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.
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.