Ka/Kb Equilibrium Constant Calculator
Estimate [H+] and pH for a weak acid from Ka and its initial concentration, compute Ka directly from equilibrium concentrations, or convert between Ka and Kb for a conjugate acid-base pair using Ka × Kb = Kw.
Reviewed by the ToolNestr Editorial Team — July 2026
Uses [H⁺] ≈ √(Ka × C₀), valid when dissociation is small (roughly <5% of C₀). The calculator flags the estimate if the approximation looks shaky.
Two ideas that trip students up
1. A weak acid stays mostly intact
A fixed, illustrative population: about 90% remains undissociated HA (grey), with only ~10% split into H⁺ (red) and A⁻ (blue) — a small Ka. A strong acid, by contrast, would show 100% split into ions.
2. pKa and pKb seesaw — they always sum to 14
Fixed points for acetic acid (pKa ≈ 4.76) and ammonium (pKa ≈ 9.25), each paired with its conjugate base's pKb on the opposite side of the 14-unit scale — a bigger pKa always means a smaller pKb.
Ka/Kb graphs
How it works
The core idea in one line: Ka and Kb measure how far a weak acid or base dissociates at equilibrium, and for a conjugate acid-base pair they are locked together by Ka × Kb = Kw — know one, and you know the other.
Ka = [H⁺][A⁻] / [HA]
acid dissociation constant
Kb = [BH⁺][OH⁻] / [B]
base dissociation constant
Ka × Kb = Kw = 1.0×10⁻¹⁴
conjugate acid-base pair, 25°C
[H⁺] ≈ √(Ka × C₀)
small-dissociation approximation
For the common textbook case — a weak acid with a known Ka dissolved at initial concentration C₀ — the shortcut [H⁺] ≈ √(Ka × C₀) gives a fast, usually accurate estimate of [H⁺] and pH, valid as long as dissociation stays small (under about 5%). When you have exact equilibrium concentrations instead, Ka = [H⁺][A⁻]/[HA] gives Ka directly. And because Ka × Kb = Kw = 1.0×10⁻¹⁴ at 25°C for any conjugate pair, converting between Ka and Kb — or their negative logs pKa and pKb — is just one division and a log away.
Worked example 1 — estimating pH of acetic acid solution
Given: A 0.10 M acetic acid (CH₃COOH) solution has Ka = 1.8 × 10⁻⁵. Estimate [H⁺] and pH using the small-dissociation approximation.
The fraction dissociated is [H⁺]/C₀ ≈ 1.34%, well under the 5% guideline, so the approximation is valid here.
Worked example 2 — converting Ka to Kb for the conjugate base
Given: Acetic acid has Ka = 1.8 × 10⁻⁵. Find Kb and pKb for its conjugate base, acetate (CH₃COO⁻).
Check: pKa ≈ −log₁₀(1.8×10⁻⁵) ≈ 4.74, and pKa + pKb ≈ 4.74 + 9.26 = 14.00, confirming the pair rule.
Ka values for common weak acids
Approximate standard reference values at 25°C — a larger Ka means a stronger (more dissociated) weak acid.
| Weak acid | Formula | Ka | pKa |
|---|---|---|---|
| Hydrofluoric acid | HF | ≈ 6.6 × 10⁻⁴ | ≈ 3.18 |
| Formic acid | HCOOH | ≈ 1.8 × 10⁻⁴ | ≈ 3.75 |
| Acetic acid | CH₃COOH | ≈ 1.8 × 10⁻⁵ | ≈ 4.74 |
| Carbonic acid (Ka1) | H₂CO₃ | ≈ 4.3 × 10⁻⁷ | ≈ 6.37 |
| Hypochlorous acid | HOCl | ≈ 3.0 × 10⁻⁸ | ≈ 7.52 |
HF has the largest Ka here, so among these it dissociates the most (though it is still a weak acid, not a strong one); hypochlorous acid dissociates the least.
Where Ka and Kb actually matter
🩺 Predicting solution pH
Given Ka and the concentration of a weak acid being dissolved, chemists estimate the resulting pH before ever touching a pH meter — essential for preparing reagents and predicting reaction conditions.
⚗️ Buffer design
Choosing a weak acid/conjugate base pair for a buffer starts with picking a Ka (and therefore pKa) close to the target pH — see the Henderson-Hasselbalch calculator for the next step, computing the exact mixing ratio.
🧬 Biochemistry
Amino acid side chains, enzyme active sites, and drug molecules all have characteristic Ka/Kb values that determine their ionization state at physiological pH, which in turn controls solubility, binding, and reactivity.
🌊 Environmental water chemistry
Natural water systems involve weak acid/base equilibria (carbonic acid, phosphates, ammonia) whose Ka and Kb values govern buffering capacity, nutrient availability, and how pollutants partition in rivers, lakes, and oceans.
Common misconceptions
"Ka and Kb for a conjugate pair are independent of each other."
They are directly linked: Ka × Kb = Kw = 1.0×10⁻¹⁴ at 25°C (equivalently pKa + pKb = 14). Knowing one of the pair automatically gives you the other — they are never independent for a true conjugate acid-base pair.
"A stronger acid always has a stronger conjugate base."
The opposite is true. Because Ka × Kb = Kw is fixed, a larger Ka (stronger acid) forces a smaller Kb (weaker conjugate base), and vice versa. A strong acid's conjugate base is typically extremely weak.
"[H+] ≈ √(Ka × C0) always works."
This shortcut assumes dissociation is small enough (usually under about 5%) that C0 barely changes at equilibrium. For a relatively large Ka or a very dilute C0, dissociation can exceed 5%, and you need the full quadratic equilibrium expression for an accurate [H+].
"A small Ka means the acid does not react at all."
A small Ka just means dissociation is limited — most of the acid stays as intact HA at equilibrium, with only a small fraction ionized. The acid still reacts and establishes a real (if lopsided) equilibrium; it is simply a weak acid, not an unreactive one.
Formula sources & further reading
The formulas here are standard, traceable to:
- • OpenStax, Chemistry 2e — Chapter 14, Acid-Base Equilibria (free, peer-reviewed). openstax.org
- • Brown, LeMay & Bursten, Chemistry: The Central Science — Chapter 16, Acid-Base Equilibria.
- • Zumdahl & Zumdahl, Chemistry — Chapter 14, Acids and Bases.
Ka = [H⁺][A⁻]/[HA]; Kb = [BH⁺][OH⁻]/[B]; Ka × Kb = Kw = 1.0×10⁻¹⁴ at 25°C. The [H⁺] ≈ √(Ka × C₀) approximation assumes small dissociation (typically <5%). Reference Ka values are standard approximations at 25°C. Results are rounded for display.
How to use this calculator
Pick the mode
Estimate [H+] from Ka and C₀ (default), compute Ka from exact equilibrium concentrations, or convert Ka ⇄ Kb.
Enter the values
Type Ka and C₀, or [H+]/[A-]/[HA], or Ka (or Kb) for the conversion mode.
See it visually
The 3D diagrams show a weak acid mostly undissociated, and the fixed pKa/pKb seesaw for common acids.
Related tools
Frequently asked questions
What is Ka?
Ka is the acid dissociation constant — the equilibrium constant for a weak acid HA breaking apart into H⁺ and its conjugate base A⁻: HA ⇌ H⁺ + A⁻, so Ka = [H⁺][A⁻]/[HA]. A larger Ka means the acid dissociates more, so it is a (relatively) stronger weak acid.
What is Kb?
Kb is the base dissociation constant — the equilibrium constant for a weak base B reacting with water to form its conjugate acid BH⁺ and OH⁻: B + H₂O ⇌ BH⁺ + OH⁻, so Kb = [BH⁺][OH⁻]/[B]. A larger Kb means the base ionizes more, so it is a (relatively) stronger weak base.
How are Ka and Kb related?
For a conjugate acid-base pair (like acetic acid CH₃COOH and its conjugate base acetate CH₃COO⁻), Ka × Kb = Kw, where Kw = 1.0 × 10⁻¹⁴ at 25°C is the ion-product constant of water. Equivalently, pKa + pKb = 14. This means the two constants are locked together — you only ever need one to find the other.
What does a small Ka mean?
A small Ka (much less than 1, e.g. 10⁻⁵ or smaller) means the acid barely dissociates — at equilibrium, the solution is mostly still intact HA molecules, with only a small fraction ionized into H⁺ and A⁻. This is the defining feature of a weak acid, in contrast to a strong acid like HCl, which dissociates essentially 100%.
When is the [H+] ≈ √(Ka × C0) approximation valid?
This shortcut assumes the fraction of acid that dissociates is small enough that C0 (the initial concentration) is approximately unchanged at equilibrium — a good approximation when dissociation is under about 5%, which usually holds when Ka is small and C0 is not too dilute. If Ka is relatively large or C0 is very small, dissociation exceeds 5% and you should solve the full quadratic equilibrium expression instead for an accurate answer.