Buffer Calculations ( Henderson Hasselbalch )

Biology • Solutions Concentrations, and Dilutions

Written by STEM Calculators Team Published January 3, 2026 Updated February 24, 2026

Buffer calculations (Henderson–Hasselbalch)

Uses \( \displaystyle pH = pK_a + \log_{10}\!\left(\frac{[A^-]}{[HA]}\right) \). Compute pH, find the required ratio, or prep a buffer from total concentration.

Inputs

Choose a mode, enter values, then calculate.

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Mode

pKₐ

Example: acetic acid \(pK_a \approx 4.76\).

Basis

Units update automatically (no invalid mixing).

Actions

A⁻ (concentration)

Enter \( [A^-] \) or \( n_{A^-} \). Must be > 0.

HA (concentration)

Enter \( [HA] \) or \( n_{HA} \). Must be > 0.

The ratio \( \frac{[A^-]}{[HA]} \) is unitless (as long as both are the same type of quantity).

Batch mode (CSV / paste)

Columns: mode,pKa plus fields. Modes: find_ph, find_ratio, prep. Fields: A,HA for find_ph; pH for find_ratio; CT,V and either pH or ratio for prep.

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Tip: Use scientific notation like 1e-3.

Buffer region on pH scale

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Ratio → pH guide (Henderson–Hasselbalch)

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ratio = — —

Preview ratio (log scale)

Slider controls \( \log_{10}(A^-/HA) \). 0 means ratio = 1.

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Buffer calculations (Henderson–Hasselbalch)

A buffer is usually made from a weak acid HA and its conjugate base A⁻. It resists pH changes because added H⁺ reacts with A⁻ and added OH⁻ reacts with HA.

\begin{aligned} pH &= pK_a + \log_{10}\!\left(\frac{[A^-]}{[HA]}\right) \end{aligned}

The fraction \(\dfrac{[A^-]}{[HA]}\) is a unitless ratio. That means you can use either:

Concentrations (for example, molarities), or
Moles (if both are in the same volume).

In practice, using moles is often convenient when you’re preparing a buffer from solids or stock solutions.

Mode 1: Find pH from \(pK_a\), \(A^-\), and \(HA\)

If you know the amounts of conjugate base and acid, first compute the ratio:

\begin{aligned} \text{ratio} &= \frac{[A^-]}{[HA]} \end{aligned}

Then substitute the ratio into Henderson–Hasselbalch:

\begin{aligned} pH &= pK_a + \log_{10}(\text{ratio}) \end{aligned}

Buffer quality rule of thumb
The buffer works best when \(\text{ratio}\) stays between about 0.1 and 10, which corresponds roughly to \(pH \approx pK_a \pm 1\).

Mode 2: Find the ratio needed for a target pH

Starting from the same equation, isolate the logarithm and undo the log:

\begin{aligned} pH - pK_a &= \log_{10}\!\left(\frac{[A^-]}{[HA]}\right) \\ \frac{[A^-]}{[HA]} &= 10^{(pH - pK_a)} \end{aligned}

This mode is useful when you know the acid system (so you know \(pK_a\)) and you need a buffer at a specific pH.

Warning
If the computed ratio is very large (> 10) or very small (< 0.1), the buffer capacity will be poor because one form dominates.

Mode 3: Prep helper from total concentration \(C_T\) and volume

Sometimes you want a buffer with a specific total concentration: \(C_T = [A^-] + [HA]\). If you also know the required ratio \(r = \dfrac{[A^-]}{[HA]}\), you can solve for each component:

\begin{aligned} r &= \frac{[A^-]}{[HA]} \\ [HA] &= \frac{C_T}{1 + r} \\ [A^-] &= C_T - [HA] \end{aligned}

With total volume \(V\), you can also compute the moles needed:

\begin{aligned} n_{A^-} &= [A^-]\cdot V \\ n_{HA} &= [HA]\cdot V \end{aligned}

This calculator keeps the math in aligned rows (not a single long line) to reduce horizontal overflow on small screens.

Frequently Asked Questions

What is the Henderson-Hasselbalch equation for a buffer?

The calculator uses pH = pKa + log10([A-]/[HA]), where HA is the weak acid and A- is its conjugate base. The ratio [A-]/[HA] can be formed from concentrations or from moles if both are in the same volume.

How do I find the A-/HA ratio needed for a target pH?

Rearrange the equation to get [A-]/[HA] = 10^(pH - pKa). A very large or very small ratio indicates weak buffer capacity because one form dominates.

How do you compute [A-] and [HA] from total concentration CT?

If CT = [A-] + [HA] and r = [A-]/[HA], then [HA] = CT/(1 + r) and [A-] = CT - [HA]. With total volume V, moles are nA- = [A-] x V and nHA = [HA] x V.

When does a buffer work best around pKa?

Buffer performance is best when the ratio stays roughly between 0.1 and 10, which corresponds to pH about pKa ± 1. Outside this range, the buffer resists pH change less effectively.

Can I use moles instead of concentrations in Henderson-Hasselbalch calculations?

Yes, because the ratio is unitless, so using nA-/nHA is valid when both species are in the same total volume. This is convenient when planning buffer prep from measured amounts.

Calculation steps

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