pH Calculator
pH measures hydrogen-ion activity on a logarithmic scale from 0 to 14. This calculator covers five practical modes: direct conversion from [H+] concentration, reverse-solve from a known pH, weak-acid equilibrium from Ka, weak-base equilibrium from Kb, and Henderson-Hasselbalch buffer pH.
Formula
Worked example
Direct: [H+] = 1x10-4 mol/L gives pH = 4.00 and pOH = 10.00. Buffer: acetic acid (pKa = 4.74) with [A-] = [HA] = 0.1 mol/L gives pH = 4.74 + log(1) = 4.74. Weak acid: acetic acid 0.1 mol/L Ka = 1.8x10-5 gives [H+] = 1.34x10-3, pH = 2.87.
How each mode works
The calculator offers five modes. The simplest is from [H+] concentration: you supply the molar H+ concentration and the calculator applies pH = -log10([H+]). Reverse-solve goes the other way, converting a known pH back to [H+] and [OH-] by computing [H+] = 10^(-pH). The weak-acid mode solves the equilibrium expression Ka = [A-][H+] / [HA] exactly using the quadratic formula (x^2 + Ka*x - Ka*C = 0), so the result stays accurate even for relatively strong weak acids where the approximation [H+] = sqrt(Ka * C) breaks down. The weak-base mode is symmetric: it solves for [OH-] first, then converts to pH via pOH. The buffer mode applies the Henderson-Hasselbalch equation pH = pKa + log([A-]/[HA]) and is most accurate when the [A-]/[HA] ratio is between 0.1 and 10 (within one pH unit of pKa).
pH, pOH and the water equilibrium
In any dilute aqueous solution at 25 degrees C, the product [H+][OH-] equals Kw = 1.0 x 10-14, which is why pH + pOH = 14. A pH of 7 is neutral because [H+] and [OH-] are both 1.0 x 10-7 mol/L. At higher temperatures Kw increases: at 37 degrees C (body temperature) Kw is about 2.4 x 10-14, giving a neutral pH of roughly 6.8. The calculator assumes 25 degrees C throughout.
Weak acids, Ka and the approximation
A weak acid HA partially dissociates: HA is in equilibrium with H+ and A-. The acid dissociation constant Ka = [A-][H+] / [HA] quantifies how far dissociation goes. For a simple estimate many textbooks use [H+] = sqrt(Ka * C), which assumes x << C (less than 5% dissociation). This calculator avoids that assumption by solving the exact quadratic, which matters when Ka is not very small relative to C. For example, a 0.01 mol/L solution of a weak acid with Ka = 1 x 10-3 has about 30% dissociation, where the approximation introduces meaningful error.
Buffer calculations and Henderson-Hasselbalch
A buffer contains a weak acid and its conjugate base (or a weak base and its conjugate acid). The Henderson-Hasselbalch equation, pH = pKa + log([A-]/[HA]), describes the pH of the mixture. Buffers resist pH change because adding H+ consumes A- and adding OH- consumes HA, both reactions tilting the ratio without causing a large swing in pH. The equation is most reliable when concentrations are well above the Ka and the ratio [A-]/[HA] stays between 0.1 and 10. This calculator flags when the ratio falls outside that window in the insight panel.
pH of common substances (approximate, 25 degrees C)
| Substance | Approximate pH | Classification |
|---|---|---|
| Battery acid (H2SO4 conc.) | < 1 | Strongly acidic |
| Gastric acid | 1.5-2.0 | Strongly acidic |
| Lemon juice | 2.0-2.6 | Strongly acidic |
| Vinegar (acetic acid 5%) | 2.5-3.5 | Acidic |
| Orange juice | 3.3-4.2 | Acidic |
| Coffee | 4.8-5.1 | Acidic |
| Rain (clean) | 5.6 | Acidic |
| Milk | 6.3-6.8 | Mildly acidic |
| Pure water (25 C) | 7.0 | Neutral |
| Blood (normal) | 7.35-7.45 | Mildly basic |
| Seawater | 7.8-8.3 | Basic |
| Baking soda (1% solution) | 8.3 | Basic |
| Ammonia (household) | 11.0-11.5 | Strongly basic |
| Bleach (sodium hypochlorite) | 12.5 | Strongly basic |
| Sodium hydroxide (0.1 mol/L) | 13.0 | Strongly basic |
These values represent typical ranges; exact pH depends on concentration, temperature, and preparation.
Frequently asked questions
What is the difference between pH and [H+] concentration?
pH is the negative base-10 logarithm of the molar H+ concentration: pH = -log10([H+]). A concentration of 0.0001 mol/L corresponds to pH 4. The logarithmic scale means each whole pH unit is a tenfold difference in [H+], so pH 3 has ten times more H+ than pH 4 and 100 times more than pH 5.
How does the weak-acid mode differ from just using sqrt(Ka * C)?
The textbook approximation [H+] = sqrt(Ka * C) assumes that the acid dissociates only a tiny amount, keeping [HA] close to C. This works when Ka << C (roughly less than 5% dissociation). For stronger weak acids or dilute solutions the approximation overestimates [H+]. This calculator solves the exact quadratic x^2 + Ka*x - Ka*C = 0, giving the correct answer at all concentrations.
When is the Henderson-Hasselbalch equation most accurate?
The Henderson-Hasselbalch equation pH = pKa + log([A-]/[HA]) is most accurate when the ratio [A-]/[HA] is between 0.1 and 10 (that is, the pH is within one unit of the pKa). It also assumes concentrations are high enough that the dissociation of water and the partial dissociation of the weak acid itself are negligible. For very dilute buffers or extreme ratios, a full equilibrium calculation gives more accurate results.
Why does neutral pH equal 7 only at 25 degrees C?
Neutrality occurs when [H+] = [OH-], which depends on the water dissociation constant Kw. At 25 degrees C, Kw = 1.0 x 10-14, giving neutral pH = 7. At 37 degrees C (body temperature) Kw rises to about 2.4 x 10-14, so neutral pH drops to roughly 6.8. Blood at pH 7.4 is actually slightly alkaline relative to the body-temperature neutral point.
Can pH be negative or above 14?
Yes. Concentrated strong acids like 1 mol/L HCl give [H+] = 1 mol/L, pH = 0. At higher concentrations [H+] > 1 mol/L and pH < 0. Similarly, 1 mol/L NaOH gives pH = 14 and higher concentrations exceed 14. At these extremes the simple formula is still mathematically valid but activity coefficients deviate significantly from 1, so the measured (electrode) pH differs from the calculated value.
What is pKa and how does it relate to Ka?
pKa = -log10(Ka), the same logarithmic transform as pH to [H+]. A smaller pKa means a larger Ka and a stronger acid (more dissociation). Acetic acid has pKa = 4.74 (Ka = 1.8 x 10-5), making it a weak acid. Hydrochloric acid has pKa far below zero, making it a strong acid that dissociates almost completely. For buffer design, the most effective buffering occurs within one pH unit of the pKa.