pH Calculator
Work out pH, pOH, [H⁺] and [OH⁻] for strong and weak acids and bases and for buffers. Weak acids are solved exactly with the quadratic, next to the square-root shortcut, so you can see when the shortcut fails.
How to Use
- Choose the kind of solution: a conversion between pH, pOH, [H⁺] and [OH⁻], a strong acid or base, a weak acid or base, or a buffer.
- Enter the concentration with its unit (M, mM, µM or nM). For a strong acid or base, say how many H⁺ or OH⁻ each formula unit releases, such as 2 for Ca(OH)₂.
- For a weak acid or base, enter Ka or pKa (for a base: Kb, pKb or the pKa of its conjugate acid), or pick acetic acid, ammonium or carbonic acid from the list.
- For a buffer, enter the pKa and the concentrations of the weak acid and its conjugate base.
- Read the pH on the scale and in the readouts. Show Work gives the exact answer and the shortcut side by side; change pKw for temperatures other than 25 °C.
Worked Example
0.10 M acetic acid, pKa 4.76. Ka = 10−4.76 = 1.738 × 10⁻⁵. With x = [H⁺], Ka = x² ÷ (0.10 − x), so x² + Ka·x − 0.10·Ka = 0 and x = (−Ka + √(Ka² + 0.40·Ka)) ÷ 2 = 0.00131 M. pH = −log₁₀(0.00131) = 2.883, with 1.31% of the acid ionised. The shortcut x ≈ √(Ka × 0.10) = 0.001318 M gives pH 2.880, close enough because less than 5% ionises.
An acetate buffer. 0.10 M acetic acid with 0.15 M sodium acetate: pH = 4.76 + log₁₀(0.15 ÷ 0.10) = 4.76 + 0.176 = 4.936.
The common mistake: forgetting water in a very dilute acid. For 1.0 × 10⁻⁸ M HCl, −log₁₀(1.0 × 10⁻⁸) = 8.000 would make an acid solution basic. Water already supplies about 10⁻⁷ M of H⁺, so [H⁺] = (C + √(C² + 4Kw)) ÷ 2 = 1.051 × 10⁻⁷ M and the pH is 6.978, just on the acidic side of neutral.
Show Work
Formulas
Sørensen’s Scale
The Danish chemist Søren Sørensen introduced the pH scale in 1909 at the Carlsberg Laboratory in Copenhagen, where the acidity of brewing mashes and proteins had to be measured precisely. Writing hydrogen ion concentrations as negative powers of ten turned numbers like 0.0000001 into a simple 7.
Svante Arrhenius had described acids as sources of hydrogen ions in the 1880s, and in 1923 Johannes Brønsted and Thomas Lowry widened the idea to proton donors and acceptors, which is what makes ammonia a base and the ammonium ion its conjugate acid. Lawrence Henderson wrote the buffer equation in 1908 and Karl Hasselbalch put it into logarithmic form in 1916. The pKa values used here (acetic acid 4.76, ammonium 9.25, carbonic acid 6.35) are standard 25 °C values from data tables such as the CRC Handbook.
About This Calculator
This calculator converts between pH, pOH, [H⁺] and [OH⁻], and works out the pH of strong acids and bases, weak acids and bases, and buffers. Weak acids and bases are solved with the exact quadratic and shown next to the square-root shortcut, with a warning when more than 5% ionises and the shortcut breaks down. Very dilute solutions use the full charge balance, so water’s own ions are counted.
The scale marks your result against everyday references, and pKw can be changed for temperatures other than 25 °C. Real solutions above about 1 M depart from these ideal results because of activity effects. Everything runs in your browser; nothing is sent anywhere.
Related tools: Dilution Calculator, Molarity Calculator, and Chemical Equation Balancer.
Frequently Asked Questions
How do you calculate pH from concentration?
For a strong acid, pH = −log₁₀[H⁺] and [H⁺] is the acid concentration: 0.010 M HCl has pH 2.000. For a strong base find pOH = −log₁₀[OH⁻] first, then pH = 14.00 − pOH: 0.050 M NaOH has pOH 1.301 and pH 12.699.
How do I find the pH of a weak acid?
Solve Ka = x² ÷ (C − x) for x = [H⁺]. For 0.10 M acetic acid, Ka = 10^−4.76 = 1.738 × 10⁻⁵ and the quadratic gives x = 0.00131 M, pH 2.883. The shortcut x ≈ √(KaC) gives 2.880, close because only 1.3% is ionised. It fails when more than about 5% ionises: at 1.0 × 10⁻⁴ M it gives 4.380 against the true 4.470.
Is Kw always 1.0 × 10⁻¹⁴?
Only at 25 °C. Water ionises more as it warms: pKw is about 14.94 at 0 °C and about 13.26 at 50 °C, so neutral water is pH 7.47 at 0 °C and pH 6.63 at 50 °C. Neutral means [H⁺] = [OH⁻], not pH 7. Change pKw in the calculator to work at another temperature.
How does the Henderson–Hasselbalch equation work?
pH = pKa + log₁₀([A⁻] ÷ [HA]). An acetate buffer of 0.10 M acetic acid and 0.15 M acetate is 4.76 + log₁₀(1.5) = 4.936. With equal amounts the log term is 0 and pH = pKa. A buffer works best within pKa ± 1, a base-to-acid ratio between 0.1 and 10.
How do I find the pH of a weak base like ammonia?
Use Kb, or get it from the pKa of the conjugate acid: for ammonia, pKb = 14.00 − 9.25 = 4.75 and Kb = 1.778 × 10⁻⁵. For 0.10 M ammonia the quadratic gives [OH⁻] = 0.001325 M, pOH 2.878 and pH 11.122.
How do I use the pH Calculator?
Simply type your numbers and read the result, which refreshes the instant you change something. There is nothing to submit and nothing to wait for.
Does it cost anything or need an account?
No. The tool is completely free, there is no account to create, and it keeps working offline after the page first loads.
Is anything I type uploaded?
No. The tool works entirely on your device, so the values you enter never leave your browser.
Common Use Cases
Vinegar
Vinegar with 50 g/L of acetic acid is 0.833 M, which gives pH 2.421 with only 0.46% of the acid ionised.
Blood chemistry
Blood at pH 7.4 has [H⁺] = 3.981 × 10⁻⁸ M, about 40 nanomoles per litre.
Buffer preparation
0.10 M acetic acid with 0.15 M sodium acetate holds pH 4.936, inside its 3.76–5.76 range.
Cleaning solutions
0.10 M ammonia is pH 11.122; 0.050 M sodium hydroxide is pH 12.699.
Salt solutions
0.10 M ammonium chloride is slightly acidic: the NH₄⁺ ion (pKa 9.25) gives pH 5.125.
Very dilute acid
1.0 × 10⁻⁸ M HCl is pH 6.978, not 8, because water itself supplies 10⁻⁷ M of H⁺.
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