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To get molarity from pH, raise 10 to the power of minus pH: [H+] = 10−pH mol/L. A solution at pH 8.5 therefore has a hydrogen ion concentration of about 3.2 × 10−9 M. That number is the molarity of hydrogen ions, not automatically the molarity of the acid or base you dissolved, and the difference is where most mistakes happen. This guide gives the formula, a lookup table, worked examples, and code for Excel, R and Python.
The formula: [H+] = 10−pH
pH is defined as the negative base-10 logarithm of the hydrogen ion concentration, pH = −log[H+]. Inverting it gives [H+] = 10−pH, with the result in mol/L (molarity, M). This is the form used in the Windward Community College biochemistry text on LibreTexts (checked 2026-10-29), which also gives the worked case pH 9.14 → [H+] = 7.24 × 10−10 M.
Because the scale is logarithmic, each whole pH unit is a tenfold change. The USGS Water Science School (checked 2026-10-29) puts it this way: each number represents a 10-fold change in the acidity or basicness of the water, so pH 5 is ten times more acidic than pH 6. In concentration terms, going down one pH unit multiplies [H+] by 10.
pH to molarity table
The table lists [H+] = 10−pH and [OH−] = 10−14 / [H+], both in mol/L. Whole-number rows are exact powers of ten; half-unit rows are rounded to three significant figures. The 10−14 ion-product value is the one used in the LibreTexts examples cited above, which treat it as a constant for the calculation.
| pH | [H+] (M) | [OH−] (M) |
|---|---|---|
| 0.0 | 1.00 | 1.00 × 10−14 |
| 0.5 | 3.16 × 10−1 | 3.16 × 10−14 |
| 1.0 | 1.00 × 10−1 | 1.00 × 10−13 |
| 1.5 | 3.16 × 10−2 | 3.16 × 10−13 |
| 2.0 | 1.00 × 10−2 | 1.00 × 10−12 |
| 2.5 | 3.16 × 10−3 | 3.16 × 10−12 |
| 3.0 | 1.00 × 10−3 | 1.00 × 10−11 |
| 3.5 | 3.16 × 10−4 | 3.16 × 10−11 |
| 4.0 | 1.00 × 10−4 | 1.00 × 10−10 |
| 4.5 | 3.16 × 10−5 | 3.16 × 10−10 |
| 5.0 | 1.00 × 10−5 | 1.00 × 10−9 |
| 5.5 | 3.16 × 10−6 | 3.16 × 10−9 |
| 6.0 | 1.00 × 10−6 | 1.00 × 10−8 |
| 6.5 | 3.16 × 10−7 | 3.16 × 10−8 |
| 7.0 | 1.00 × 10−7 | 1.00 × 10−7 |
| 7.5 | 3.16 × 10−8 | 3.16 × 10−7 |
| 8.0 | 1.00 × 10−8 | 1.00 × 10−6 |
| 8.5 | 3.16 × 10−9 | 3.16 × 10−6 |
| 9.0 | 1.00 × 10−9 | 1.00 × 10−5 |
| 9.5 | 3.16 × 10−10 | 3.16 × 10−5 |
| 10.0 | 1.00 × 10−10 | 1.00 × 10−4 |
| 10.5 | 3.16 × 10−11 | 3.16 × 10−4 |
| 11.0 | 1.00 × 10−11 | 1.00 × 10−3 |
| 11.5 | 3.16 × 10−12 | 3.16 × 10−3 |
| 12.0 | 1.00 × 10−12 | 1.00 × 10−2 |
| 12.5 | 3.16 × 10−13 | 3.16 × 10−2 |
| 13.0 | 1.00 × 10−13 | 1.00 × 10−1 |
| 13.5 | 3.16 × 10−14 | 3.16 × 10−1 |
| 14.0 | 1.00 × 10−14 | 1.00 |
Worked examples
Example 1: pH 8.5
[H+] = 10−8.5 = 3.16 × 10−9 M, which rounds to 3.2 × 10−9 M at two significant figures. The hydroxide concentration is 10−14 / (3.16 × 10−9) = 3.16 × 10−6 M.
Example 2: from a base solution back to the base molarity
LibreTexts works a sodium hydroxide case in the forward direction: 1.0 g of NaOH in 1.0 L gives 0.025 M OH−, so [H+] = 1.0 × 10−14 / 0.025 = 4.0 × 10−13 M and pH 12.40. Run it backwards from a measured pH of 12.40: [H+] = 10−12.40 = 4.0 × 10−13 M, then [OH−] = 10−14 / (4.0 × 10−13) = 0.025 M. For a base that releases one hydroxide per formula unit, as NaOH does, the base molarity equals [OH−], so 0.025 M NaOH. The source reports the pH to two decimal places because the original mass and volume have two significant figures; carry the same discipline in reverse and do not quote more digits than the pH reading supports. For the mass and mole bookkeeping behind this, see NaOH molarity.
From [H+] to the molarity of the acid or base
The molarity you get from pH is the hydrogen ion concentration. Turning it into the concentration of a dissolved substance needs an assumption about how that substance behaves in water:
- Monoprotic acid that dissociates completely: each formula unit supplies one H+, so acid molarity = [H+]. Treat this as an assumption you state, not a result.
- Base that releases one OH− per formula unit (NaOH): compute [OH−] = 10−14 / [H+] first, as in Example 2, and take the base molarity as that value.
- Weak acids, polyprotic acids and buffers: [H+] alone does not give the total molarity. You also need the acid dissociation constant, and the half-way point of a titration is one way to read it; see half-titration point.
For the opposite direction, from a known molarity to pH, see how to calculate pH from molarity. For converting moles and volume into molarity once you know the amount of substance, see mol to molarity.
Calculate molarity from pH in Excel, R or Python
Each snippet takes a pH value and returns [H+] in mol/L.
Excel (pH in A1): =10^(-A1)
Excel, [OH-]: =10^(A1-14)
R: ph <- 8.5; h <- 10^(-ph); oh <- 1e-14 / h
Python: ph = 8.5; h = 10**(-ph); oh = 1e-14 / hApplied to 8.5, all three return 3.16 × 10−9 for [H+]. Format the output in scientific notation, since decimal display hides the exponent.
Why 10−pH is an approximation
pH is a conventional quantity rather than a directly measured concentration (IUPAC Recommendations 2002, Pure and Applied Chemistry 74(11), 2169-2200, doi:10.1351/pac200274112169). The 10−pH formula therefore gives an approximate hydrogen ion concentration. A reading from a meter also depends on calibration; see pH meter calibration and buffer selection and what a pH meter is.
Safety note: read the SDS first
Solutions at the extremes of the scale, strong acids near pH 0 and strong bases near pH 14, can be corrosive. Before preparing or handling any acid or base, read its safety data sheet; how to read a safety data sheet explains the sections. This page is a calculation reference and does not replace your institution’s procedures.
Frequently asked questions
How do you get molarity from pH?
Calculate [H+] = 10−pH. The result is in mol/L, which is the molarity of hydrogen ions.
Is the hydrogen ion concentration the same as the acid molarity?
Only if the acid is monoprotic and dissociates completely, an assumption you should state. For weak or polyprotic acids you need more information, such as the dissociation constant.
How do you get the molarity of a base from pH?
Find [H+] = 10−pH, then [OH−] = 10−14 / [H+]. For a base that releases one hydroxide per formula unit, such as NaOH, that is the base molarity.
Why does one pH unit change the concentration tenfold?
pH is a base-10 logarithm, so a change of one unit multiplies or divides [H+] by 10, as the USGS describes.
Sources
- LibreTexts, Windward Community College BIOC 141, section 10.5 Calculating pH of Acids and Bases, checked 2026-10-29: chem.libretexts.org
- USGS Water Science School, pH and Water, checked 2026-10-29: usgs.gov
- IUPAC, Measurement of pH. Definition, standards, and procedures (IUPAC Recommendations 2002), Pure and Applied Chemistry 2002, 74(11), 2169-2200, checked 2026-10-29: doi.org/10.1351/pac200274112169
