OneTaskBy Tim King · Updated
pH Calculator
Ka or Kb and Concentration Inputs, Worked Steps Shown for Each Answer
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How the pH Calculator works
This pH calculator converts between pH, pOH, hydrogen ion concentration [H⁺] and hydroxide concentration [OH⁻], and works out the pH of a weak acid or weak base from its Ka or Kb and concentration. Every answer shows the working, how acidic or basic the solution is and how it compares with pure water.
pH is a logarithmic scale for acidity. Each step of one pH unit is a tenfold change in hydrogen ion concentration, so lemon juice at pH 2 has a hundred thousand times more H⁺ than pure water at pH 7. The scale is set at 25 °C, where pH + pOH = 14.
How the pH calculator works
The formula is pH = −log₁₀[H⁺], and pOH = −log₁₀[OH⁻] = 14 − pH. Going the other way, [H⁺] = 10^−pH. For a weak acid HA at concentration C, the calculator solves Ka = x² ÷ (C − x) exactly with the quadratic formula, x = (−Ka + √(Ka² + 4KaC)) ÷ 2, then takes pH = −log₁₀ x. A weak base uses Kb the same way to find [OH⁻].
First example. 0.1 M acetic acid has Ka = 1.8 × 10⁻⁵. The quadratic gives [H⁺] = 1.333 × 10⁻³ mol/L, so pH = 2.875 and only 1.33% of the acid molecules are ionised.
Second example. A solution with [H⁺] = 0.0025 mol/L has pH = −log₁₀(0.0025) = 2.602 and pOH = 11.398.
How many times more acidic is pH 3 than pH 5? Two pH units apart means 10² = 100 times more hydrogen ions.
pH of common substances
| Substance | Typical pH | [H⁺] (mol/L) | pOH | Acidic, neutral or basic |
|---|---|---|---|---|
| Battery acid | 0.5 | 3.16 × 10⁻¹ | 13.5 | Acidic |
| Stomach acid | 1.5 | 3.16 × 10⁻² | 12.5 | Acidic |
| Lemon juice | 2.2 | 6.31 × 10⁻³ | 11.8 | Acidic |
| Cola | 2.5 | 3.16 × 10⁻³ | 11.5 | Acidic |
| Vinegar | 2.8 | 1.58 × 10⁻³ | 11.2 | Acidic |
| Orange juice | 3.5 | 3.16 × 10⁻⁴ | 10.5 | Acidic |
| Tomato juice | 4.2 | 6.31 × 10⁻⁵ | 9.8 | Acidic |
| Beer | 4.5 | 3.16 × 10⁻⁵ | 9.5 | Acidic |
| Black coffee | 5 | 1.00 × 10⁻⁵ | 9.0 | Acidic |
| Rainwater (unpolluted) | 5.6 | 2.51 × 10⁻⁶ | 8.4 | Acidic |
| Milk | 6.6 | 2.51 × 10⁻⁷ | 7.4 | Acidic |
| Pure water at 25 °C | 7 | 1.00 × 10⁻⁷ | 7.0 | Neutral |
| Human blood | 7.4 | 3.98 × 10⁻⁸ | 6.6 | Basic |
| Seawater | 8.1 | 7.94 × 10⁻⁹ | 5.9 | Basic |
| Baking soda solution | 8.3 | 5.01 × 10⁻⁹ | 5.7 | Basic |
| Hand soap | 10 | 1.00 × 10⁻¹⁰ | 4.0 | Basic |
| Milk of magnesia | 10.5 | 3.16 × 10⁻¹¹ | 3.5 | Basic |
| Washing soda | 11.5 | 3.16 × 10⁻¹² | 2.5 | Basic |
| Household ammonia | 11.6 | 2.51 × 10⁻¹² | 2.4 | Basic |
| Bleach | 12.5 | 3.16 × 10⁻¹³ | 1.5 | Basic |
| Oven cleaner | 13.5 | 3.16 × 10⁻¹⁴ | 0.5 | Basic |
| 1 M sodium hydroxide | 14 | 1.00 × 10⁻¹⁴ | 0.0 | Basic |
Tips and pitfalls
- Enter small numbers in decimal or e-notation. 1.8e-5 and 0.000018 are the same Ka.
- Strong acids are simpler. For 0.01 M HCl, [H⁺] is just 0.01, so use From [H⁺] rather than the weak-acid mode.
- The √(KC) shortcut. It is fine when less than 5% ionises; the calculator shows whether it would have been close enough.
- pH 14 assumes 25 °C. At body temperature neutral water is about pH 6.8, not 7.
FAQ
How do you calculate pH from concentration?
For a strong acid, the hydrogen ion concentration equals the acid concentration, so pH = −log₁₀ of it. A 0.001 M solution of hydrochloric acid has pH 3. For a weak acid you also need Ka, because only part of it ionises; choose the weak acid mode for that.
What is the difference between pH and pOH?
pH measures hydrogen ion concentration and pOH measures hydroxide ion concentration, both on a negative log scale. In water at 25 °C they always add up to 14, so a solution with pH 4 has pOH 10. Low pH means acidic and low pOH means basic.
How do I find the pH of a weak acid?
Enter the acid dissociation constant Ka and the concentration. Acetic acid has Ka 1.8 × 10⁻⁵, so a 0.1 M solution has pH about 2.87, much higher than a strong acid at the same concentration, because only about 1% of the molecules release their hydrogen ion.
Can pH be negative or above 14?
Yes. Very concentrated strong acids, such as 2 M hydrochloric acid, have pH below zero, and concentrated sodium hydroxide can go above 14. The 0 to 14 range only covers the solutions most people meet in labs, homes and gardens.
What pH is neutral?
At 25 °C neutral is pH 7, where hydrogen and hydroxide ions are equal at 1.0 × 10⁻⁷ mol/L each. Neutral pH falls slightly as water warms, so neutral water at 37 °C is about 6.8 even though it is still neither acidic nor basic.
See also: all Chemistry tools, Physics, Electronics.
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