How do you calculate pH from hydrogen ion concentration?

Take the negative logarithm of the concentration of 10. The pH is defined as: pH = -log10[H+]. For example, if [H+] is equal to 0.001 moles then the pH would be 3. The reverse formula is: [H+] = 10 to the power of minus pH.

What is the difference between pH and pOH?

The pH value indicates the concentration of hydrogen ions, while the pOH indicates the concentration of hydroxide ions. At 25 degrees Celsius, the sum of both values is always 14, so that it applies: if the pOH value is 4, then the pH value is 10.

Why can't you use the formula pH = -log(C) for weak acids?

This simplification is only true for strong acids that fully dissociate. Weak acids only partially dissociate, so the concentration of hydrogen ions will be determined by Ka and the initial acid concentration. This tool solves the quadratic equation of equilibrium exactly to give you results.

What is the use of the Henderson Hasselbalch equation?

This equation is used to calculate the pH of a buffer from its pKa and the ratio of conjugate base to weak acid. The formula is: pH = pKa + log10([A-]/[HA]). When the amounts of both components are equal, the pH will be equal to the pKa.

Are the calculation results affected by temperature?

Yes. The relationships Kw = 1e-14 and pH + pOH = 14 apply at 25 degrees. At other temperatures, Kw changes so that the pH of a neutral solution is no longer exactly 7, and also the sum of both values changes slightly.

Acid-Base Calculator

Choose your calculation

What do you want to calculate?

Pick what you want to work out: convert between pH, pOH and ion concentrations, find the pH of a weak or strong acid or base, or size a buffer with the Henderson-Hasselbalch equation.

Enter what you know

Only the boxes your chosen calculation needs are shown. Set each concentration's unit with the switch on its right; the answer updates as you type.

Which value do you know?

Choose which value you already have. The calculator returns the other three.

Results

pOH

Hydrogen ion concentration [H+]

Hydroxide ion concentration [OH-]

This solution is acidic - its pH is below 7, so hydrogen ions outnumber hydroxide ions.

pOH
[H+]: M
[OH-]: M

From your one known value the calculator finds the other three using [H+] times [OH-] = 1e-14, pH = -log10[H+] and pH + pOH = 14.

The acid-base equilibria calculator links various values that describe the acidity or basicity of an aqueous solution. If you enter a value for pH, pOH, hydrogen ion concentration [H+], or hydroxide ion concentration [OH-], it can calculate the remaining values.

It also supports more complex calculations. If you enter a concentration and the pKa or pKb value, it can determine the pH of a weak acid or base solution taking into account the dissociation equilibrium. For strong acids or bases, you only need to specify the concentration. If you enter a conjugate acid-base pair, you can calculate the mixing ratio for a buffer using the Henderson-Hasselbalch equation.

The significance of pH and pOH:

The pH value indicates the concentration of free hydrogen ions in a solution. As this concentration can range over several decimal places, chemists use logarithms to represent and handle values.

\text{pH} = -\log_{10}[\text{H}^+] \qquad \text{pOH} = -\log_{10}[\text{OH}^-]

Even water itself dissociates to a small extent, forming hydrogen and hydroxide ions. At a temperature of 25 degrees Celsius the product of the concentrations of both ions is constant and called the ion product of water.

[\text{H}^+]\,[\text{OH}^-] = K_w = 1.0 \times 10^{-14}

If you take the negative logarithm of this relationship, then both quantities can be related to each other. So the sum of pH and pOH at that temperature is always constant and it's equal to 14.

\text{pH} + \text{pOH} = 14

If the pH is below 7, the solution is acidic; at exactly 7 it is neutral; above 7 means a basic solution. A change in pH by one whole number represents a tenfold change in [H+]. So a solution with a pH of 4 has ten times more hydrogen ions than a solution with a pH of 5.

How to use this calculator:

First select the type of calculation you want to perform from the top. The first option is for direct conversions. If you pick known values and enter numbers, it will show you both the pH, pOH, [H+], and [OH-].

The other options calculate the acid-base equilibrium of a real solution. For weak acids or bases you enter the pKa or pKb and the concentration. For strong acids or bases you only need to enter the concentration. For buffers, you enter the pKa, amount of conjugate base and amount of weak acid. Only the fields required for the current calculation are shown on the screen, and in each field for entering a concentration, you can switch between units of moles, millimoles, micromoles or nanomoles.

Strong acids and strong bases:

Strong acids such as hydrochloric acid dissociate completely in water so the number of moles of acid is equal to the number of hydrogen ions released. Since the concentration of hydrogen ions is equal to the concentration of strong acid, then pH can be calculated directly using the formula:

[\text{H}^+] = C \qquad \text{pH} = -\log_{10}(C)

Thus a strong acid solution with a concentration of 0.01 mol has a pH of 2. For strong bases this can be calculated in the same way using [OH-]. A strong base with a concentration of 0.01 mol will have a pOH of 2, which corresponds to a pH of 12.

Weak acids and bases: ionization

Weak acids only partially ionize. The degree of ionization is determined by the acid dissociation constant Ka, where the relationship between Ka and pKa is given by Ka = 10^-pKa. By rearranging the equilibrium expression one obtains a quadratic equation in terms of x, which represents the hydrogen ion concentration.

K_a = \frac{x^2}{C - x} \;\Rightarrow\; x = \frac{-K_a + \sqrt{K_a^2 + 4 K_a C}}{2}

This tool solves this quadratic equation exactly and not just by general simplification, thus ensuring high accuracy even for relatively strong acids or dilute solutions. The degree of ionization is the value obtained when the ionized concentration is divided by the initial concentration.

For example, acetic acid has a pKa of 4.76 and is at a concentration of 0.1 mol. The hydrogen ion concentration would be approximately 0.0013 mol if calculated exactly, the pH would be about 2.88, and the degree of ionization would be about 1.3%. Most of the acetic acid exists as the un-ionized molecule, making it a weak acid. For weak bases this can be calculated similarly using Kb and [OH-].

Buffer solutions and the Henderson Hasselbach equation.

Buffer solutions consist of a weak acid and its conjugate base, and can resist changes in pH. The pH of a buffer solution is determined by the pKa value and ratio of both components.

\text{pH} = \mathrm{p}K_a + \log_{10}\!\left(\frac{[\text{A}^-]}{[\text{HA}]}\right)

When the amounts of conjugate base and weak acid are equal, then the log term is zero, so that pH equals pKa. This is the range where the buffer solution works most effectively, and also the point at which the pH will be held most stably. If the amount of conjugate base is doubled relative to the weak acid, the pH will rise by about 0.3 units. A calculation tool shows the ratio of both components in a pie chart so that you can see the mixing ratio at a glance.

List of input fields:

The table below explains what each field means and gives typical values.

Symbol	Meaning	Example
pH	Acidity on the log scale	2.88
pOH	Basicity on the log scale	11.12
[H+]	Hydrogen ion concentration (mol/L)	0.0013
[OH-]	Hydroxide ion concentration (mol/L)	7.6e-12
pKa	Acid strength on the log scale	4.76
pKb	Base strength on the log scale	4.75
C	Starting concentration (mol/L)	0.1
[A-] / [HA]	Buffer conjugate base / weak acid	0.1 / 0.1

Examples of calculations:

Below are some solutions and their calculation results at 25 degrees.

Solution	Input	pH
Strong acid	0.01 M	2.00
Strong base	0.01 M	12.00
Weak acid (acetic)	pKa 4.76, 0.1 M	2.88
Weak base (ammonia)	pKb 4.75, 0.1 M	11.12
Equal buffer	pKa 4.76, 0.1 / 0.1 M	4.76

This calculator assumes a dilute aqueous solution at 25 degrees Celsius and neglects the minor effects of activity coefficients and ionization of water itself. The latter becomes relevant only if the solution is very dilute or near neutral pH. This tool is for learning and planning purposes only, not to replace accurate laboratory measurements.

Frequently asked questions

How do you calculate pH from hydrogen ion concentration?: Take the negative logarithm of the concentration of 10. The pH is defined as: pH = -log10[H+]. For example, if [H+] is equal to 0.001 moles then the pH would be 3. The reverse formula is: [H+] = 10 to the power of minus pH.
What is the difference between pH and pOH?: The pH value indicates the concentration of hydrogen ions, while the pOH indicates the concentration of hydroxide ions. At 25 degrees Celsius, the sum of both values is always 14, so that it applies: if the pOH value is 4, then the pH value is 10.
Why can't you use the formula pH = -log(C) for weak acids?: This simplification is only true for strong acids that fully dissociate. Weak acids only partially dissociate, so the concentration of hydrogen ions will be determined by Ka and the initial acid concentration. This tool solves the quadratic equation of equilibrium exactly to give you results.
What is the use of the Henderson Hasselbalch equation?: This equation is used to calculate the pH of a buffer from its pKa and the ratio of conjugate base to weak acid. The formula is: pH = pKa + log10([A-]/[HA]). When the amounts of both components are equal, the pH will be equal to the pKa.
Are the calculation results affected by temperature?: Yes. The relationships Kw = 1e-14 and pH + pOH = 14 apply at 25 degrees. At other temperatures, Kw changes so that the pH of a neutral solution is no longer exactly 7, and also the sum of both values changes slightly.

Related calculators

Buffer Capacity CalculatorWork out a buffer's capacity beta three ways: from pKa, total concentration and pH with the Van Slyke equation, from a measured pH change, or straight from the weak acid and conjugate base concentrations.

Buffer pH CalculatorFind the pH of a buffer from its components or from the masses you weighed, and plan the recipe for a target pH with the Henderson-Hasselbalch equation, buffer capacity and effective range.

Arrhenius Equation CalculatorSolve the Arrhenius equation k = A*exp(-Ea/RT) for any variable, or find the activation energy from a rate constant measured at two temperatures. Per mole or per molecule, with an Arrhenius plot.

Avogadro's Number CalculatorConvert between moles, mass, molar mass, and the number of atoms, molecules, or ions using Avogadro's number.

Beer–Lambert Law CalculatorSolve the Beer–Lambert law A = εlc for absorbance, molar absorptivity, path length or concentration; convert between absorbance, transmittance and %T; and find ε from a calibration.

Boiling Point Elevation CalculatorWork out how far a dissolved solute raises a solvent's boiling point from the van't Hoff factor, the ebullioscopic constant and the molality, or run the equation backwards to recover the molality, the factor, the constant or the molar mass of an unknown solute.

Disclaimer: This calculator is provided for general informational and educational purposes only. Our calculators are under active development, and results may be inaccurate, incomplete, or unsuitable for your situation. Always verify the figures independently and seek advice from a qualified professional before relying on them. We make no warranties and accept no liability for any loss or decision arising from use of this tool.

References

LibreTexts Chemistry: pH and pOH
University-level reference on pH, pOH, Kw and acid-base equilibria.
IUPAC: Definition of pH
The international standards body's definition of the pH scale.