How do you calculate pH from hydrogen ion concentration?

pH is defined as the negative base-10 logarithm of the hydrogen ion activity. For dilute aqueous solutions, this is approximated by the hydrogen ion concentration: pH = -log10([H+]). For example, if [H+] = 1.0×10^-4 mol/L, then pH = 4.00.

What is the relationship between pH, pOH, [H+], and [OH−]?

In water at 25 °C, pH + pOH = 14.0 and [H+][OH−] = 1.0×10^-14. You can convert between them using pH = -log10([H+]), pOH = -log10([OH−]), [H+] = 10^-pH, and [OH−] = 10^-pOH.

What pH values are considered acidic, neutral, or basic?

On the usual 0–14 pH scale at 25 °C, solutions with pH 7 is basic (alkaline). Strong acids typically have pH below about 3, and strong bases have pH above about 11.

Can pH be less than 0 or greater than 14?

Yes. The 0–14 range is typical for dilute aqueous solutions at 25 °C, but very concentrated acids can have pH 14. The definition pH = -log10([H+]) does not impose a strict limit.

What is the difference between pH and acidity?

pH measures the activity of hydrogen ions in solution on a logarithmic scale. Acidity more broadly can refer to how readily a substance donates protons (its acid strength, often quantified by Ka or pKa) or to the total amount of acid present (titratable acidity). Two solutions can have the same pH but different buffering capacities and total acidity.

pH Calculator

Convert between pH, hydrogen ion concentration [H⁺], hydroxide ion concentration [OH⁻], and pOH. Instantly classify a solution as acidic, neutral, or basic and visualize its position on the pH scale.

Interactive pH Converter

Known quantity

Value

For concentrations, use mol/L (M). Example: 1e-4 for 1×10⁻⁴ M.

Temperature (°C)

Used to estimate the ionic product of water K_w. At 25 °C, K_w ≈ 1.0×10⁻¹⁴.

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pOH

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[H⁺] (mol/L)

–

[OH⁻] (mol/L)

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Solution type: –

Assuming aqueous solution

K_w ≈ 1.0×10⁻¹⁴

0 (strong acid) 7 (neutral) 14 (strong base)

What is pH?

pH is a logarithmic measure of the acidity or basicity of an aqueous solution. It is defined in terms of the activity of hydrogen ions, and for most dilute solutions it is approximated using the hydrogen ion concentration \([H^+]\) in moles per liter (mol/L).

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

At 25 °C, pure water has \([H^+] = 1.0 \times 10^{-7}\,\text{mol/L}\), so its pH is 7.0 (neutral). Lower pH values indicate acidic solutions, and higher pH values indicate basic (alkaline) solutions.

Relationships between pH, pOH, [H⁺], and [OH⁻]

In water, hydrogen ions and hydroxide ions are linked through the ionic product of water \(K_w\). At 25 °C:

\( K_w = [H^+][OH^-] \approx 1.0 \times 10^{-14} \)
\( \Rightarrow \text{pH} + \text{pOH} = 14.0 \)

From these definitions, you can convert between all four quantities:

From pH to \([H^+]\): \( [H^+] = 10^{-\text{pH}} \)
From pH to pOH: \( \text{pOH} = \text{p}K_w - \text{pH} \) (≈ 14.0 − pH at 25 °C)
From pOH to \([OH^-]\): \( [OH^-] = 10^{-\text{pOH}} \)
From \([H^+]\) to \([OH^-]\): \( [OH^-] = \dfrac{K_w}{[H^+]} \)

Temperature dependence of K_w

The value of \(K_w\) (and therefore the neutral pH) depends on temperature. As temperature increases, water autoionizes more, so both \([H^+]\) and \([OH^-]\) increase and the neutral pH decreases slightly.

This calculator uses an empirical approximation for \(K_w(T)\) between about 0–60 °C to keep the pH–pOH relationship realistic outside 25 °C.

How to interpret pH values

pH < 7: acidic solution (more \(H^+\) than pure water)
pH = 7: neutral at 25 °C (pure water)
pH > 7: basic (alkaline) solution (more \(OH^-\) than pure water)

Common examples at 25 °C (approximate):

Battery acid: pH ~ 0
Gastric acid (stomach): pH ~ 1–2
Black coffee: pH ~ 5
Pure water: pH 7
Sea water: pH ~ 8.1
Household bleach: pH ~ 12–13

Worked examples

Example 1 – pH from [H⁺]

A solution has \([H^+] = 2.5 \times 10^{-5}\,\text{mol/L}\). What is its pH?

\( \text{pH} = -\log_{10}(2.5 \times 10^{-5}) \approx 4.60 \)

This solution is acidic (pH < 7).

Example 2 – [H⁺] and [OH⁻] from pH

A solution has pH = 9.0 at 25 °C. Find \([H^+]\), \([OH^-]\), and pOH.

\( [H^+] = 10^{-9.0} = 1.0 \times 10^{-9}\,\text{mol/L} \)
\( \text{pOH} = 14.0 - 9.0 = 5.0 \)
\( [OH^-] = 10^{-5.0} = 1.0 \times 10^{-5}\,\text{mol/L} \)

The solution is basic (alkaline).

Limitations and good practices

The simple formulas assume dilute aqueous solutions where activity ≈ concentration. Highly concentrated or non-aqueous solutions require more advanced treatment.
Very strong acids and bases can have pH values below 0 or above 14. This calculator will still compute those values mathematically.
For accurate laboratory work, pH is often measured with a calibrated pH meter rather than calculated purely from nominal concentrations.

pH Calculator FAQ

How do I use this pH calculator?

Choose which quantity you know (pH, pOH, [H⁺], or [OH⁻]), enter its value, optionally adjust the temperature, and click “Calculate”. The tool will compute all related quantities and show where the solution lies on the pH scale, along with whether it is acidic, neutral, or basic.

What units should I use for concentration?

Enter hydrogen or hydroxide ion concentration in mol/L (moles per liter), often written as M. For very small values, scientific notation is convenient: for example, 1×10⁻⁴ M can be entered as 1e-4.

Why does neutral pH change with temperature?

The autoionization of water is an equilibrium process that depends on temperature. As temperature increases, water ionizes more, increasing both [H⁺] and [OH⁻]. Their product K_w increases, so the pH of pure water drops below 7 even though the solution is still neutral (because [H⁺] = [OH⁻]).

Is pH exactly the same as acidity?

pH measures the hydrogen ion activity at a given moment. Acidity in a broader sense can refer to how strongly a substance donates protons (its acid strength, quantified by Ka or pKa) or to the total amount of acid present (titratable acidity). Two solutions can have the same pH but very different buffering capacities and total acidity.