pH Calculator
pH from [H⁺], [H⁺] from pH, pH from pOH, or the pH of a strong acid or base from its concentration — with [OH⁻], the log steps and a temperature-aware Kw.
pH Calculator: with the default inputs, ph is 2.
Used in the [H⁺] → pH mode. Enter 1e-7 for 0.0000001.
Used in the pH → [H⁺] mode.
Used in the pOH → pH mode.
Used in the strong acid/base mode.
- Solution is
- Strongly acidic
- pOH
- 12
- [H⁺] (mol/L)
- 1.000 × 10⁻² mol/L
- [OH⁻] (mol/L)
- 1.000 × 10⁻¹² mol/L
Assumptions
- Ideal (activity = concentration) behaviour — accurate for dilute solutions.
- Strong acids and bases dissociate completely; H₂SO₄'s second proton is treated as fully released.
- pKw = 14.00 (25 °C) unless you change it under More options.
| Substance | Typical pH | Note |
|---|---|---|
| Battery acid | 0.0 | Concentrated sulfuric acid |
| Stomach acid | 1.5 – 3.5 | Hydrochloric acid, roughly 0.03–0.1 M |
| Lemon juice | 2.0 – 2.6 | Citric acid |
| Vinegar | 2.4 – 3.4 | Acetic acid, 5% household |
| Cola | 2.5 | Phosphoric + carbonic acid |
| Orange juice | 3.3 – 4.2 | |
| Tomato juice | 4.1 – 4.6 | |
| Black coffee | 4.8 – 5.1 | |
| Clean rain | 5.6 | Carbonic acid from atmospheric CO₂ |
| Milk | 6.5 – 6.7 | |
| Pure water at 25 °C | 7.00 | Neutral by definition: pKw ÷ 2 |
| Human blood | 7.35 – 7.45 | Tightly buffered; outside this range is a medical emergency |
| Seawater | 8.1 | Down from 8.2 pre-industrial — ocean acidification |
| Baking soda solution | 8.3 | |
| Milk of magnesia | 10.5 | |
| Household ammonia | 11.0 – 11.5 | |
| Bleach | 12.5 | Sodium hypochlorite |
| Drain cleaner | 13 – 14 | Concentrated sodium hydroxide |
Each step down the scale is ten times more hydrogen ions, so lemon juice at pH 2.3 is roughly 50,000 times more acidic than milk at pH 6.6. Your sample is pH 2 — strongly acidic.
| Water temperature (°C) | pKw | Neutral pH |
|---|---|---|
| 0 | 14.95 | 7.48 |
| 10 | 14.53 | 7.27 |
| 20 | 14.17 | 7.09 |
| 25 | 14 | 7 |
| 30 | 13.83 | 6.92 |
| 40 | 13.53 | 6.77 |
| 50 | 13.26 | 6.63 |
| 60 | 13.02 | 6.51 |
| 70 | 12.8 | 6.4 |
| 80 | 12.6 | 6.3 |
| 90 | 12.42 | 6.21 |
| 100 | 12.25 | 6.13 |
Water ionizes more readily as it warms, so pure water at 100 °C has pH 6.13 and is still perfectly neutral — it has exactly as much H⁺ as OH⁻. Enter the matching pKw under More options to work at another temperature.
How this is worked out
The formula
pH = −log₁₀[H⁺] [H⁺] = 10^(−pH) pOH = −log₁₀[OH⁻] pH + pOH = pKw = 14.00 at 25 °C Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25 °C Strong acid: [H⁺] = n × C Strong base: [OH⁻] = n × C (n = protons or hydroxides per formula unit; below ~10⁻⁶ M include water's own ions)
Open How it’s calculated above to see this worked through with your own numbers.
What you enter
- What do you know?
- Choose one of 4 options.[H⁺] concentration → pH · pH → [H⁺] and [OH⁻] · pOH → pH · Strong acid or base concentration → pH
- Hydrogen-ion concentration [H⁺]
- Used in the [H⁺] → pH mode. Enter 1e-7 for 0.0000001.0 or more · defaults to 0.01
- pH
- Used in the pH → [H⁺] mode.from -2 to 16 · defaults to 7
- pOH
- Used in the pOH → pH mode.from -2 to 16 · defaults to 3
- Acid or base concentration
- Used in the strong acid/base mode.0 or more · defaults to 0.01
- Strong acid or base
- Choose one of 4 options.Monoprotic strong acid (HCl, HNO₃, HBr, HClO₄) — 1 H⁺ · Sulfuric acid H₂SO₄ — 2 H⁺ (approximation) · Strong base with 1 OH⁻ (NaOH, KOH) · Strong base with 2 OH⁻ (Ca(OH)₂, Ba(OH)₂)
- pKw (water's ionization constant)(under More options)
- 14.00 at 25 °C. 14.95 at 0 °C, 13.26 at 50 °C, 12.25 at 100 °C (Bandura & Lvov 2006).from 10 to 16 · defaults to 14
What you get back
- pHmain answer
- Solution is
- pOH
- [H⁺] (mol/L)
- [OH⁻] (mol/L)
What this assumes
- Ideal (activity = concentration) behaviour — accurate for dilute solutions.
- Strong acids and bases dissociate completely; H₂SO₄'s second proton is treated as fully released.
- pKw = 14.00 (25 °C) unless you change it under More options.
About this calculator
pH is a logarithmic scale for hydrogen-ion concentration: pH = −log₁₀[H⁺]. Each step down the scale is ten times more acidic, so lemon juice at pH 2 has 100,000 times the [H⁺] of pure water at 7. This calculator moves in every direction between pH, pOH, [H⁺] and [OH⁻], computes the pH of a strong acid or base straight from its molarity, and shows the logarithm steps so you can reproduce them on an exam.
How to use it
Pick what you know. For strong acids (HCl, HNO₃, HBr, HI, HClO₄) and strong bases (NaOH, KOH, Ca(OH)₂), dissociation is complete, so [H⁺] or [OH⁻] equals the concentration times the number of ions per formula unit; the calculator handles the factor of two for Ca(OH)₂ and — approximately — for H₂SO₄. Weak acids and bases (acetic acid, ammonia) only partly dissociate and need their Ka or Kb; this calculator does not treat them.
Reading the results
- pH 7 is neutral only at 25 °C. Water's ionization constant grows with temperature, so neutral is pH 6.63 at 50 °C and 6.14 at 100 °C. Open More options to set pKw for your temperature; the neutral point and the "acidic/basic" verdict follow it.
- [H⁺] and [OH⁻] always multiply to Kw. Knowing one gives the other.
- Negative pH and pH above 14 are legitimate for concentrated solutions (12 M HCl has a nominal pH of −1.1), though activity effects make the measured value differ.
The dilute-acid trap
The naive rule pH = −log C says 10⁻⁸ M HCl has pH 8 — an acid that is basic, which is absurd. Water's own 10⁻⁷ M of H⁺ can't be ignored at that dilution. The calculator solves the full charge balance, giving pH 6.98, and shows the extra step whenever it matters.
Common mistakes
- Forgetting the factor for polyprotic species: 0.01 M Ca(OH)₂ gives 0.02 M OH⁻ and pH 12.3, not 12.0.
- Rounding pH to one decimal and then back-computing concentration; a 0.1 pH error is a 26% concentration error.
- Treating a weak acid as strong. 0.1 M acetic acid has pH 2.9, not 1.0.
Significant figures
Digits before the decimal point in a pH are the exponent, so they don't count. [H⁺] = 1.2 × 10⁻³ (two significant figures) gives pH 2.92 (two decimals).
Frequently asked questions
▸How do I calculate pH from concentration?
For a strong acid, pH = −log₁₀ of the H⁺ concentration in mol/L. 0.01 M HCl gives −log(0.01) = 2. For a strong base, find pOH = −log[OH⁻] and subtract from 14.
▸How do I find [H⁺] from pH?
Raise 10 to the negative pH: [H⁺] = 10^(−pH). pH 3 is 10⁻³ = 0.001 mol/L; pH 7.4 is 10^(−7.4) = 4.0 × 10⁻⁸ mol/L.
▸What is the relationship between pH and pOH?
They add up to pKw, which is 14.00 at 25 °C. So pOH 3 means pH 11. At other temperatures the sum changes — 13.26 at 50 °C.
▸Can pH be negative or greater than 14?
Yes. The 0–14 range is just where dilute aqueous solutions fall. 10 M HCl has a nominal pH of −1, and saturated NaOH is above 15, although activity effects make measured values differ from the ideal formula.
▸Why isn't the pH of 10⁻⁸ M HCl equal to 8?
Because water itself supplies 10⁻⁷ M of H⁺, more than the acid does. Solving the full balance gives pH 6.98 — slightly acidic, as an acid solution must be. The calculator includes this correction automatically.
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