pH and pOH Calculations

Biology • Solutions Concentrations, and Dilutions

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

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pH and pOH (basic)

Uses \(pH = -\log_{10}[H^+]\), \(pOH = -\log_{10}[OH^-]\), and \(pH + pOH = pK_w\) (default \(pK_w = 14\) at 25°C).

Inputs

Choose what you have, then compute the rest.

Mode

Input value

Advanced

If you change pK_w, pH + pOH = pK_w.

pK_w

Actions

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Batch mode (CSV / paste)

Columns: mode,value (optional: pKw). Modes: ph, poh, h, oh.

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Tip: Use scientific notation like 1e-7 for concentrations.

pH scale (0–14)

Hover for values • drag to pan • wheel to zoom

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Log relationship guide

pH vs [H⁺] (M) • hover points • wheel zoom

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pH and pOH (basic relationships)

pH and pOH are logarithmic measures of acidity and basicity. They connect directly to the molar concentrations of hydrogen ions \( [H^+] \) and hydroxide ions \( [OH^-] \).

\[ \begin{aligned} pH &= -\log_{10}\left([H^+]\right) \\ pOH &= -\log_{10}\left([OH^-]\right) \end{aligned} \]

Units reminder

Concentrations \( [H^+] \) and \( [OH^-] \) are in mol/L (M).

Inverse formulas (going back to concentration)

If you know pH or pOH, you can recover the ion concentration by undoing the base-10 logarithm:

\[ \begin{aligned} [H^+] &= 10^{-pH} \\ [OH^-] &= 10^{-pOH} \end{aligned} \]

Because the scale is logarithmic, a change of 1 pH unit means a factor of 10 in \( [H^+] \).

Water autoionization and \(pK_w\)

In aqueous solutions, water establishes an equilibrium:

\[ \begin{aligned} H_2O &\rightleftharpoons H^+ + OH^- \\ K_w &= [H^+][OH^-] \end{aligned} \]

At \(25^\circ\text{C}\), \(K_w \approx 1.0\times 10^{-14}\), so \(pK_w = -\log_{10}(K_w) \approx 14\).

\[ \begin{aligned} pK_w &= -\log_{10}(K_w) \\ pH + pOH &= pK_w \end{aligned} \]

Important

The calculator uses \(pK_w = 14\) by default, but you can set a custom value if you are working at a different temperature.

How to move between pH and pOH

Once \(pK_w\) is known (often 14), pH and pOH are linked:

\[ \begin{aligned} pOH &= pK_w - pH \\ pH &= pK_w - pOH \end{aligned} \]

This is why the calculator can show the “paired” value automatically (pH ↔ pOH).

Interpreting the scale

Acidic: \(pH < 7\) ⇒ higher \( [H^+] \)
Neutral (pure water at 25°C): \(pH \approx 7\) and \(pOH \approx 7\)
Basic: \(pH > 7\) ⇒ higher \( [OH^-] \)

Quick magnitude check

If \(pH = 5\), then \( [H^+] = 10^{-5}\ \text{M} \). If \(pH = 8\), then \( [H^+] = 10^{-8}\ \text{M} \).

Common pitfalls

Log input must be positive: \( [H^+] \) and \( [OH^-] \) must be \(> 0\).
Don’t forget the unit: concentrations are in mol/L (M).
Temperature matters: \(pK_w\) changes with temperature, so \(pH + pOH\) may not equal exactly 14 away from 25°C.

Why use scientific notation?

Ion concentrations are often very small (like \(10^{-7}\ \text{M}\)), so scientific notation keeps results readable and accurate.

Frequently Asked Questions

How do you calculate pH from hydrogen ion concentration?

pH is defined as pH = -log10([H+]) where [H+] is in mol/L (M). The calculator applies this definition and also computes related quantities using pH + pOH = pKw.

How do you convert between pH and pOH?

pH and pOH are linked by pH + pOH = pKw. With pKw = 14 at 25°C, pOH = 14 - pH and pH = 14 - pOH.

Why is pH + pOH not always exactly 14?

Because pKw depends on temperature, so pH + pOH equals pKw rather than a fixed 14 in general. If temperature differs from 25°C, using a custom pKw gives more accurate paired values.

How do I get [H+] or [OH-] from pH or pOH?

Use the inverse relationships: [H+] = 10^(-pH) and [OH-] = 10^(-pOH). The calculator computes these directly from the chosen mode.

How does batch mode work for pH and pOH calculations?

In Batch mode, provide rows with mode and value (optional pKw), where mode is one of ph, poh, h, or oh. The calculator processes each row and outputs the full set of pH, pOH, [H+], and [OH-] using the row pKw if supplied.

Calculation steps

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