Weak Base pH & Kb Calculator
Calculate the pH, pOH and percent ionization of any weak base from its concentration and Kb, back-calculate the Kb and pKb of an unknown base 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 + Kb.x - Kb.C = 0, pOH = -log10[OH-]
1.333 x 10^-3 M
[OH-] at equilibrium
2.875
pOH
1.333%
Percent ionization
1.800 x 10^-5
Kb used
Interactive pH Scale
See exactly where your weak base solution sits on the 0–14 pH scale, next to everyday substances.
Step-by-Step Weak Base Calculation
Here's exactly how this answer was calculated, one step at a time.
Given: C = 0.1 mol/L, Kb = 1.8e-5
Step 1: Set up the ICE table
A weak base only partially reacts with water, so the equilibrium hydroxide concentration depends on Kb, not just on how much base you dissolved.
B + H2O <-> BH+ + OH-, Kb = [BH+][OH-] / [B]Step 2: Write the quadratic in x = [OH-]
x² + (1.800 x 10⁻⁵).x - (1.800 x 10⁻⁵)(0.1) = 0Step 3: Solve with the quadratic formula
[OH-] = (-Kb + sqrt(Kb² + 4.Kb.C)) / 2 = 1.333 x 10⁻³ MStep 4: Apply the pOH formula
pOH = -log10(1.333 x 10⁻³) = 2.875Step 5: Convert pOH to pH
pH = 14 - pOH = 14 - 2.875 = 11.125Step 6: Find percent ionization
% ionization = ([OH-] / C) x 100 = 1.333%Step 7: 5% approximation check
Percent ionization is only 1.333%, well under the 5% cutoff, so the simpler sqrt(Kb.C) shortcut (pOH = 2.872) would also have been accurate here.
Calculated pH:
11.125
Weak Base pH & Kb Calculator: Find pH, pOH, Ionization & Kb Instantly
This free weak base pH and Kb 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, pOH, and percent ionization of a weak base straight from its concentration and Kb, working backward to find the Kb and pKb of an unknown base from a measured pH, and finding exactly what concentration of a known base is needed to reach a target pH.
Every result shows the hydroxide ion concentration at equilibrium, the pOH, the pH, the percent of base molecules that actually reacted with water, a plain-language classification of how basic 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(Kb.C) shortcut, this tool always solves the exact ICE-table quadratic, so the answer stays accurate even for bases that ionize more than the usual 5% cutoff.
What Makes a Base 'Weak'?
A weak base does not fully react with water. Instead of every base molecule pulling a hydrogen ion away from water to form hydroxide, only a fraction of the dissolved base actually reacts, while the rest stays as intact, unreacted molecules. This partial reaction is described by an equilibrium constant called Kb, the base dissociation constant, which measures how far the reaction B + H2O <-> BH+ + OH- proceeds toward products at equilibrium.
A larger Kb means a stronger tendency to react with water (a 'stronger' weak base), while a smaller Kb means the base barely ionizes at all. Common weak bases include ammonia (used in household cleaners and fertilizers), methylamine, ethylamine, pyridine, aniline, and hydrazine, each with its own characteristic Kb value that has been measured experimentally and tabulated in chemistry references.
The ICE Table and the Weak Base Quadratic
Solving a weak base pH problem starts with an ICE table (Initial, Change, Equilibrium), which tracks how the concentrations of B, BH+, and OH- shift as the reaction reaches equilibrium. Starting from an initial concentration C of unreacted base and zero products, the change is -x for B and +x for both BH+ and OH-, so at equilibrium: [B] = C - x, [BH+] = x, and [OH-] = x.
Substituting these into the Kb expression, Kb = [BH+][OH-] / [B], gives Kb = x^2 / (C - x), which rearranges into the quadratic x^2 + Kb.x - Kb.C = 0. Solving this with the quadratic formula gives the exact value of x, which is [OH-], and from there pOH = -log10(x) follows directly, and pH follows from pH = 14 - pOH at 25°C. 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 Kb = x^2 / C into x = sqrt(Kb.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 ionization stays under about 5%. For very dilute solutions, or bases with a relatively large Kb, ionization can exceed 5%, and the shortcut starts giving a noticeably wrong pOH and pH. This calculator checks percent ionization automatically and flags whenever the shortcut would have been inaccurate, while always reporting the exact quadratic answer regardless.
Finding an Unknown Base's Kb From a Measured pH
A common lab exercise runs the calculation in reverse: you dissolve an unknown weak base at a known concentration, measure its pH with a meter or indicator, and need to work out its Kb. This calculator's 'Find Kb from pH' mode does exactly that. It converts the measured pH into pOH using pOH = 14 - pH, then into [OH-] using [OH-] = 10^(-pOH), and plugs that value back into the rearranged Kb expression, Kb = [OH-]^2 / (C - [OH-]), using the known starting concentration.
This is exactly how Kb values are determined experimentally in a real laboratory: prepare a solution of known concentration, measure its pH, and back-calculate Kb (and pKb = -log10(Kb)) from the result. The calculator also reports percent ionization, which is a useful sanity check — a very high percent ionization for a supposedly 'weak' base can be a sign of a measurement error or that the base is actually closer to a strong base.
Finding the Concentration Needed for a Target pH
The third mode answers a practical formulation question: if you know a base's Kb, how concentrated does your solution need to be to hit a specific target pH? This calculator first converts the target pH into the required [OH-], then rearranges the Kb expression to solve directly for concentration: C = [OH-].([OH-] + Kb) / Kb.
This is useful for preparing buffer components, adjusting a cleaning or formulation recipe to a target alkalinity, 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 ionization, so you can confirm whether the solution still behaves as a typical weak base at that concentration.
Common Weak Bases and Their Kb Values
Ammonia, the base in many household cleaners and window sprays, has a Kb of about 1.8 x 10^-5, meaning a 0.1 M solution has a pH around 11.13 and ionizes only about 1.3%. Methylamine and ethylamine, simple organic amines, have larger Kb values around 4-6 x 10^-4, making them noticeably more basic than ammonia at the same concentration, while trimethylamine sits closer to ammonia's range.
Much weaker bases like aniline (Kb around 4.3 x 10^-10) or pyridine (Kb around 1.7 x 10^-9) barely react with water at all, giving solutions that are only mildly basic even at meaningful concentrations. Hydrazine and hydroxylamine fall in between, with Kb values that make them moderately weak bases used in specialized industrial and analytical chemistry applications.
Common Mistakes to Avoid When Calculating Weak Base pH
The most frequent mistake is applying the strong-base shortcut, [OH-] = n x C, to a weak base — this drastically overstates basicity because it assumes complete reaction with water. Another common error is using the sqrt(Kb.C) shortcut without checking whether percent ionization actually stays under 5%, which silently introduces error for dilute solutions or larger Kb values.
It's also easy to mix up Kb and pKb when looking up a reference value — Kb is a small number typically written in scientific notation, while pKb is its negative base-10 logarithm and is usually a small positive number between roughly 2 and 10 for common weak bases. It's equally easy to forget the pOH-to-pH conversion (pH = 14 - pOH at 25°C) and accidentally report pOH where pH was asked for, or the other way round. Always double-check which form a textbook or database is reporting before entering a value into this calculator.
Why Weak Base Calculations Matter in Real Work
Outside the classroom, weak base 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 — ammonia and amine buffers are common choices at the alkaline end of the pH scale. Manufacturers of household and industrial cleaning products rely on weak base chemistry to control how effectively ammonia-based formulas cut through grease while staying within safe handling limits.
Environmental and agricultural chemists use weak base equilibria to model how dissolved ammonia behaves in soil, wastewater, and aquaculture systems, since the balance between ammonia (NH3) and ammonium (NH4+) is directly controlled by pH and is critical for both nutrient availability and aquatic toxicity. In every case, the same ICE-table approach and Kb expression this calculator applies is the foundation of the analysis.
Weak Base pH & Kb Calculator: Quick Reference Summary
Set up the ICE table for B + H2O <-> BH+ + OH-, giving Kb = x^2 / (C - x), which rearranges into the quadratic x^2 + Kb.x - Kb.C = 0. Solve for x = [OH-] with the quadratic formula, then apply pOH = -log10[OH-] and pH = 14 - pOH. The sqrt(Kb.C) shortcut only works when percent ionization stays under about 5% — always check before relying on it. To find Kb from a measured pH, first convert pH to [OH-] via pOH, then use Kb = [OH-]^2 / (C - [OH-]). To find the concentration needed for a target pH given Kb, use C = [OH-].([OH-] + Kb) / Kb.
This free weak base pH and Kb calculator is intended to support learning, lab planning, and everyday chemistry questions. Always confirm the base you are working with is genuinely a weak base with a known Kb 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 base?
Solve the ICE-table quadratic x^2 + Kb.x - Kb.C = 0 for x = [OH-], then apply pOH = -log10[OH-] and pH = 14 - pOH. When ionization is under about 5%, the shortcut x = sqrt(Kb.C) also works.
What is the pH of 0.1 M ammonia?
With Kb = 1.8 x 10^-5, 0.1 M ammonia has [OH-] ≈ 1.33 x 10^-3 M, giving a pOH of about 2.88, a pH of about 11.13, and roughly 1.3% ionization.
How do I find Kb from pH?
Convert the measured pH to pOH using pOH = 14 - pH, convert pOH to [OH-] using [OH-] = 10^(-pOH), then use Kb = [OH-]^2 / (C - [OH-]), where C is the known starting concentration of the base.
What is the difference between Kb and pKb?
Kb is the base dissociation constant, usually a small number in scientific notation. pKb = -log10(Kb), which converts it into a small positive number, typically between 2 and 10 for common weak bases, that's easier to compare at a glance.
When can I use the sqrt(Kb.C) shortcut instead of the quadratic?
Only when the resulting percent ionization 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 Kb a stronger or weaker base?
A higher Kb means the base reacts more with water, making it a comparatively stronger weak base. A lower Kb means less ionization and a comparatively weaker base.
Why is my weak base's percent ionization so low?
Weak bases only partially react with water by definition. Most common weak bases at typical lab concentrations (0.01–1 M) ionize somewhere between well under 1% and a few percent, unlike strong bases which dissociate essentially 100%.
How are Ka and Kb related for a conjugate acid-base pair?
Ka x Kb = Kw = 1.0 x 10^-14 at 25°C. So a base's conjugate acid's Ka can be found by dividing Kw by the base's Kb, and vice versa.