pKa to pH Calculator: Formula and How to Use It
The calculator for this page is switched off while it is checked. The formula is below, and the worked example in the article shows how to use it by hand.
This calculator converts a given pKa value and the concentrations of a weak acid and its conjugate base into the pH of the buffer solution using the Henderson–Hasselbalch equation. You enter the pKa, the molar concentration of the acid, and the molar concentration of the base, and the tool returns the pH. It also shows the ratio of base to acid, which is useful for understanding buffer composition.
Formula
The calculator uses the Henderson–Hasselbalch equation:
pH = pKa + log�₀([A�] / [HA])
- pH – the acidity of the buffer solution (unitless, typically 0–14).
- pKa – the negative base-10 logarithm of the acid dissociation constant (Ka) of the weak acid. It is unitless.
- [A�] – molar concentration of the conjugate base (the deprotonated form), in mol/L (M).
- [HA] – molar concentration of the weak acid (the protonated form), in mol/L (M).
The equation is derived from the equilibrium expression for a weak acid: Ka = [H�][A�]/[HA]. Taking the negative logarithm of both sides and rearranging gives the form above. It is valid when the acid is weak (Ka small) and the concentrations of acid and base are large compared to the amount that dissociates.
Worked Example
Using the default values from the calculator: pKa = 4.75, acid concentration = 0.10 M, base concentration = 0.10 M.
- Calculate the ratio [A�]/[HA] = 0.10 / 0.10 = 1.0.
- Take the base-10 logarithm: log�₀(1.0) = 0.
- Add to pKa: pH = 4.75 + 0 = 4.75.
The calculator returns pH = 4.75, which matches. When the acid and base concentrations are equal, the pH equals the pKa. This is the midpoint of the buffer’s useful range.
When to Use This Calculator
Use this tool when you are preparing a buffer solution in a lab, checking a recipe for a biological buffer, or solving a textbook acid–base problem. It is appropriate for mixtures of a weak acid and its conjugate base (or a weak base and its conjugate acid, if you convert pKb to pKa). Common examples include acetic acid/acetate buffers (pKa ≈ 4.75), phosphate buffers (pKa₂ ≈ 7.2), and Tris buffers (pKa ≈ 8.1 at 25°C).
The calculator is not for strong acids or strong bases, where dissociation is complete and the Henderson–Hasselbalch equation does not apply. It also assumes ideal behavior (activity coefficients ≈ 1), which is reasonable for dilute solutions (below ~0.1 M). For very concentrated buffers, the actual pH may differ by a few tenths of a unit.
How to Read the Result
The pH value tells you the acidity of the buffer. The base/acid ratio is a quick check: if the ratio is 1, the pH equals the pKa. If the ratio is 10, the pH is pKa + 1; if the ratio is 0.1, the pH is pKa − 1. This logarithmic relationship means that a tenfold change in the ratio shifts the pH by one unit.
In practice, buffers work best when the pH is within ±1 unit of the pKa. Outside that range, the buffer capacity (the ability to resist pH changes) drops sharply. For example, an acetic acid/acetate buffer with pKa 4.75 is effective from about pH 3.75 to 5.75.
Common Mistakes and Limitations
- Using the wrong pKa – For polyprotic acids, use the pKa that corresponds to the protonation state you are working with. For phosphoric acid, pKa� = 2.15, pKa₂ = 7.20, pKa₃ = 12.35. Choose the one closest to your target pH.
- Mixing up acid and base – [HA] is the protonated form, [A�] is the deprotonated form. For an amine buffer like Tris, the acid form is the protonated ammonium (Tris-H�) and the base form is the neutral amine.
- Forgetting the logarithm – The equation uses log base 10, not natural log. Use the log�₀ button on your calculator.
- Assuming the approximation always holds – The Henderson–Hasselbalch equation assumes that the acid and base concentrations are much larger than the amount that dissociates. If you are working with very dilute solutions (below ~0.01 M) or a very strong acid (Ka > 10�²), the calculated pH may be off.
- Ignoring temperature – pKa values change with temperature. For example, Tris buffer pKa decreases by about 0.03 per °C. If you need precise pH at a specific temperature, look up the pKa at that temperature.
Alternatives to the Henderson–Hasselbalch Equation
For more accurate calculations, especially when the approximation fails, you can solve the full equilibrium expression numerically. This involves setting up the charge balance and mass balance equations and solving for [H�]. Many online tools and software (like spreadsheet solvers) can do this. The Henderson–Hasselbalch equation is a simplification that works well for most buffer preparation, but for research-grade accuracy, a full equilibrium calculation is better.
Another alternative is to use a pH meter and titrate the solution directly. That is often the most reliable method for preparing a buffer at a specific pH, because it accounts for all real-world deviations (temperature, ionic strength, impurities).
Frequently Asked Questions
What is the difference between pKa and pH?
pKa is a property of a specific acid–base pair that describes how easily the acid donates a proton. It is constant for a given acid at a given temperature. pH is a property of a specific solution that describes its current acidity. The Henderson–Hasselbalch equation links the two: when you know the pKa and the ratio of base to acid, you can calculate the pH.
Can I use this calculator for a weak base?
Yes, but you need to use the pKa of the conjugate acid. For a weak base like ammonia (NH₃), the conjugate acid is ammonium (NH₄�) with a pKa of about 9.25. If you have a solution of ammonia and ammonium chloride, enter pKa = 9.25, the concentration of NH₄� as the acid, and the concentration of NH₃ as the base.
Why does the pH equal the pKa when concentrations are equal?
Because the log of 1 is 0. When [A�] = [HA], the ratio is 1, log�₀(1) = 0, so pH = pKa + 0 = pKa. This is the point of maximum buffer capacity, where the solution resists pH changes best.
What if I only know the total buffer concentration?
If you know the total concentration (C = [HA] + [A�]) and the desired pH, you can rearrange the equation to find the individual concentrations. For example, if you want a total concentration of 0.2 M and a pH of 5.0 with acetic acid (pKa 4.75), you can solve for the ratio and then find [HA] and [A�]. Many buffer calculators do this, but this tool requires you to input the individual concentrations.
Does the calculator work for strong acids?
No. Strong acids (like HCl) dissociate completely, so there is no significant concentration of the undissociated acid. The Henderson–Hasselbalch equation assumes a weak acid in equilibrium with its conjugate base. For a strong acid solution, the pH is simply the negative log of the acid concentration (for monoprotic acids).
How does temperature affect the result?
Temperature changes the pKa value. For example, the pKa of Tris buffer decreases by about 0.03 per °C. If you are preparing a buffer at 37°C, use the pKa at that temperature, not the room-temperature value. The calculator does not adjust for temperature; you must enter the correct pKa for your conditions.
Related
Formula used
in pka | pKa | - | 4.75 | 0 in acid | Acid concentration (M) | mol/L | 0.10 | 0 in base | Base concentration (M) | mol/L | 0.10 | 0 out pH | pH of buffer | - | pka + log10(base / acid) | 2 out ratio | Base/Acid ratio | - | base / acid | 3
Each line is one input (in, sel, list) or one result (out: label, unit, formula, decimals). How the calculators work
Method: the standard formula for this calculation, rounded as each result states. See how the calculators work or report an error.