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Henderson Hasselbalch Calculator

Calculate pH of buffer solutions using the Henderson-Hasselbalch equation from pKa and concentrations.

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Chemistry

Henderson-Hasselbalch Calculator

Calculate pH of buffer solutions using the Henderson-Hasselbalch equation from pKa and concentrations of acid and conjugate base.

Last updated: December 2025

Calculator

Adjust values & calculate
4.76
0.1 M
0.1 M
Buffer pH
4.7600
Acidic solution | Within effective buffer range
[H+] Concentration
1.7378e-5 M
[OH-] Concentration
5.7544e-10 M
pOH
9.2400
[A-]/[HA] Ratio
1.0000
log([A-]/[HA])
0.0000
Effective Buffer Range
3.76 - 5.76
pKa +/- 1.0 pH unit
0714
Note: The Henderson-Hasselbalch equation assumes dilute solutions and that equilibrium concentrations approximate analytical concentrations. For very dilute or concentrated solutions, more rigorous calculations may be needed.
Your Result
pH = 4.7600 | pOH = 9.2400 | [H+] = 1.7378e-5 M | Buffer range: 3.76 - 5.76
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Understand the Math

Formula

pH = pKa + log([A-] / [HA])

Where pH is the acidity of the buffer solution, pKa is the negative log of the acid dissociation constant, [A-] is the molar concentration of the conjugate base, and [HA] is the molar concentration of the weak acid. When [A-] = [HA], the log term becomes zero and pH = pKa.

Last reviewed: December 2025

Worked Examples

Example 1: Acetate Buffer pH Calculation

Calculate the pH of a buffer containing 0.15 M acetic acid and 0.20 M sodium acetate (pKa = 4.76).
Solution:
pH = pKa + log([A-]/[HA]) pH = 4.76 + log(0.20/0.15) pH = 4.76 + log(1.333) pH = 4.76 + 0.125 pH = 4.885 [H+] = 10^(-4.885) = 1.303 x 10^(-5) M
Result: Buffer pH = 4.885 (slightly above pKa due to excess base)

Example 2: Phosphate Buffer for Cell Culture

A phosphate buffer (pKa = 7.20) uses 0.05 M NaH2PO4 and 0.08 M Na2HPO4. Find the pH.
Solution:
pH = pKa + log([HPO4 2-]/[H2PO4-]) pH = 7.20 + log(0.08/0.05) pH = 7.20 + log(1.60) pH = 7.20 + 0.204 pH = 7.404 This is very close to physiological pH (7.4)
Result: Buffer pH = 7.404 (ideal for cell culture and biological experiments)
Expert Insights

Background & Theory

The Henderson-Hasselbalch Calculator applies the following established principles and formulas. Chemistry is the science of matter's composition, structure, properties, and transformations. At the heart of quantitative chemistry lies the mole concept. One mole of any substance contains exactly 6.022ร—10ยฒยณ entities (Avogadro's number, Nโ‚), and the molar mass of an element or compound in grams per mole is numerically equal to its atomic or molecular mass in atomic mass units. This allows chemists to convert between measurable mass and the number of reacting particles. Stoichiometry uses balanced chemical equations to relate the amounts of reactants and products. A balanced equation conserves both mass and charge. Molarity, the most common concentration unit, is defined as M = n/V, where n is moles of solute and V is volume of solution in liters, giving units of mol/L. Acidity and basicity are quantified by the pH scale, defined as pH = โˆ’logโ‚โ‚€[Hโบ], where [Hโบ] is the molar concentration of hydrogen ions. Pure water at 25ยฐC has pH 7.00; acids have lower values and bases higher values. Each unit change represents a tenfold change in hydrogen ion concentration. Gas behavior is described by the ideal gas law PV = nRT, where P is pressure in pascals, V is volume in cubic meters, n is moles, R = 8.314 J/(molยทK), and T is temperature in kelvin. Special cases include Boyle's Law (Pโ‚Vโ‚ = Pโ‚‚Vโ‚‚ at constant temperature) and Charles's Law (Vโ‚/Tโ‚ = Vโ‚‚/Tโ‚‚ at constant pressure). Thermochemistry quantifies heat changes in reactions through enthalpy, H. Hess's Law states that the total enthalpy change for a reaction is the sum of enthalpy changes for any sequence of steps leading to the same overall reaction, making it possible to calculate enthalpies for reactions that cannot be measured directly. Electron configuration describes the distribution of electrons in atomic orbitals according to the Aufbau principle, Pauli exclusion principle, and Hund's rule. Periodic trends including atomic radius, ionization energy, and electronegativity arise systematically from electron configuration and nuclear charge, enabling chemists to predict and rationalize chemical behavior across the periodic table.

History

The history behind the Henderson-Hasselbalch Calculator traces back through the following developments. Chemistry's roots lie in alchemy, the medieval practice combining proto-scientific experimentation with mystical aims. Alchemists developed practical techniques including distillation, calcination, and the preparation of acids, building a body of empirical knowledge despite their theoretical misunderstandings. Modern chemistry is conventionally dated to Antoine Lavoisier (1743โ€“1794), often called the father of modern chemistry. Lavoisier demonstrated the law of conservation of mass in 1789, showing that matter is neither created nor destroyed in chemical reactions. He identified oxygen's role in combustion, dismantling the phlogiston theory, and co-authored the first systematic chemical nomenclature, establishing the language still used today. John Dalton proposed the first modern atomic theory in 1803, asserting that all matter is composed of indivisible atoms, that atoms of the same element are identical in mass, and that compounds form from fixed ratios of different atoms. This provided a physical basis for Lavoisier's conservation law and Proust's law of definite proportions. Dmitri Mendeleev published his periodic table in 1869, arranging the 63 known elements by atomic mass and revealing repeating patterns of chemical behavior. He boldly left gaps for undiscovered elements and predicted their properties with remarkable accuracy, predictions confirmed by the subsequent discovery of gallium, scandium, and germanium. Ernest Rutherford's gold foil experiment in 1911 revealed the nuclear model of the atom: a tiny, dense, positively charged nucleus surrounded by electrons. Niels Bohr refined this in 1913 with a quantized model of electron orbits that explained the hydrogen emission spectrum. Quantum chemistry and molecular orbital theory, developed through the 1920s and 1930s, provided the full quantum mechanical description of chemical bonding. The latter 20th century saw the rise of computational chemistry, enabling molecular simulation at unprecedented scale. The green chemistry movement, articulated in the 12 Principles of Green Chemistry in 1998, reoriented the field toward sustainability, waste reduction, and benign chemical design, reflecting chemistry's growing awareness of its environmental responsibilities.

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Frequently Asked Questions

The Henderson-Hasselbalch equation is a mathematical relationship that relates the pH of a buffer solution to the pKa of the acid and the ratio of conjugate base to acid concentrations. The equation is pH = pKa + log([A-]/[HA]), where [A-] is the concentration of the conjugate base and [HA] is the concentration of the weak acid. It was derived independently by Lawrence Joseph Henderson in 1908 and Karl Albert Hasselbalch in 1917. The equation is a rearrangement of the acid dissociation constant expression and provides a convenient way to calculate the pH of buffer solutions without solving quadratic equations. It is one of the most frequently used equations in biochemistry, pharmacology, and analytical chemistry.
The Henderson-Hasselbalch equation has several important limitations that users should understand. It assumes that the equilibrium concentrations of the acid and conjugate base are approximately equal to the analytical (prepared) concentrations, which is only valid when the acid is weak and concentrations are not too dilute. For very dilute solutions (below 0.001 M) or very strong acids, the approximation breaks down significantly. The equation also ignores activity coefficients, which become important at high ionic strengths above 0.1 M. It does not account for the autoionization of water, which matters when pH is very high or very low. Polyprotic acids require separate Henderson-Hasselbalch calculations for each ionizable group, adding complexity that the simple equation does not address.
You may use the results for reference and educational purposes. For professional reports, academic papers, or critical decisions, we recommend verifying outputs against peer-reviewed sources or consulting a qualified expert in the relevant field.
All calculations use established mathematical formulas and are performed with high-precision arithmetic. Results are accurate to the precision shown. For critical decisions in finance, medicine, or engineering, always verify results with a qualified professional.
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The Formula section on this page shows the equation used. You can reproduce the calculation manually or in a spreadsheet using those steps. Compare your answer against the worked examples in the Examples section, which use known reference values so you can confirm the calculator is behaving as expected.
Educational Note: This calculator is provided for educational and informational purposes. Results are based on the formulas and inputs provided. Always verify important calculations independently. NovaCalculator processes calculator inputs client-side; optional analytics follow visitor consent settings. ยฉ 2024โ€“2026 NovaCalculator.

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Formula

pH = pKa + log([A-] / [HA])

Where pH is the acidity of the buffer solution, pKa is the negative log of the acid dissociation constant, [A-] is the molar concentration of the conjugate base, and [HA] is the molar concentration of the weak acid. When [A-] = [HA], the log term becomes zero and pH = pKa.

Worked Examples

Example 1: Acetate Buffer pH Calculation

Problem: Calculate the pH of a buffer containing 0.15 M acetic acid and 0.20 M sodium acetate (pKa = 4.76).

Solution: pH = pKa + log([A-]/[HA])\npH = 4.76 + log(0.20/0.15)\npH = 4.76 + log(1.333)\npH = 4.76 + 0.125\npH = 4.885\n[H+] = 10^(-4.885) = 1.303 x 10^(-5) M

Result: Buffer pH = 4.885 (slightly above pKa due to excess base)

Example 2: Phosphate Buffer for Cell Culture

Problem: A phosphate buffer (pKa = 7.20) uses 0.05 M NaH2PO4 and 0.08 M Na2HPO4. Find the pH.

Solution: pH = pKa + log([HPO4 2-]/[H2PO4-])\npH = 7.20 + log(0.08/0.05)\npH = 7.20 + log(1.60)\npH = 7.20 + 0.204\npH = 7.404\nThis is very close to physiological pH (7.4)

Result: Buffer pH = 7.404 (ideal for cell culture and biological experiments)

Frequently Asked Questions

What is the Henderson-Hasselbalch equation?

The Henderson-Hasselbalch equation is a mathematical relationship that relates the pH of a buffer solution to the pKa of the acid and the ratio of conjugate base to acid concentrations. The equation is pH = pKa + log([A-]/[HA]), where [A-] is the concentration of the conjugate base and [HA] is the concentration of the weak acid. It was derived independently by Lawrence Joseph Henderson in 1908 and Karl Albert Hasselbalch in 1917. The equation is a rearrangement of the acid dissociation constant expression and provides a convenient way to calculate the pH of buffer solutions without solving quadratic equations. It is one of the most frequently used equations in biochemistry, pharmacology, and analytical chemistry.

What are the limitations of the Henderson-Hasselbalch equation?

The Henderson-Hasselbalch equation has several important limitations that users should understand. It assumes that the equilibrium concentrations of the acid and conjugate base are approximately equal to the analytical (prepared) concentrations, which is only valid when the acid is weak and concentrations are not too dilute. For very dilute solutions (below 0.001 M) or very strong acids, the approximation breaks down significantly. The equation also ignores activity coefficients, which become important at high ionic strengths above 0.1 M. It does not account for the autoionization of water, which matters when pH is very high or very low. Polyprotic acids require separate Henderson-Hasselbalch calculations for each ionizable group, adding complexity that the simple equation does not address.

How do I get the most accurate result?

Enter values as precisely as possible using the correct units for each field. Check that you have selected the right unit (e.g. kilograms vs pounds, meters vs feet) before calculating. Rounding inputs early can reduce output precision.

How do I verify Henderson Hasselbalch Calculator's result independently?

The Formula section on this page shows the equation used. You can reproduce the calculation manually or in a spreadsheet using those steps. Compare your answer against the worked examples in the Examples section, which use known reference values so you can confirm the calculator is behaving as expected.

How do I interpret the result?

Results are displayed with a label and unit to help you understand the output. Many calculators include a short explanation or classification below the result (for example, a BMI category or risk level). Refer to the worked examples section on this page for real-world context.

Can I use Henderson Hasselbalch Calculator on a mobile device?

Yes. All calculators on NovaCalculator are fully responsive and work on smartphones, tablets, and desktops. The layout adapts automatically to your screen size.

References

Reviewed by Manoj Kumar, Mathematics Educator ยท Editorial policy