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Hydroxide Ion Concentration: Formula and Examples

Updated · Standard formula, shown below

The calculator for this page is switched off while it is checked. The formula is below, and the worked example in the article shows how to use it by hand.

Hydroxide Ion Concentration: Formula and Examples

This calculator finds hydroxide ion concentration, [OH⁻], from pH or from hydrogen ion concentration, [H⁺]. Enter the value you know; the result is in moles per liter (mol/L), using the standard 25°C relationship between pH, pOH, and water’s ion product.

Formula

For a pH input, hydroxide concentration is found from pOH = 14.00 − pH and [OH⁻] = 10−pOH. Combining those steps gives [OH⁻] = 10(pH − 14.00) mol/L at 25°C.

For a hydrogen ion concentration input, use the water ion product: [H⁺][OH⁻] = Kw, so [OH⁻] = Kw/[H⁺]. At 25°C, Kw is approximately 1.0 × 10−14 (mol/L)2.

The calculator’s input x is the pH number when “From pH” is selected. When “From hydrogen ion concentration” is selected, x is [H⁺] in mol/L. Its output, oh, is [OH⁻] in mol/L. The calculator applies the pH equation, so use the “From pH” option for pH values. For a concentration input, the equivalent calculation is 1.0 × 10−14/[H⁺]; see the steps below. The calculator assumes 25°C and the standard concentration-based approximation.

Worked Example

Using the calculator defaults: select “From pH” and enter pH = 7.

  1. Calculate pOH: 14.00 − 7.00 = 7.00.
  2. Convert pOH to hydroxide concentration: [OH⁻] = 10−7.00 mol/L.
  3. Result: [OH⁻] = 0.0000001 mol/L, or 1.0000000 × 10−7 mol/L to seven decimal places.

This is neutral water at 25°C in the idealized textbook model: [H⁺] and [OH⁻] are equal. The calculator’s output is rounded to seven decimal places in ordinary decimal notation, so very small answers may display as 0.0000000. For scientific notation and meaningful precision, use the calculation steps or a scientific calculator.

What You’ll Need

  • A measured pH value or hydrogen ion concentration, [H⁺], in mol/L.
  • A calculator capable of powers of ten, unless you use the calculator block above.
  • The sample temperature, if accuracy beyond the usual 25°C approximation matters.

Step-by-Step

  1. Identify the value you have. A pH reading is a logarithmic number, commonly between 0 and 14 for introductory examples. A hydrogen ion concentration is a positive numerical amount in mol/L. Do not treat the two as interchangeable inputs.
  2. If you have pH, calculate pOH. At 25°C, use pH + pOH = 14.00, so pOH = 14.00 − pH. For example, if pH is 9.25, pOH is 4.75.
  3. Convert pOH to [OH⁻]. Use [OH⁻] = 10−pOH mol/L. For pOH 4.75, calculate 10−4.75, approximately 1.78 × 10−5 mol/L. Keep the result in scientific notation rather than rounding it to zero.
  4. If you have [H⁺], check its units. Convert the value to mol/L before using the relationship. For instance, 2.0 × 10−6 mol/L is ready to use; a value in mmol/L must be divided by 1,000 first.
  5. Use the ion product for a concentration input. At 25°C, calculate [OH⁻] = 1.0 × 10−14/[H⁺]. If [H⁺] = 2.0 × 10−6 mol/L, then [OH⁻] = (1.0 × 10−14)/(2.0 × 10−6) = 5.0 × 10−9 mol/L.
  6. State the answer with units and suitable precision. Write the result as mol/L, also called molar (M). Keep roughly as many significant figures as the measurement supports; a calculator’s displayed digits do not make the original measurement more precise.
  7. Check whether the temperature assumption applies. The value 14.00 follows from pKw ≈ 14.00 at 25°C. At other temperatures, obtain the appropriate Kw or pKw and use pOH = pKw − pH, or [OH⁻] = Kw/[H⁺].

Common Mistakes

  • Using pH where pOH belongs: After finding pOH, the concentration is 10−pOH, not 10pOH.
  • Reversing the subtraction: At 25°C, pOH = 14.00 − pH, not pH − 14.00.
  • Mixing concentration units: The simple ion-product equation expects compatible mol/L values. Convert mmol/L, µmol/L, or other units first.
  • Assuming 14.00 at every temperature: The neutral pH and water ion product vary with temperature. The 25°C relationship is not universal.
  • Rounding too early: Keep pOH and powers of ten unrounded through the calculation, then round the final answer to a sensible number of significant figures.
  • Reading a tiny decimal as zero: Values such as 1 × 10−9 mol/L are small but not zero. Use scientific notation.

Tips

  • For a quick sense check at 25°C, pH below 7 gives pOH above 7 and [OH⁻] below 10−7 mol/L; pH above 7 gives [OH⁻] above 10−7 mol/L.
  • If you know pH, you can calculate the answer directly with [OH⁻] = 10(pH−14.00) mol/L. The two-step pOH route makes sign errors easier to spot.
  • Record whether your pH is measured or calculated, the sample temperature, and the units used. These details help make the result reproducible.
  • For real solutions, pH electrodes and chemical conditions introduce uncertainty. A computed concentration from pH is an estimate based on the measurement and model, not a substitute for a validated lab method when precision is critical.

Troubleshooting

The answer is displayed as zero: The value may be smaller than the decimal display can show. Rewrite it in scientific notation, for example 0.000000005 = 5 × 10−9.

The result seems much too large or small: Check that the exponent has a minus sign, that you used pOH rather than pH in 10−pOH, and that the pH-to-pOH subtraction is in the right order. Recalculate with a known check value such as pH 7 at 25°C, which gives [OH⁻] = 1 × 10−7 mol/L.

You started with [H⁺] but the calculator asks for pH: Either select the concentration option and use [OH⁻] = Kw/[H⁺], or first calculate pH = −log10([H⁺]) when [H⁺] is in mol/L, then use the pH method. Do not enter a concentration as if it were a pH number.

Your sample is not at 25°C: Do not assume pH + pOH = 14.00. Use the temperature-specific pKw or Kw from a reliable chemistry reference, then apply the corresponding formula.

Frequently Asked Questions

What is the formula for hydroxide ion concentration?
At 25°C, from pH use [OH⁻] = 10(pH−14.00) mol/L. From [H⁺], use [OH⁻] = 1.0 × 10−14/[H⁺].

What is the hydroxide concentration at pH 7?
At 25°C, pOH is 7 and [OH⁻] is 1 × 10−7 mol/L.

Can hydroxide concentration be greater than 1 mol/L?
It can be in sufficiently concentrated solutions, though simple ideal concentration relationships become less reliable as solutions become concentrated. Consider activities and appropriate analytical methods for precise work.

Does a higher pH mean more hydroxide ions?
At a fixed temperature, yes: a higher pH corresponds to a lower pOH and a greater hydroxide concentration in the standard model.

Why can neutral pH differ from 7?
Water’s ion product changes with temperature. Neutrality means [H⁺] equals [OH⁻], not that pH must always equal 7.

What unit should I use for [OH⁻]?
The usual unit is mol/L (M). Keep [H⁺] and Kw in compatible units when using the ion-product equation.

Related

Formula used
sel method | Known value | From pH=1, From hydrogen ion concentration=2
in x | pH or [H+] | - | 7 | 0
out oh | Hydroxide ion concentration | mol/L | 10^(-14 + x) | 7

Each line is one input (in, sel, list) or one result (out: label, unit, formula, decimals). How the calculators work

Method: the standard formula for this calculation, rounded as each result states. See how the calculators work or report an error.