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pKa Calculator

Convert between pKa, Ka, pH, and percent dissociation for weak acids, using the exact quadratic solution and the 5% approximation check. Free.

Frequently Asked Questions

What is pKa and what does it measure?

pK<sub>a</sub> = -log<sub>10</sub>(K<sub>a</sub>), where K<sub>a</sub> is the acid dissociation constant. It measures the strength of a weak acid: lower pK<sub>a</sub> means a stronger acid (more dissociated at a given pH). Strong acids like HCl have pK<sub>a</sub> < 0; weak acids range from about 2 (stronger weak acid) to 12 (very weak acid). At pH = pK<sub>a</sub>, exactly half of the acid is dissociated.

How do I calculate the pH of a weak acid solution?

For weak acid HA at concentration C, set up the equilibrium: K<sub>a</sub> = [H<sup>+</sup>][A<sup>-</sup>]/[HA]. If C/K<sub>a</sub> > 100, the approximation [H<sup>+</sup>] ≈ √(K<sub>a</sub>·C) is accurate to within about 5%. Otherwise, solve the exact quadratic: [H<sup>+</sup>] = (-K<sub>a</sub> + √(K<sub>a</sub><sup>2</sup> + 4·K<sub>a</sub>·C)) / 2. Then pH = -log<sub>10</sub>([H<sup>+</sup>]).

What is the relationship between pKa and pKb?

For a conjugate acid-base pair: pK<sub>a</sub> + pK<sub>b</sub> = pK<sub>w</sub> = 14.00 at 25 °C. So if acetic acid has pK<sub>a</sub> = 4.76, its conjugate base (acetate ion) has pK<sub>b</sub> = 14.00 - 4.76 = 9.24. The stronger the acid (low pK<sub>a</sub>), the weaker its conjugate base (high pK<sub>b</sub>), and vice versa.

Can I use this for weak bases and pKb?

Yes. The tool reports K<sub>b</sub> and pK<sub>b</sub> alongside the acid values, using pK<sub>b</sub> = 14 - pK<sub>a</sub> at 25 °C. If you know a weak base by its own pK<sub>b</sub>, convert to the conjugate acid with pK<sub>a</sub> = 14 - pK<sub>b</sub> and enter that. To estimate the pH of a weak base of concentration C, solve for [OH<sup>-</sup>] with the same quadratic using K<sub>b</sub> = 10<sup>-pKb</sup> in place of K<sub>a</sub>, then pH = 14 - pOH.

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How This Calculator Works

This calculator converts between K_a and pK_a, finds the pH of a weak acid solution from pK_a and initial concentration, and reports percent dissociation. It uses the exact quadratic solution for [H⁺] rather than just the square-root approximation, and it tells you whether the 5% approximation rule is satisfied.

Choose a mode from the dropdown or load a preset common acid. For pH calculation, enter both the pK_a and the initial molar concentration of the undissociated acid.

Ka and pKa Explained

K_a is the acid dissociation constant for the equilibrium HA ↔ H⁺ + A^-. It equals [H⁺][A^-] / [HA] at equilibrium. A larger K_a means stronger acid dissociation. pK_a = -log₁₀(K_a) is the negative logarithm, so a lower pK_a means a stronger acid (just as lower pH means more acidic). Strong acids have pK_a below about 0; common weak acids fall between pK_a 2 and 12.

Strong vs. Weak Acids

Strong acids (HCl, HBr, HI, HNO₃, HClO₄, H₂SO₄ first proton) dissociate essentially completely: K_a is very large and pK_a is negative or very small. Weak acids dissociate only partially. The distinction matters for pH calculations: for strong acids, [H⁺] equals the initial concentration; for weak acids, you must solve the equilibrium expression.

pH of a Weak Acid Solution

The equilibrium expression x² + K_a·x - K_a·C₀ = 0 (where x = [H⁺]) solves exactly to:

x = (-K_a + √(K_a² + 4·K_a·C₀)) / 2
pH = -log₁₀(x)

The approximation assumes x is small compared to C₀, giving x ≈ √(K_a·C₀). This is valid when C₀/K_a is greater than 100, where the approximate [H⁺] stays accurate to within about 5%. For dilute weak acid solutions or stronger weak acids, use the exact quadratic result.

Worked Example

Find the pH of 0.10 M acetic acid, pK_a = 4.76. First convert to K_a, then solve the quadratic for x = [H⁺]:

K_a = 10^-4.76 ≈ 1.74 × 10^-5
x = (−K_a + √(K_a² + 4·K_a·C₀)) ÷ 2 = (−1.74×10^-5 + √((1.74×10^-5)² + 4·1.74×10^-5·0.10)) ÷ 2 ≈ 1.31 × 10^-3 M
pH = -log₁₀(1.31 × 10^-3) ≈ 2.88
Percent dissociation = (1.31 × 10^-3 ÷ 0.10) × 100 ≈ 1.3%

Since dissociation is well under 5%, the simple approximation x ≈ √(K_a·C₀) = √(1.74×10^-5 × 0.10) ≈ 1.32 × 10^-3 M gives essentially the same pH of 2.88 here.

The 5% Rule for the Approximation

If percent dissociation ([H⁺] / C₀ × 100) is less than 5%, the approximation is considered acceptable and x can be treated as much smaller than C₀. When dissociation exceeds 5%, the quadratic solution is needed for accurate results. The 5% threshold corresponds roughly to C₀/K_a greater than 400, though textbooks vary on the exact cutoff.

Do not confuse this with the looser C₀/K_a > 100 rule mentioned earlier: that cutoff keeps the approximate [H⁺] within about 5% of the exact value, whereas this rule keeps the fraction of acid that actually dissociates under 5%. They are two different 5% figures. To avoid the ambiguity entirely, this calculator always reports the exact quadratic [H⁺] and simply flags whether C₀/K_a is at least 100. The results row labeled "5% approximation valid?" reads Yes when C₀/K_a ≥ 100 and No otherwise, so the displayed Yes/No criterion is exactly that ratio test.

Conjugate Acid-Base Pairs

Every weak acid has a conjugate base (A^-) with pK_b = 14 - pK_a (at 25 °C, where K_w = 10^-14). A strong acid (low pK_a) has a weak conjugate base (high pK_b, close to inert). A weak acid (high pK_a) has a relatively strong conjugate base. This relationship governs buffer selection, hydrolysis reactions, and the behavior of salts in water. For example, sodium acetate dissolves to give acetate ion, which hydrolyzes to raise the pH because acetic acid is a weak acid (pK_a 4.76, so pK_b of acetate = 9.24).