pH is the negative logarithm of hydrogen ion concentration
pH is the base-10 logarithm of the hydrogen ion concentration [H⁺] in moles per liter, with the sign reversed. An [H⁺] of 1.0×10⁻³ M gives pH 3.00, and 1.0×10⁻⁷ M gives pH 7.00. Because the scale is logarithmic, every drop of one pH unit means ten times as many hydrogen ions. pH 3 and pH 6 are only three units apart, yet their hydrogen ion concentrations differ by a factor of 1,000.
Most problems do not give [H⁺] directly. They give the concentration of the dissolved acid, such as "0.1 M acetic acid". The calculator above solves for pH straight from that concentration. In 0.1 M acetic acid only 1.32% of the molecules split into ions, giving pH 2.88, while the same concentration of hydrochloric acid splits completely and gives pH 1.00. Because the ions supplied by water itself are included, the result is more accurate than textbook shortcuts for very dilute solutions and for polyprotic acids such as phosphoric acid.
When do you need to calculate pH?
A pH meter or test strip measures a solution that already exists. A calculation helps before that, or when you want to check whether a measurement makes sense.
- Checking answers to chemistry problems: For strong and weak acids given by concentration, the calculator shows when a shortcut such as √(Ka·C) holds, when it fails, and by how much.
- Estimating a solution before an experiment: Change the concentration to see roughly what pH an acid or base solution will have and how dilution shifts it. A 0.1 M sodium hydroxide solution is pH 13.00, and each tenfold dilution lowers it to 12.00, then 11.00.
- Understanding "slightly acidic" or "slightly alkaline" on a label: The acidity classes used for detergent labeling are marked on the color scale.
- Getting a feel for pH differences: The US National Oceanic and Atmospheric Administration (NOAA) reports that surface ocean pH has fallen by 0.1 since the Industrial Revolution, which it describes as an increase in acidity of about 30%. Because the scale is logarithmic, even a small difference in the first decimal place means a difference of tens of percent in hydrogen ion concentration.
How to use it
- Choose a mode: If you know the concentration of a dissolved acid or base, choose "From solution concentration". If you know one of pH, pOH, [H⁺] or [OH⁻], choose "Convert pH and ion concentration".
- Enter the substance and concentration: Pick an acid or base from the list and enter its concentration in mol/L (M). Formats such as 0.1, 1e-3, 2.5×10^-4 and 2.5×10⁻⁴ are all read. The chemical formula and pKa (or pKb) of the chosen substance appear alongside.
- Acids and bases not on the list: Choose "Custom", then pick strong acid, weak acid, strong base or weak base and enter the dissociation constant. A switch at the right of the field lets you enter pKa or Ka. For a salt such as sodium acetate, enter its conjugate base as a weak base with Kb = 1.0×10⁻¹⁴ ÷ Ka.
- Converting values: Enter any one of the four fields and the other three are filled in. The field with the heavier border is the one currently used as the starting point.
- Color scale: Drag the strip or press ← and → to change the pH. Selecting a name such as lemon juice or seawater jumps to its pH.
- Sharing results: "Copy result" copies the pH, pOH, ion concentrations and explanation as text. "Copy link" copies an address that holds your current input.
How the calculation works
pH, pOH, [H⁺] and [OH⁻]
In water at 25°C, [H⁺] × [OH⁻] = Kw = 1.0×10⁻¹⁴, so pH + pOH = 14. Knowing one value gives the rest directly: [H⁺] = 10−pH, pOH = 14 − pH and [OH⁻] = 10−pOH. In this mode [H⁺] is the concentration of hydrogen ions actually present in solution, not the concentration of acid you dissolved.
Strong acids and strong bases
Acids and bases that split completely in water, such as hydrochloric acid, nitric acid and sodium hydroxide, are approximated by [H⁺] ≈ C (or [OH⁻] ≈ C for a base). A base that releases two OH⁻ per unit, such as calcium hydroxide, gives 2C. Below about 10⁻⁶ M, the 1.0×10⁻⁷ M contributed by water can no longer be ignored, and the solution must be found from [H⁺] = (C + √(C² + 4Kw)) ÷ 2.
Weak acids and weak bases
A weak acid HA splits only partly. If x is the amount that splits, Ka = x² ÷ (C − x), and if x is much smaller than C, x ≈ √(Ka·C). This shortcut works well when ionization is below 5%. For 0.1 M acetic acid (1.32% ionized), the shortcut and the exact value both give pH 2.88. For 0.001 M acetic acid, 12.4% splits, and the shortcut value 3.88 and the exact value 3.91 no longer agree.
The equation this calculator solves
Instead of choosing among those formulas, the calculator solves one charge balance. For an acid it is [H⁺] = [OH⁻] + [A⁻] + 2[A²⁻] + …, and for a base [OH⁻] = [H⁺] + [BH⁺] + …. Each ion's concentration is fixed by the dissociation constants and [H⁺], so the calculator varies [H⁺] until both sides match (bisection on a log scale). Strong acids, weak acids, polyprotic acids and very dilute solutions are therefore all handled the same way.
Formulas pH = −log[H⁺] · pOH = 14 − pH · weak-acid shortcut [H⁺] ≈ √(Ka·C) · exact solution: [H⁺] = Kw ÷ [H⁺] + C·n̄([H⁺]), where n̄ = average number of H⁺ released per molecule · 25°C, Kw = 1.0×10⁻¹⁴, activity taken as equal to concentration
pH by concentration
At the same concentration, pH differs widely depending on whether the substance is strong or weak and how many ions it releases. The values in the table were calculated the same way as in the calculator above. The 10⁻⁸ M column shows that adding an acid still leaves the pH below 7, and adding a base still leaves it above 7.
| Substance | 1 M | 0.1 M | 10⁻² M | 10⁻³ M | 10⁻⁶ M | 10⁻⁸ M |
|---|---|---|---|---|---|---|
| Hydrochloric acid HCl | 0.00 | 1.00 | 2.00 | 3.00 | 6.00 | 6.98 |
| Sulfuric acid H₂SO₄ | 0.00 | 0.96 | 1.85 | 2.73 | 5.70 | 6.96 |
| Acetic acid CH₃COOH | 2.38 | 2.88 | 3.39 | 3.91 | 6.02 | 6.98 |
| Phosphoric acid H₃PO₄ | 1.10 | 1.64 | 2.26 | 3.05 | 5.97 | 6.97 |
| Ammonia NH₃ | 11.62 | 11.12 | 10.62 | 10.10 | 7.98 | 7.02 |
| Sodium hydroxide NaOH | 14.00 | 13.00 | 12.00 | 11.00 | 8.00 | 7.02 |
Counting both H⁺ of 0.1 M sulfuric acid, as textbooks do, gives pH 0.70, but the second step has pKa₂ = 1.99, so the actual calculation gives 0.96. For phosphoric acid too, the shortcut that counts only the first step (1.58 at 0.1 M) differs from the exact value (1.64), because 23% of the first step ionizes and the assumption C − x ≈ C no longer holds.
Comparison with measured values
PubChem, from the US National Institutes of Health, lists the measured pH of aqueous solutions of several substances at different concentrations. The calculated values agree with every measurement at the precision it was reported.
| Substance | Concentration | PubChem measured pH | This calculator |
|---|---|---|---|
| Acetic acid CH₃COOH | 1.0 M | 2.4 | 2.38 |
| Acetic acid CH₃COOH | 0.1 M | 2.9 | 2.88 |
| Acetic acid CH₃COOH | 0.01 M | 3.4 | 3.39 |
| Ammonia NH₃ | 1.0 M | 11.6 | 11.62 |
| Ammonia NH₃ | 0.1 M | 11.1 | 11.12 |
| Ammonia NH₃ | 0.01 M | 10.6 | 10.62 |
| Sodium hydroxide NaOH | 0.05% (about 0.0125 M) | ≈12 | 12.10 |
| Sodium hydroxide NaOH | 0.5% (about 0.125 M) | ≈13 | 13.10 |
The International Union of Pure and Applied Chemistry (IUPAC) defines pH in terms of the activity of hydrogen ions rather than their concentration. In more concentrated solutions, ions attract one another, so the concentration that actually takes part in reactions (the activity) falls below the amount added, and the gap between calculated and measured values can grow.
pH of everyday substances and acidity classes
These are the pH values of the substances marked on the color strip, with their sources. The pH of foods varies with variety and processing, so treat the figures as representative values.
| Substance | Condition | pH | [H⁺] (M) | Source |
|---|---|---|---|---|
| Lemon juice | Juice | 2.2 | 6.31×10⁻³ | USDA ARS |
| Red wine | Red wine | 3.63 | 2.34×10⁻⁴ | USDA ARS |
| Orange juice | Juice | 4.2 | 6.31×10⁻⁵ | USDA ARS |
| Rain | Typical rain | ≈5.6 | 2.51×10⁻⁶ | USGS |
| Milk | Whole milk powder mixed with water | 6.5 | 3.16×10⁻⁷ | USDA ARS |
| Pure water | 25°C | 7.00 | 1.00×10⁻⁷ | Kw |
| Blood | Normal range | 7.35~7.45 | 3.55×10⁻⁸~4.47×10⁻⁸ | MSD Manual |
| Seawater | Ocean average | ≈8.1 | 7.94×10⁻⁹ | NOAA |
| Baking soda | Sodium bicarbonate, 0.1 M | 8.3 | 5.01×10⁻⁹ | PubChem |
| Ammonia | 0.1 N (0.1 M) | 11.1 | 7.94×10⁻¹² | PubChem |
| Limewater | Saturated calcium hydroxide (25°C) | 12.4 | 3.98×10⁻¹³ | PubChem |
| Lye | Sodium hydroxide, 0.5% | ≈13 | 1.00×10⁻¹³ | PubChem |
Labels that say "slightly acidic" or "slightly alkaline" on detergents follow pH boundaries set by the Japan Consumer Affairs Agency in its labeling standard for household goods. The liquid is measured at 25°C, undiluted (powders are dissolved to a set concentration). The acidity chips in this calculator use the same boundaries.
| Class | pH range | Everyday examples |
|---|---|---|
| Acidic | pH below 3.0 | Lemon juice 2.2 |
| Slightly acidic | pH 3.0 to below 6.0 | Red wine 3.6, Orange juice 4.2, Rain 5.6 |
| Neutral | pH 6.0 to 8.0 | Milk 6.5, Pure water 7.0, Blood 7.4 |
| Slightly alkaline | pH above 8.0 to 11.0 | Seawater 8.1, Baking soda 8.3 |
| Alkaline | pH above 11.0 | Ammonia 11.1, Limewater 12.4, Lye 13.0 |
Common mistakes
- Calculating 10⁻⁸ M hydrochloric acid as pH 8: Using −log(10⁻⁸) = 8 as is would make an acid basic. Adding the H⁺ that water supplies gives pH 6.98.
- Mistaking a strong acid for a strongly acidic solution: "Strong" only means it splits completely. 1.0×10⁻⁴ M hydrochloric acid is pH 4.00, in the slightly acidic range, and is less acidic than 1 M acetic acid (pH 2.38).
- Reading a pH difference as a multiple: pH 3 is not "twice" as acidic as pH 6. It has 1,000 times as many hydrogen ions.
- Entering the acid concentration in the [H⁺] field: In "Convert pH and ion concentration", [H⁺] is the actual hydrogen ion concentration. Entering the concentration of a weak acid there gives a pH that is far too low, so use "From solution concentration" instead.
- Entering mM as M: 5 mM is 0.005 M (5e-3). A thousandfold unit error shifts the pH of a strong acid by 3.
Neutral pH changes with temperature
pH + pOH = 14 holds only at 25°C. The ion product of water grows as temperature rises, so the neutral pH of pure water (half of pKw) falls. Water at pH 6.1 and 100°C is neutral, not acidic.
| Temperature | pKw | Neutral pH |
|---|---|---|
| 0°C | 14.95 | ≈7.5 |
| 25°C | 13.99 | ≈7.0 |
| 50°C | 13.26 | ≈6.6 |
| 100°C | 12.25 | ≈6.1 |
This calculator uses 25°C and pKw = 14.00 (Kw = 1.0×10⁻¹⁴), as most textbooks do. In the same table, pKw at 25°C is 13.99, a difference of 0.01 in the second decimal place.
Limitations
- 25°C only: Both Kw and the dissociation constants are 25°C values. At other temperatures, neutral pH and the degree of ionization of weak acids both change.
- Ideal solutions: Concentration is treated as activity. Solutions above 1 M, or with a lot of dissolved salt, can differ greatly from the real pH.
- One substance at a time: Neutralization of an acid with a base, buffer solutions and mixtures of two or more substances are not calculated.
- Amount dissolved: Sparingly soluble substances such as calcium hydroxide are treated as if the full amount entered had dissolved.
- Carbonic acid: The calculation treats all dissolved carbon dioxide as carbonic acid. The pH of a solution that loses carbon dioxide, such as a fizzy drink, changes over time.
- Not a substitute for measurement: If you need the actual pH of a real solution, measure it with a calibrated pH meter.
Sources
- 01LibreTexts: E1 Acid Dissociation Constants at 25°CValues from the CRC Handbook of Chemistry and Physics, 84th ed. Acetic acid pKa 4.756, formic acid 3.75, hydrofluoric acid 3.20, benzoic acid 4.204, hypochlorous acid 7.40, hydrocyanic acid 9.21, carbonic acid 6.35 and 10.33, phosphoric acid 2.16, 7.21 and 12.32, citric acid 3.13, 4.76 and 6.40, sulfuric acid second step 1.99
- 02LibreTexts: E2 Base Dissociation Constants at 25°CCRC Handbook, 84th ed. Ammonia pKb 4.75, methylamine 3.34, pyridine 8.77
- 03IAPWS R11-24: Revised Release on the Ionization Constant of H₂O (2024)Table 3, at 0.1 MPa: pKw 14.95 at 0°C, 13.99 at 25°C, 13.26 at 50°C, 12.25 at 100°C
- 04PubChem: Acetic Acid (CID 176)Aqueous solution pH 2.4 at 1.0 M, 2.9 at 0.1 M, 3.4 at 0.01 M
- 05PubChem: Ammonia (CID 222)Aqueous solution pH 11.6 at 1.0 N, 11.1 at 0.1 N, 10.6 at 0.01 N
- 06PubChem: Sodium Bicarbonate (CID 516892)Freshly prepared 0.1 M aqueous solution at 25°C: pH 8.3
- 07PubChem: Sodium Hydroxide (CID 14798)Aqueous solution pH about 12 at 0.05% (by weight), about 13 at 0.5%, about 14 at 5%
- 08PubChem: Calcium Hydroxide (CID 6093208)Saturated aqueous solution at 25°C: pH 12.4
- 09USDA Agricultural Research Service (ARS): pH of Selected FoodsLemon juice 2.2, orange juice 4.2, red wine 3.63, milk made from whole milk powder 6.5
- 10US Geological Survey (USGS): pH and WaterTypical rain pH about 5.6 (from atmospheric carbon dioxide); one pH unit is a tenfold difference
- 11NOAA: Ocean acidificationOcean average pH about 8.1; surface pH down 0.1 since the Industrial Revolution, an increase in acidity of about 30%
- 12MSD Manual: Overview of Acid-Base BalanceNormal blood pH about 7.35–7.45
- 13Japan Consumer Affairs Agency: Labeling standard for household goods (synthetic detergents and cleaners)Acidity classes: below pH 3.0 acidic, 3.0 to below 6.0 slightly acidic, 6.0 to 8.0 neutral, above 8.0 to 11.0 slightly alkaline, above 11.0 alkaline; measured at 25°C
- 14IUPAC Gold Book: pHpH = −lg a(H⁺), defined by the activity of hydrogen ions (Measurement of pH, IUPAC Recommendations 2002, Pure Appl. Chem. 74, 2169)
Frequently asked questions
How do you calculate pH?
pH is the base-10 logarithm of the hydrogen ion concentration [H⁺] (mol/L) with the sign reversed: pH = −log[H⁺]. An [H⁺] of 1.0×10⁻³ M gives pH 3.00, and diluting it tenfold to 1.0×10⁻⁴ M gives pH 4.00. At 25°C the rest follow from pOH = 14 − pH and [OH⁻] = 1.0×10⁻¹⁴ ÷ [H⁺].
What is the pH of 0.1 M acetic acid?
Using the pKa of 4.756 (Ka 1.75×10⁻⁵, CRC Handbook 84th ed.), it is pH 2.88. Only 1.32% of the molecules split into ions, so [H⁺] is 76 times lower than in hydrochloric acid of the same concentration (pH 1.00). The acetic acid entry in PubChem, from the US National Institutes of Health, also lists a 0.1 M solution at pH 2.9.
Why is 10⁻⁸ M hydrochloric acid not pH 8?
Water itself supplies 1.0×10⁻⁷ M each of H⁺ and OH⁻. The H⁺ added by the acid (1.0×10⁻⁸ M) is smaller than what water provides, so solving with the ionization of water included gives [H⁺] = 1.05×10⁻⁷ M, or pH 6.98. Adding an acid cannot make a solution basic (pH 8).
Is the pH of 0.1 M sulfuric acid 0.70?
If you assume, as textbooks do, that sulfuric acid gives up both H⁺, then [H⁺] = 0.2 M and pH = 0.70. In reality the second step has Ka₂ = 1.0×10⁻² (pKa₂ 1.99), so only 8.61% more of the HSO₄⁻ splits, and this calculator gives [H⁺] = 0.109 M and pH 0.96. For exam questions, follow the assumptions the problem sets.
Do pH and pOH always add up to 14?
Only at 25°C. The ion product of water, pKw, changes with temperature. In the International Association for the Properties of Water and Steam (IAPWS) table it is 14.95 at 0°C, 13.99 at 25°C, 13.26 at 50°C and 12.25 at 100°C. The neutral pH of pure water is therefore about 7.5 at 0°C and about 6.1 at 100°C. This calculator uses 25°C and pKw = 14.00, as textbooks do.
Can pH be below 0 or above 14?
Yes. A strong acid above 1 M has a calculated pH below 0, and a strong base above 1 M above 14. But in such concentrated solutions the ions interact, and the real pH can differ greatly from the value calculated from concentration. This calculator accepts concentrations only up to 10 M and adds a note above 1 M.
Is a strong acid always strongly acidic?
No. Strong and weak describe how completely an acid splits into ions in water, while how acidic a solution is depends on its pH. 1.0×10⁻⁴ M hydrochloric acid splits completely, but at pH 4.00 it is in the slightly acidic range. 1 M acetic acid is a weak acid, yet at pH 2.38 it falls in the acidic range.
What pH counts as slightly acidic, neutral or slightly alkaline?
The Japan Consumer Affairs Agency's labeling standard for household goods classifies detergents as acidic below pH 3.0, slightly acidic from 3.0 to below 6.0, neutral from 6.0 to 8.0, slightly alkaline above 8.0 up to 11.0, and alkaline above 11.0 (measured at 25°C). The acidity classes in this calculator use the same boundaries. In chemistry, neutral at 25°C means exactly pH 7.00.