pH measures how acidic or basic a water solution is on a logarithmic scale: pH = −log₁₀[H⁺], where [H⁺] is the hydrogen-ion (strictly hydronium) concentration in mol/L. Pure water at 25 °C has [H⁺] = [OH⁻] = 1.0 × 10⁻⁷ M and a pH of 7. Every unit down the scale means ten times more H⁺ – lemon juice at pH 2 is about 100,000 times more acidic than pure water.
Strong acids such as HCl and HNO₃ dissociate completely, so [H⁺] is simply their concentration. Weak acids such as acetic acid only partly dissociate, and the extent is set by the acid dissociation constant Ka (or pKa = −log Ka). A 0.1 M acetic acid solution is only about 1.3% ionised, so its pH is 2.88 rather than 1. Bases work the same way through [OH⁻] and Kb.
Choose a mode: an acid or base from the list (pKa values at 25 °C from standard tables) with its concentration, or with the mass dissolved and the solution volume, or simply convert a known [H⁺], [OH⁻] or pOH into pH. For polyprotic acids only the first dissociation is used, apart from sulfuric acid, whose second proton is included.
How to use the pH Calculator
- Calculate the pH from
- Acid
- Acid dissociation constant Ka
- Base
- Base dissociation constant Kb
- Molar mass of the acid
- Molar mass of the base
- Concentration
- Mass of compound
- Volume of solution
- Hydrogen-ion concentration [H⁺]
- Hydroxide-ion concentration [OH⁻]
- pOH
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
For acids and bases the calculator finds [H⁺] that satisfies the charge balance of the solution exactly – including the water autoionisation (Kw = 1.0 × 10⁻¹⁴) – instead of using the square-root shortcut, so the result is correct for weak, strong and very dilute solutions alike. Then pH = −log[H⁺], pOH = 14 − pH and [OH⁻] = Kw ÷ [H⁺].
Worked example
0.1 M acetic acid, pKa 4.756 (Ka = 1.754 × 10⁻⁵). Solving Ka = x² ÷ (0.1 − x) gives x = [H⁺] = 1.316 × 10⁻³ M, so pH = 2.88, pOH = 11.12 and only 1.32% of the acid is ionised. Compare 0.01 M sulfuric acid: the first proton is fully released (0.01 M) and the second partly (pKa₂ 1.99), giving [H⁺] = 0.0142 M and pH 1.85 rather than 1.70. In mass mode, 2 g of NaOH (39.997 g/mol) in 500 mL is 0.050 mol in 0.5 L = 0.100 M, so pH = 13.00.
pH of everyday substances
| Substance | Approximate pH |
|---|---|
| Battery acid | below 1 |
| Stomach acid | 1.5–3.5 |
| Lemon juice | about 2 |
| Coffee | about 5 |
| Pure water (25 °C) | 7.0 |
| Human blood | 7.35–7.45 |
| Seawater | about 8.1 |
| Household ammonia | about 11–12 |
| Bleach | 12–13 |
Tips
- Use the final volume of the solution, not the volume of solvent added, for molarity.
- For dilutions, C₁V₁ = C₂V₂ only holds when both concentrations use the same unit.
- Add acid to water, never water to acid.
- Everything is calculated in your browser.
Common mistakes to avoid
- Mixing w/w, w/v and v/v percentages.
- Forgetting that pH is logarithmic – one unit is a tenfold change in [H⁺].
- Using pKa where Ka is asked for (or the other way round).
Formula
pH = −log₁₀[H⁺] · pOH = −log₁₀[OH⁻] · pH + pOH = 14 (25 °C)Strong acid: [H⁺] ≈ n·c · Weak acid: Ka = x² ÷ (c − x)The calculator solves the full charge balance [H⁺] = [A⁻] + [OH⁻], so very dilute solutions come out right too.Worked example
Inputs — Calculate the pH from: Concentration of an acid; Acid: Acetic acid – pKa 4.76; Concentration: 0.1 mol/L (M).
Results — pH = 2.881; Character = Strongly acidic; [H⁺] = 1.316 × 10⁻³ mol/L; Hydrogen-ion concentration [H⁺] = 0.001316; pOH = 11.119; Hydroxide-ion concentration [OH⁻] = 7.6011e-12.
Key terms
- pH
- Negative base-10 logarithm of the hydrogen-ion concentration.
- pOH
- Negative logarithm of the hydroxide-ion concentration; pH + pOH = 14 at 25 °C.
- Ka / pKa
- Acid dissociation constant and its negative logarithm; measures acid strength.
- Kb / pKb
- Base dissociation constant and its negative logarithm.
- Kw
- Ion product of water, 1.0 × 10⁻¹⁴ at 25 °C.
Frequently asked questions
How do I calculate pH from concentration?
For a strong monoprotic acid, pH = −log₁₀(c): 0.01 M HCl has pH 2. For a weak acid, solve Ka = x²/(c − x) for x = [H⁺] first – 0.1 M acetic acid gives pH 2.88.
What is the pH of 0.1 M formic acid?
With Ka = 1.78 × 10⁻⁴, [H⁺] = 4.13 × 10⁻³ M and the pH is 2.38.
What is the pH of 0.1 M ammonia?
Kb = 1.78 × 10⁻⁵ gives [OH⁻] = 1.32 × 10⁻³ M, pOH 2.88 and pH 11.12.
Why is the pH of 10⁻⁸ M HCl not 8?
An acid cannot make water basic. Water itself supplies 10⁻⁷ M H⁺, and the exact charge balance gives pH 6.98 – this calculator includes that.
Does pH + pOH always equal 14?
Only at 25 °C, where Kw = 1.0 × 10⁻¹⁴. At 37 °C, pKw is about 13.6, so neutral water has pH 6.8.
Can pH be negative?
Yes – concentrated strong acids above 1 M have pH below 0, although at such concentrations activity effects make the simple formula approximate.
What is the difference between Ka and pKa?
pKa = −log₁₀ Ka. A smaller pKa means a stronger acid; each unit lower is ten times stronger.
How accurate is the result for polyprotic acids?
The first dissociation dominates for most of them, so the pH is usually within a few hundredths. Sulfuric acid's significant second proton (pKa₂ 1.99) is included.
What formula does the pH Calculator use?
pH = −log₁₀[H⁺] · pOH = −log₁₀[OH⁻] · pH + pOH = 14 (25 °C).