Skip to content
Calcapedia
Menu
Science

Henderson–Hasselbalch Calculator

Find the pH of a buffer from its pKa and concentrations. Or find the base-to-acid ratio and amounts that reach a target pH.

Level: Grade 12 to college

  • Common Core standard HSF.BF.B.5(+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.
Printable worksheet

Henderson–Hasselbalch Calculator

Know the answer you need? Pick an input to work backward.

Inputs
Solve for

pKa = −log₁₀(Ka). Acetic acid is about 4.76 at 25 °C.

Concentration of the salt or base form, for example acetate. Any unit, as long as [HA] uses the same one.

Concentration of the acid form, in the same unit as [A⁻].

Result

Buffer pH

4.9361

The buffer pH is 4.9361.

Ratio [A⁻] ÷ [HA]
1.5
Share in the base form
60%
Buffering
Within pKa ± 1 (effective)

See the step-by-step solution ↓

Step-by-step solution

  1. Divide the base concentration by the acid concentration, because the pH depends only on this ratio

    [A⁻][HA]=0.150.1=1.5

  2. Take the base-10 logarithm of the ratio, which turns it into a pH shift

    log₁₀(1.5)=0.176091

  3. Add that shift to the pKa to get the buffer's pH

    pH=4.76+0.176091=4.936091

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

What this calculator does

Find the pH of a buffer, or work out how to mix one that lands on the pH you want. A buffer is a mix of a weak acid (HA) and its matching base form (A⁻, called the conjugate base). It keeps its pH steady when you add small amounts of acid or base. The Henderson–Hasselbalch equation links the buffer's pH to just two things. One is the acid's pKa, a number that tells you how strong the acid is. The other is the ratio of base to acid. Double the base compared with the acid and the pH rises by about 0.3, whatever the actual concentrations are.

You can use this calculator in three ways. Find the pH of a buffer you already have. Find the base-to-acid ratio that gives a pH you want. Or split a total buffer concentration into the amounts of acid and base to weigh out. It also tells you whether the target sits in the range where the buffer works well.

Where it's used

Why this math matters outside the classroom:

  • Lab buffers. Biochemists making a pH 7.4 phosphate buffer with pKa 7.2 need a base-to-acid ratio of 10^0.2, about 1.58.
  • Equal amounts. Students see that a buffer with equal acid and base concentrations has a pH exactly equal to the acid's pKa.
  • Acetate buffer. An acetate buffer with pKa 4.76 and twice as much acetate as acetic acid sits at about 4.76 + 0.30 = 5.06.
  • Blood chemistry. Physiology courses use the bicarbonate system to explain how blood holds its pH within a narrow range.
  • Product stability. Food and cosmetics makers buffer their products so the pH stays steady during storage.

Grade level and standards: Grade 12 to college; Common Core State Standards for Mathematics HSF.BF.B.5. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. Choose whether you want the buffer pH, the ratio for a target pH, or the concentrations for a target pH.
  2. Enter the pKa of the weak acid. Look it up for the temperature you're working at.
  3. Enter the base and acid concentrations. Or enter the target pH and, for the last mode, the total buffer concentration.
  4. Read the result, the share of the buffer in its base form, and whether the pH is within one unit of the pKa.

What the inputs mean

pKa of the weak acid
The pKa is the negative logarithm of Ka, the acid's dissociation constant (how readily it gives up H⁺). If you have Ka, take −log₁₀(Ka). For Ka = 1.8 × 10⁻⁵ that gives 4.74.
Conjugate base [A⁻]
Concentration of the conjugate base. It's often added as a salt, such as sodium acetate.
Weak acid [HA]
Concentration of the weak acid. Only the ratio matters, so moles or millimoles work as well as mol/L.
Total buffer concentration ([HA] + [A⁻])
The sum [HA] + [A⁻] you want in the finished buffer. A higher total gives more buffering capacity (power to soak up added acid or base) at the same pH.

Formula and method

pH = pKa + log₁₀([A⁻] ÷ [HA])
[A⁻] ÷ [HA] = 10^(pH − pKa)
[HA] = C ÷ (1 + ratio)        [A⁻] = C × ratio ÷ (1 + ratio)

[A⁻] is the concentration of the base form and [HA] is the concentration of the weak acid. C is the total of the two, and "ratio" is [A⁻] ÷ [HA]. log₁₀ is the base-10 logarithm, which counts powers of 10.

The equation comes from rearranging the acid's dissociation expression, Ka = [H⁺][A⁻] ÷ [HA], and taking negative logarithms. When the acid and base concentrations are equal, the log term is zero. Then pH = pKa, the midpoint where a buffer resists change best.

To aim for a particular pH, subtract the pKa and raise 10 to that power to get the ratio. Then, for a fixed total concentration C, the ratio splits C into two parts. Out of (1 + ratio) shares, the acid gets one share and the base gets 'ratio' shares.

Worked example

An acetate buffer contains 0.15 mol/L sodium acetate and 0.10 mol/L acetic acid. Acetic acid has a pKa of 4.76. What is the pH?

  1. Ratio: 0.15 ÷ 0.1 = 1.5.
  2. log₁₀(1.5) = 0.176091.
  3. pH = 4.76 + 0.176091 = 4.936091.

Result: The buffer pH is about 4.9361. Sixty percent of the buffer is in the acetate (base) form, and the pH is within one unit of the pKa.

Understanding the result

A buffer works well when the pH is within about one unit of the pKa. That means a base-to-acid ratio between 0.1 and 10. Outside that range, one form is so scarce that adding acid or base quickly uses it up. The calculator then labels the buffering as weak.

The ratio sets the pH, and the total concentration sets the capacity. A 0.01 M and a 0.5 M acetate buffer at the same ratio have the same pH. But the stronger one soaks up far more added acid before the pH moves.

Assumptions and limitations

  • Concentrations stand in for activities (the "effective" concentrations chemists use). That's reasonable for dilute buffers, roughly 0.001 to 0.1 mol/L.
  • The weak acid and its base are present at the amounts you enter. They don't break apart or react with water enough to matter (dissociation or hydrolysis). This holds when both are well above the H⁺ and OH⁻ concentrations.
  • The pKa is for the temperature and ionic strength (salt level) of your solution.
  • At very low concentrations, or for acids with pKa near 0 or 14, the shortcut breaks down. You then need an exact equilibrium calculation.
  • Acids that can give up more than one H⁺, such as phosphate, need the pKa for the specific pair you're using. For example, it's 7.21 for H₂PO₄⁻/HPO₄²⁻.
  • The calculator doesn't predict how much pH changes when you add a strong acid or base to the buffer.

Frequently asked questions

What happens when [A⁻] equals [HA]?

The ratio is 1 and log₁₀(1) = 0, so the pH equals the pKa exactly. This is the point of maximum buffer capacity. That's why people choose a buffer with a pKa close to the target pH.

Can I use moles instead of concentrations?

Yes. Both forms are in the same volume, so the volume cancels out in the ratio. Moles, millimoles or mol/L all give the same pH, as long as both inputs use the same unit.

How do I make a buffer at a specific pH?

Pick a weak acid whose pKa is within one unit of the target. Choose a total concentration, and use the concentrations mode. It tells you how much of the acid and its salt to include. Check the final pH with a meter, since real solutions drift slightly from the ideal equation.

Does this work for basic buffers like ammonia?

Yes. Use the pKa of ammonium (about 9.25), which is ammonia's conjugate acid. Treat ammonia as the base and ammonium as the acid.

How this calculator is checked

Method: Henderson–Hasselbalch equation pH = pKa + log₁₀([A⁻]/[HA]), derived from the acid dissociation constant; algebraic rearrangement for ratio and mass balance [HA] + [A⁻] = C. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

Embed this calculator

Put this Henderson–Hasselbalch Calculator on your own website or blog for free. Paste this code where you want it to appear: