Formula
How pH is calculated
pH =−log₁₀[H⁺]
The pH scale describes the concentration of hydrogen ions in an aqueous solution. Because the scale is logarithmic, a change of one pH unit represents a tenfold change in hydrogen-ion concentration.
Acid-base relationships
pH, pOH, H⁺, and OH⁻ formulas
- pH = −log₁₀[H⁺]
- pOH = −log₁₀[OH⁻]
- pH + pOH = 14 at 25 °C
- [H⁺] = 10⁻ᵖᴴ
- [OH⁻] = 10⁻ᵖᴼᴴ
- [H⁺][OH⁻] = 1 × 10⁻¹⁴at 25 °C
Worked example
Calculate pH from hydrogen-ion concentration
Suppose a solution has a hydrogen-ion concentration of 1 × 10⁻⁵ mol/L.
- Use the formula pH = −log₁₀[H⁺].
- Substitute the concentration: pH = −log₁₀(1 × 10⁻⁵).
- Calculate the logarithm: pH = 5.
- Since pH 5 is below 7, the solution is acidic.
pH scale
Acidic, neutral, and basic solutions
- pH below 7: acidic solution
- pH equal to 7: neutral solution
- pH above 7: basic or alkaline solution
The neutral value of 7 and the pH plus pOH relationship of 14 apply specifically to aqueous solutions near 25 °C. Temperature changes the ionization constant of water.
Chemistry guidance
Common pH calculation mistakes
- Entering ion concentration as a negative value.
- Forgetting the negative sign in the logarithm formula.
- Confusing hydrogen-ion concentration with hydroxide-ion concentration.
- Assuming every pH value must remain between 0 and 14.
- Applying the pH plus pOH equals 14 relationship without considering temperature.
Model limits
Assumptions and limitations
The standard pH equations assume that the entered hydrogen-ion or hydroxide-ion concentration represents the effective concentration used by the model. Units must be mol/L, and the logarithm requires a positive, non-zero concentration.
Real solutions may differ because of activity effects, temperature, incomplete dissociation, buffering, concentrated-solution behavior, or interactions between dissolved species. Laboratory measurements may therefore require calibrated instrumentation and a more advanced equilibrium model.
Related chemistry tools
Continue with solution calculations
Use the Molarity Calculator to calculate the molar concentration of a solution.
Use the Dilution Calculator when preparing a lower-concentration solution from a stock solution.
Use the Mass to Moles Calculator to convert between solute mass and amount in moles.
Questions and answers
pH calculator FAQ
What formula is used to calculate pH?
pH is calculated using pH = −log₁₀[H⁺], where [H⁺] is the hydrogen-ion concentration in moles per liter.
How are pH and pOH related?
At 25 degrees Celsius, pH and pOH add to 14. Therefore, pH = 14 − pOH and pOH = 14 − pH.
What pH value is neutral?
At 25 degrees Celsius, a solution with pH 7 is neutral. Values below 7 are acidic and values above 7 are basic.
Can pH be below 0 or above 14?
Yes. Highly concentrated solutions can have pH values below 0 or above 14, although the 0 to 14 range is commonly used for typical dilute aqueous solutions.