases only partly dissociate and need an equilibrium constant, which is outside this table.
Molarity to pH table
Values are computed from the formulas above and rounded to two decimal places. The acid column assumes a strong monoprotic acid such as HCl; the base column assumes a strong monohydroxide base such as NaOH, at 25 °C.
| Molarity (mol/L) | Strong acid pH | Strong base pH |
|---|---|---|
| 1 | 0.00 | 14.00 |
| 0.1 | 1.00 | 13.00 |
| 0.05 | 1.30 | 12.70 |
| 0.01 | 2.00 | 12.00 |
| 0.005 | 2.30 | 11.70 |
| 0.001 | 3.00 | 11.00 |
| 0.0001 | 4.00 | 10.00 |
| 0.00001 | 5.00 | 9.00 |
| 0.000001 | 6.00 | 8.00 |
Worked examples
Example 1: strong acid
What is the pH of 0.025 M nitric acid (HNO3)?
- Nitric acid is a strong monoprotic acid, so [H+] = 0.025 mol/L.
- pH = −log10(0.025) = 1.602.
- Rounded to two decimal places, the pH is 1.60.
Example 2: strong base that releases two hydroxide ions
What is the pH of 0.010 M barium hydroxide, Ba(OH)2?
- Each formula unit releases two OH−, so [OH−] = 2 × 0.010 = 0.020 mol/L.
- pOH = −log10(0.020) = 1.699, or 1.70.
- pH = 14 − 1.70 = 12.30 (at 25 °C).
The same multiplication applies to acids that release more than one H+ per formula unit when they dissociate fully; check that the acid really dissociates fully before multiplying.
Calculate pH from molarity in Excel, R or Python
| Tool | pH of a strong acid | pH of a strong base |
|---|---|---|
| Excel / Sheets (molarity in A1) | =-LOG10(A1) |
=14+LOG10(A1) |
| R | -log10(m) |
14 + log10(m) |
| Python | -math.log10(m) |
14 + math.log10(m) |
For a base that releases two hydroxide ions, multiply the molarity by 2 first, for example =14+LOG10(2*A1). In Python, run import math first.
How to calculate molarity
Molarity = moles of solute ÷ litres of solution. To get moles from a weighed mass, divide the mass in grams by the molar mass in g/mol. Then divide by the final solution volume in litres, not the volume of solvent added. For the full routine, see mol to molarity. Once you have the molarity, apply the table above.
Why a pH meter reading can differ from your calculation
The calculation uses concentration, while a meter responds to hydrogen ion activity (EPA CADDIS). Calibration and electrode condition also matter; see pH meter calibration and buffer selection. Solutions in aqueous media that contain buffers behave differently from the strong-acid case; see buffer and solution preparation.
Safety note: read the SDS first
Strong acids and strong bases are corrosive. Before preparing or handling a solution, read the supplier’s Safety Data Sheet (SDS) for the specific chemical and follow it and your laboratory’s own procedures for protective equipment and diluting. The pH arithmetic on this page tells you nothing about hazards.
Frequently asked questions
How do you calculate molarity?
Divide moles of solute by litres of solution. Moles are mass in grams divided by molar mass.
Does molarity equal the hydrogen ion concentration?
Only for a strong monoprotic acid that dissociates completely. For acids that release more than one H+, or for weak acids, the hydrogen ion concentration differs.
How do I calculate pH from molarity for a base?
Take pOH = −log10[OH−], then pH = 14 − pOH at 25 °C.
Why does a tenfold dilution change pH by exactly 1?
pH is a base-10 logarithm, so each tenfold change in hydrogen ion concentration changes pH by one unit (EPA CADDIS).
Sources
- U.S. EPA, CADDIS: pH, https://www.epa.gov/caddis/ph (checked 2026-10-29).
- USGS Water Science School, pH and Water, https://www.usgs.gov/special-topics/water-science-school/science/ph-and-water (checked 2026-10-29).
- Purdue University, General Chemistry Help, Calculating pH and pOH, https://www.chem.purdue.edu/gchelp/howtosolveit/Equilibrium/Calculating_pHandpOH.htm (checked 2026-10-29).
