Weak Acid pH & Ka Calculator
Calculate the pH and percent dissociation of any weak acid from its concentration and Ka, back-calculate the Ka and pKa of an unknown acid from a measured pH, or find the concentration needed to reach a target pH — with the exact ICE-table quadratic solved every time, not just the 5% shortcut.
Pick a calculation, then enter the known values.
pH value
Formula used: x^2 + Ka.x - Ka.C = 0, pH = -log10[H+]
1.333 x 10^-3 M
[H+] at equilibrium
1.333%
Percent dissociation
1.800 x 10^-5
Ka used
Yes
5% rule shortcut valid?
Interactive pH Scale
See exactly where your weak acid solution sits on the 0–14 pH scale, next to everyday substances.
Step-by-Step Weak Acid Calculation
Here's exactly how this answer was calculated, one step at a time.
Given: C = 0.1 mol/L, Ka = 1.8e-5
Step 1: Set up the ICE table
A weak acid only partially dissociates, so the equilibrium concentrations depend on Ka, not just on how much acid you dissolved.
HA <-> H+ + A-, Ka = [H+][A-] / [HA]Step 2: Write the quadratic in x = [H+]
x² + (1.800 x 10⁻⁵).x - (1.800 x 10⁻⁵)(0.1) = 0Step 3: Solve with the quadratic formula
[H+] = (-Ka + sqrt(Ka² + 4.Ka.C)) / 2 = 1.333 x 10⁻³ MStep 4: Apply the pH formula
pH = -log10(1.333 x 10⁻³) = 2.875Step 5: Find percent dissociation
% dissociation = ([H+] / C) x 100 = 1.333%Step 6: 5% approximation check
Percent dissociation is only 1.333%, well under the 5% cutoff, so the simpler sqrt(Ka.C) shortcut (pH = 2.872) would also have been accurate here.
Calculated pH:
2.875
Weak Acid pH & Ka Calculator: Find pH, Dissociation & Ka in Seconds
This free weak acid pH and Ka calculator is built for chemistry students, lab technicians, and anyone studying acid-base equilibrium who needs a fast, reliable answer without hand-solving a quadratic equation. It covers three real situations: finding the pH and percent dissociation of a weak acid straight from its concentration and Ka, working backward to find the Ka and pKa of an unknown acid from a measured pH, and finding exactly what concentration of a known acid is needed to reach a target pH.
Every result shows the hydrogen ion concentration at equilibrium, the percent of acid molecules that actually broke apart, a plain-language classification of how acidic the solution is, an interactive pH scale, and a complete written solution so you can follow exactly how the answer was reached. Unlike simplified calculators that only apply the sqrt(Ka.C) shortcut, this tool always solves the exact ICE-table quadratic, so the answer stays accurate even for acids that dissociate more than the usual 5% cutoff.
What Makes an Acid 'Weak'?
A weak acid does not fully break apart in water. Instead of every molecule donating its hydrogen ion, only a fraction of the dissolved acid actually dissociates, while the rest stays as intact, un-ionized molecules. This partial dissociation is described by an equilibrium constant called Ka, the acid dissociation constant, which measures how far the reaction HA <-> H+ + A- proceeds toward products at equilibrium.
A larger Ka means a stronger tendency to dissociate (a 'stronger' weak acid), while a smaller Ka means the acid barely ionizes at all. Common weak acids include acetic acid (found in vinegar), formic acid, benzoic acid, hydrofluoric acid, lactic acid, and carbonic acid, each with its own characteristic Ka value that has been measured experimentally and tabulated in chemistry references.
The ICE Table and the Weak Acid Quadratic
Solving a weak acid pH problem starts with an ICE table (Initial, Change, Equilibrium), which tracks how the concentrations of HA, H+, and A- shift as the reaction reaches equilibrium. Starting from an initial concentration C of undissociated acid and zero products, the change is -x for HA and +x for both H+ and A-, so at equilibrium: [HA] = C - x, [H+] = x, and [A-] = x.
Substituting these into the Ka expression, Ka = [H+][A-] / [HA], gives Ka = x^2 / (C - x), which rearranges into the quadratic x^2 + Ka.x - Ka.C = 0. Solving this with the quadratic formula gives the exact value of x, which is [H+], and from there pH = -log10(x) follows directly. This calculator solves that exact quadratic every time, rather than relying on an approximation that can break down.
The 5% Approximation Shortcut — and When It Fails
Many textbooks teach a shortcut: if C is much larger than x, the C - x term in the denominator can be approximated as just C, simplifying Ka = x^2 / C into x = sqrt(Ka.C). This avoids the quadratic formula entirely and is quick to calculate by hand.
The catch is that this shortcut is only valid when percent dissociation stays under about 5%. For very dilute solutions, or acids with a relatively large Ka, dissociation can exceed 5%, and the shortcut starts giving a noticeably wrong pH. This calculator checks percent dissociation automatically and flags whenever the shortcut would have been inaccurate, while always reporting the exact quadratic answer regardless.
Finding an Unknown Acid's Ka From a Measured pH
A common lab exercise runs the calculation in reverse: you dissolve an unknown weak acid at a known concentration, measure its pH with a meter or indicator, and need to work out its Ka. This calculator's 'Find Ka from pH' mode does exactly that. It converts the measured pH into [H+] using [H+] = 10^(-pH), then plugs that value back into the rearranged Ka expression, Ka = [H+]^2 / (C - [H+]), using the known starting concentration.
This is exactly how Ka values are determined experimentally in a real laboratory: prepare a solution of known concentration, measure its pH, and back-calculate Ka (and pKa = -log10(Ka)) from the result. The calculator also reports percent dissociation, which is a useful sanity check — a very high percent dissociation for a supposedly 'weak' acid can be a sign of a measurement error or that the acid is actually closer to a strong acid.
Finding the Concentration Needed for a Target pH
The third mode answers a practical formulation question: if you know an acid's Ka, how concentrated does your solution need to be to hit a specific target pH? This calculator rearranges the same Ka expression to solve directly for concentration: C = [H+].([H+] + Ka) / Ka, where [H+] comes from the target pH.
This is useful for preparing buffer components, adjusting a recipe or formulation to a target acidity, or planning a titration experiment where you need to start from a solution at a known, specific pH. The calculator also reports the resulting percent dissociation, so you can confirm whether the solution still behaves as a typical weak acid at that concentration.
Common Weak Acids and Their Ka Values
Acetic acid, the acid in vinegar, has a Ka of about 1.8 x 10^-5, meaning a 0.1 M solution has a pH around 2.87 and dissociates only about 1.3%. Hydrofluoric acid, unusually for a hydrogen halide, is a weak acid with a Ka around 6.6 x 10^-4, noticeably stronger than acetic acid but still far from complete dissociation. Formic acid and lactic acid sit in a similar range, with Ka values a bit larger than acetic acid.
Much weaker acids like hydrocyanic acid (HCN, Ka around 6.2 x 10^-10) barely dissociate at all, giving solutions that are only mildly acidic even at meaningful concentrations. Carbonic acid, formed when carbon dioxide dissolves in water, has a first Ka of about 4.3 x 10^-7, which is part of why carbonated water and rainwater are both mildly acidic.
Common Mistakes to Avoid When Calculating Weak Acid pH
The most frequent mistake is applying the strong-acid shortcut, [H+] = C, to a weak acid — this drastically overstates acidity because it assumes 100% dissociation. Another common error is using the sqrt(Ka.C) shortcut without checking whether percent dissociation actually stays under 5%, which silently introduces error for dilute solutions or larger Ka values.
It's also easy to mix up Ka and pKa when looking up a reference value — Ka is a small number typically written in scientific notation, while pKa is its negative base-10 logarithm and is usually a small positive number between roughly 2 and 10 for common weak acids. Always double-check which form a textbook or database is reporting before entering a value into this calculator.
Why Weak Acid Calculations Matter in Real Work
Outside the classroom, weak acid equilibrium calculations underpin buffer preparation in biochemistry and pharmaceutical labs, where a solution's pH must be held steady within a narrow range for an experiment or formulation to work correctly. Food scientists rely on weak acid chemistry to understand and control the tartness and preservation properties of vinegar, citrus juice, and fermented products.
Environmental chemists use weak acid equilibria to model the pH of natural water systems, since dissolved carbon dioxide, humic acids, and other weak acids control the acidity of rain, rivers, and soil. In every case, the same ICE-table approach and Ka expression this calculator applies is the foundation of the analysis.
Weak Acid pH & Ka Calculator: Quick Reference Summary
Set up the ICE table for HA <-> H+ + A-, giving Ka = x^2 / (C - x), which rearranges into the quadratic x^2 + Ka.x - Ka.C = 0. Solve for x = [H+] with the quadratic formula, then apply pH = -log10[H+]. The sqrt(Ka.C) shortcut only works when percent dissociation stays under about 5% — always check before relying on it. To find Ka from a measured pH, use Ka = [H+]^2 / (C - [H+]). To find the concentration needed for a target pH given Ka, use C = [H+].([H+] + Ka) / Ka.
This free weak acid pH and Ka calculator is intended to support learning, lab planning, and everyday chemistry questions. Always confirm the acid you are working with is genuinely a weak acid with a known Ka before using these formulas, and for safety-critical, regulated, clinical, or industrial work, always confirm results with validated lab instruments and your organisation's approved procedures.
Frequently Asked Questions
What is the formula for the pH of a weak acid?
Solve the ICE-table quadratic x^2 + Ka.x - Ka.C = 0 for x = [H+], then apply pH = -log10[H+]. When dissociation is under about 5%, the shortcut x = sqrt(Ka.C) also works.
What is the pH of 0.1 M acetic acid?
With Ka = 1.8 x 10^-5, 0.1 M acetic acid has [H+] ≈ 1.33 x 10^-3 M, giving a pH of about 2.87 and roughly 1.3% dissociation.
How do I find Ka from pH?
Convert the measured pH to [H+] using [H+] = 10^(-pH), then use Ka = [H+]^2 / (C - [H+]), where C is the known starting concentration of the acid.
What is the difference between Ka and pKa?
Ka is the acid dissociation constant, usually a small number in scientific notation. pKa = -log10(Ka), which converts it into a small positive number, typically between 2 and 10 for common weak acids, that's easier to compare at a glance.
When can I use the sqrt(Ka.C) shortcut instead of the quadratic?
Only when the resulting percent dissociation is under about 5%. This calculator checks this automatically and always reports the exact quadratic answer regardless, so you never have to worry about the shortcut being wrong.
Is a higher Ka a stronger or weaker acid?
A higher Ka means the acid dissociates more, making it a comparatively stronger weak acid. A lower Ka means less dissociation and a comparatively weaker acid.
Why is my weak acid's percent dissociation so low?
Weak acids only partially ionize by definition. Most common weak acids at typical lab concentrations (0.01–1 M) dissociate somewhere between well under 1% and a few percent, unlike strong acids which dissociate essentially 100%.
Can this calculator handle polyprotic weak acids like carbonic acid?
This calculator models a single dissociation step using one Ka value, which is appropriate for the first (dominant) dissociation of a polyprotic acid like carbonic acid. Later dissociation steps have their own, much smaller Ka values and contribute negligibly to the overall pH in most cases.