The pH Formula is pH = −log[H⁺], where [H⁺] is the hydrogen ion concentration of a solution in moles per litre.
It can also be written as pH = −log[H₃O⁺], because hydrogen ions in water usually exist as hydronium ions.
The pH Formula helps students calculate whether a solution is acidic, neutral or basic. A low pH means the solution has a higher concentration of hydrogen ions, while a high pH means the solution has fewer hydrogen ions and is more basic. This makes the formula important in Chemistry chapters on acids, bases and salts.
In Class 10, Class 11 and Class 12 Chemistry, pH is used in acid-base reactions, indicators, buffer solutions, water ionisation and numerical problems. CBSE, ICSE, state board and competitive foundation exams may ask students to calculate pH from [H⁺], find [H⁺] from pH, use the pOH formula or apply the relation pH + pOH = 14.
Key Takeaways
- pH Formula: pH = −log[H⁺]
- Hydronium Form: pH = −log[H₃O⁺]
- pOH Formula: pOH = −log[OH⁻]
- pH and pOH Formula: pH + pOH = 14 at 25°C
- pH Scale: pH < 7 is acidic, pH = 7 is neutral and pH > 7 is basic.
pH Formula Structure 2026
| Concept |
Formula |
Key Meaning |
| pH formula |
pH = −log[H⁺] |
Finds acidity from hydrogen ion concentration |
| Hydronium ion formula |
pH = −log[H₃O⁺] |
Used because H⁺ exists as H₃O⁺ in water |
| pOH formula |
pOH = −log[OH⁻] |
Finds basicity from hydroxide ion concentration |
| pH and pOH formula |
pH + pOH = 14 |
Connects acidity and basicity at 25°C |
| Hydrogen ion formula |
[H⁺] = 10⁻ᵖᴴ |
Finds hydrogen ion concentration from pH |
What is pH Formula?
The pH Formula is used to calculate the acidity or basicity of a solution using hydrogen ion concentration.
Formula:
pH = −log[H⁺]
Where:
- pH = measure of acidity or basicity
- [H⁺] = hydrogen ion concentration
- log = logarithm to base 10
- [H⁺] is measured in mol L⁻¹ or M
Since hydrogen ions combine with water to form hydronium ions, the formula can also be written as:
pH = −log[H₃O⁺]
Where:
- [H₃O⁺] = hydronium ion concentration
- H₃O⁺ represents hydrated hydrogen ions in water
pH Formula Chemistry
In Chemistry, pH tells how acidic or basic a solution is. The formula depends on the concentration of hydrogen ions.
Main formula:
pH = −log[H⁺]
Hydronium ion form:
pH = −log[H₃O⁺]
A solution with more H⁺ ions has a lower pH. A solution with fewer H⁺ ions has a higher pH.
Example:
If [H⁺] = 1 × 10⁻³ M, then:
pH = −log(1 × 10⁻³)
pH = 3
So, the solution is acidic.
Chemical Formula for pH
The chemical formula for pH is based on hydrogen ion concentration. It uses the negative logarithm of [H⁺].
Formula:
pH = −log[H⁺]
In aqueous solutions, it is often written as:
pH = −log[H₃O⁺]
Both formulas are used in school Chemistry. H⁺ is the simpler form, while H₃O⁺ is the more accurate form for water-based solutions.
pH Calculation Formula
The pH calculation formula is used when hydrogen ion concentration is given.
Formula:
pH = −log[H⁺]
Example:
Find the pH of a solution with:
[H⁺] = 1 × 10⁻⁵ M
Substitute:
pH = −log(1 × 10⁻⁵)
pH = 5
Answer:
The pH of the solution is 5.
Since pH < 7, the solution is acidic.
pH Value Formula
The pH value formula gives the numerical pH of a solution. This value helps classify the solution as acidic, neutral or basic.
Formula:
pH = −log[H⁺]
If [H⁺] is written as a power of 10, calculation becomes easier.
Examples:
| Hydrogen Ion Concentration |
pH Value |
| [H⁺] = 1 × 10⁻¹ M |
1 |
| [H⁺] = 1 × 10⁻³ M |
3 |
| [H⁺] = 1 × 10⁻⁷ M |
7 |
| [H⁺] = 1 × 10⁻¹⁰ M |
10 |
As [H⁺] decreases, pH value increases.
Hydrogen Ion Concentration Formula
The hydrogen ion concentration formula is used when pH is given and [H⁺] has to be calculated.
Formula:
[H⁺] = 10⁻ᵖᴴ
Example:
Find [H⁺] when pH = 4.
Formula:
[H⁺] = 10⁻ᵖᴴ
Substitute:
[H⁺] = 10⁻⁴ M
Answer:
The hydrogen ion concentration is 1 × 10⁻⁴ M.
Hydronium Ion Concentration Formula
In water, hydrogen ions usually exist as hydronium ions. So, hydronium ion concentration can also be calculated from pH.
Formula:
[H₃O⁺] = 10⁻ᵖᴴ
Example:
If pH = 6, then:
[H₃O⁺] = 10⁻⁶ M
Answer:
The hydronium ion concentration is 1 × 10⁻⁶ M.
For school-level questions, [H⁺] and [H₃O⁺] are often used in the same way.
pOH Formula
The pOH formula is used to calculate the concentration of hydroxide ions in a solution. It is useful for basic solutions.
Formula:
pOH = −log[OH⁻]
Where:
- pOH = measure based on hydroxide ion concentration
- [OH⁻] = hydroxide ion concentration
- [OH⁻] is measured in mol L⁻¹ or M
Example:
If [OH⁻] = 1 × 10⁻³ M, then:
pOH = −log(1 × 10⁻³)
pOH = 3
The pOH of the solution is 3.
pH and pOH Formula
The pH and pOH formula connects hydrogen ion concentration and hydroxide ion concentration.
Formula:
pH + pOH = 14
This relation is generally used for aqueous solutions at 25°C.
If pOH is given, pH can be found using:
pH = 14 − pOH
If pH is given, pOH can be found using:
pOH = 14 − pH
Example:
If pOH = 4, then:
pH = 14 − 4
pH = 10
Answer:
The pH of the solution is 10, so the solution is basic.
pH Scale
The pH scale shows whether a solution is acidic, neutral or basic.
| pH Range |
Nature of Solution |
Examples |
| pH < 7 |
Acidic solution |
Lemon juice, vinegar, battery acid |
| pH = 7 |
Neutral solution |
Pure water |
| pH > 7 |
Basic or alkaline solution |
Baking soda solution, soap solution, bleach |
The pH scale commonly ranges from 0 to 14 in school-level Chemistry.
- Lower pH means stronger acidic nature.
- pH 7 means neutral nature.
- Higher pH means stronger basic nature.
Acidic Solution and pH Formula
An acidic solution has pH less than 7. It contains more hydrogen ions than hydroxide ions.
Condition:
pH < 7
Examples:
- Lemon juice
- Vinegar
- Hydrochloric acid
- Battery acid
Formula used:
pH = −log[H⁺]
Example:
If [H⁺] = 1 × 10⁻² M, then:
pH = −log(1 × 10⁻²)
pH = 2
Since pH = 2, the solution is acidic.
Neutral Solution and pH Formula
A neutral solution has pH equal to 7 at 25°C. Pure water is the most common example.
Condition:
pH = 7
For pure water:
[H⁺] = 1 × 10⁻⁷ M
So:
pH = −log(1 × 10⁻⁷)
pH = 7
In a neutral solution:
[H⁺] = [OH⁻]
This means hydrogen ion concentration and hydroxide ion concentration are equal.
Basic Solution and pH Formula
A basic solution, also called an alkaline solution, has pH greater than 7.
Condition:
pH > 7
Examples:
- Baking soda solution
- Soap solution
- Bleach
- Sodium hydroxide solution
For basic solutions, pOH is often useful.
Formula:
pOH = −log[OH⁻]
Then:
pH = 14 − pOH
Example:
If pOH = 2, then:
pH = 14 − 2
pH = 12
Since pH = 12, the solution is basic.
Acid Base pH Formula
The acid base pH formula helps compare acidic and basic solutions using hydrogen ion and hydroxide ion concentrations.
For acids:
pH = −log[H⁺]
For bases:
pOH = −log[OH⁻]
Relation:
pH + pOH = 14
For acidic solutions:
[H⁺] > [OH⁻]
For neutral solutions:
[H⁺] = [OH⁻]
For basic solutions:
[H⁺] < [OH⁻]
This makes pH useful for identifying acids, bases and neutral substances.
How to Calculate pH
To calculate pH, first check whether the question gives [H⁺], [H₃O⁺], [OH⁻] or pOH.
Case 1: When [H⁺] is given
Use:
pH = −log[H⁺]
Example:
[H⁺] = 1 × 10⁻⁴ M
pH = −log(1 × 10⁻⁴)
pH = 4
Case 2: When [H₃O⁺] is given
Use:
pH = −log[H₃O⁺]
Example:
[H₃O⁺] = 1 × 10⁻⁶ M
pH = −log(1 × 10⁻⁶)
pH = 6
Case 3: When [OH⁻] is given
Use:
pOH = −log[OH⁻]
Then:
pH = 14 − pOH
Example:
[OH⁻] = 1 × 10⁻³ M
pOH = −log(1 × 10⁻³)
pOH = 3
pH = 14 − 3
pH = 11
Molecular Meaning of pH Formula
The pH Formula measures hydrogen ion concentration on a logarithmic scale. This means a change of 1 pH unit represents a 10 times change in hydrogen ion concentration.
Example:
A solution with pH = 3 has:
[H⁺] = 10⁻³ M
A solution with pH = 4 has:
[H⁺] = 10⁻⁴ M
So, the pH 3 solution has 10 times more hydrogen ions than the pH 4 solution.
This is why small changes in pH can represent large changes in acidity.
Solved Examples on pH Formula
pH Formula questions usually test hydrogen ion concentration, hydronium ion concentration, pOH relation and pH scale classification.
Example 1: Find the pH when [H⁺] = 1 × 10⁻³ M
Given:
[H⁺] = 1 × 10⁻³ M
Formula:
pH = −log[H⁺]
Substitute:
pH = −log(1 × 10⁻³)
pH = 3
Answer:
The pH of the solution is 3. Since pH < 7, the solution is acidic.
Example 2: Find the pH when [H₃O⁺] = 1 × 10⁻⁵ M
Given:
[H₃O⁺] = 1 × 10⁻⁵ M
Formula:
pH = −log[H₃O⁺]
Substitute:
pH = −log(1 × 10⁻⁵)
pH = 5
Answer:
The pH of the solution is 5. The solution is acidic.
Example 3: Find pH when pOH = 6
Given:
pOH = 6
Formula:
pH + pOH = 14
Substitute:
pH + 6 = 14
pH = 14 − 6
pH = 8
Answer:
The pH of the solution is 8. Since pH > 7, the solution is basic.
Example 4: Find pH when [OH⁻] = 1 × 10⁻⁴ M
Given:
[OH⁻] = 1 × 10⁻⁴ M
Formula:
pOH = −log[OH⁻]
Substitute:
pOH = −log(1 × 10⁻⁴)
pOH = 4
Now use:
pH + pOH = 14
pH + 4 = 14
pH = 10
Answer:
The pH of the solution is 10. The solution is basic.
Example 5: Find [H⁺] when pH = 2
Given:
pH = 2
Formula:
[H⁺] = 10⁻ᵖᴴ
Substitute:
[H⁺] = 10⁻² M
Answer:
The hydrogen ion concentration is 1 × 10⁻² M.
Common Mistakes in pH Formula
Many pH Formula mistakes happen when students miss the negative sign before log or confuse pH with pOH.
Important checks:
- Write the formula as pH = −log[H⁺].
- Use pH = −log[H₃O⁺] when hydronium ion concentration is given.
- Use pOH = −log[OH⁻] when hydroxide ion concentration is given.
- Use pH + pOH = 14 for aqueous solutions at 25°C.
- Classify pH < 7 as acidic, pH = 7 as neutral and pH > 7 as basic.
- Remember that lower pH means higher hydrogen ion concentration.
For numerical questions, check whether the concentration is written as H⁺, H₃O⁺ or OH⁻ before applying the formula.
Applications of pH Formula
The pH Formula is used in Chemistry, Biology, medicine, agriculture, environmental science and daily life. It helps measure acidity and basicity in different substances.
Main applications:
- It identifies acidic, neutral and basic solutions.
- It helps study acids, bases and salts.
- It is used in water quality testing.
- It helps check soil acidity for crops.
- It is used in blood pH and biological systems.
- It helps in laboratory titration and buffer calculations.
- It is used in industries such as food, medicine and cosmetics.