pH Calculator
Calculate pH from hydrogen ion concentration or find H⁺ concentration from a known pH value. This calculator also determines pOH, hydroxide ion concentration, and classifies the solution as acidic, neutral, or basic. See also our Buffer pH Calculator and Molarity Calculator for related chemistry computations.
How to Calculate pH
The pH scale is a logarithmic measure of the hydrogen ion concentration in a solution. It was introduced by Danish chemist Søren Peder Lauritz Sørensen in 1909 to provide a convenient way to express the acidity or basicity of aqueous solutions. The pH scale typically ranges from 0 to 14, with 7 being neutral (pure water at 25°C), values below 7 indicating acidic solutions, and values above 7 indicating basic (alkaline) solutions.
- Determine the hydrogen ion concentration [H⁺] in moles per liter (mol/L or M).
- Take the negative base-10 logarithm of the H⁺ concentration: pH = -log₁₀[H⁺].
- To find pOH, subtract pH from 14: pOH = 14 - pH (at 25°C).
- To find [OH⁻], use: [OH⁻] = 10^(-pOH).
- Classify the solution: pH < 7 is acidic, pH = 7 is neutral, pH > 7 is basic.
The relationship pH + pOH = 14 holds true at 25°C because the ion product of water (Kw) equals 1.0 × 10⁻¹⁴ at this temperature. At different temperatures, Kw changes, and the neutral pH shifts accordingly. For example, at 37°C (body temperature), Kw = 2.4 × 10⁻¹⁴, making neutral pH approximately 6.8 rather than 7.0.
pH Formula
pH = -log₁₀[H⁺]
[H⁺] = 10^(-pH)
pOH = -log₁₀[OH⁻]
[OH⁻] = 10^(-pOH)
pH + pOH = 14 (at 25°C)
[H⁺] × [OH⁻] = Kw = 1.0 × 10⁻¹⁴ (at 25°C)
Where:
[H⁺] = hydrogen ion concentration (mol/L)
[OH⁻] = hydroxide ion concentration (mol/L)
Kw = ion product constant of water
The logarithmic nature of the pH scale means that each unit change in pH represents a tenfold change in hydrogen ion concentration. A solution with pH 3 has ten times more H⁺ ions than a solution with pH 4, and one hundred times more than a solution with pH 5. This logarithmic compression allows the enormous range of H⁺ concentrations found in nature (from about 10 M in concentrated acids to 10⁻¹⁵ M in concentrated bases) to be expressed on a manageable 0-14 scale.
Example Calculation
Problem: Calculate the pH of a solution with [H⁺] = 0.001 M (1.0 × 10⁻³ M).
Given:
• [H⁺] = 0.001 mol/L = 1.0 × 10⁻³ M
Solution:
pH = -log₁₀(0.001)
pH = -log₁₀(10⁻³)
pH = -(-3) = 3
pOH = 14 - 3 = 11
[OH⁻] = 10⁻¹¹ = 1.0 × 10⁻¹¹ M
Answer: pH = 3 (Acidic solution)
Reverse Example: Find [H⁺] for a solution with pH = 5.6:
• [H⁺] = 10⁻⁵·⁶ = 2.512 × 10⁻⁶ M
• pOH = 14 - 5.6 = 8.4
• [OH⁻] = 10⁻⁸·⁴ = 3.981 × 10⁻⁹ M
pH Reference Table
| Substance | pH | [H⁺] (mol/L) | Classification |
|---|---|---|---|
| Battery acid | 0.5 | 3.16 × 10⁻¹ | Strongly acidic |
| Stomach acid (HCl) | 1.5 | 3.16 × 10⁻² | Strongly acidic |
| Lemon juice | 2.0 | 1.0 × 10⁻² | Acidic |
| Vinegar | 2.9 | 1.26 × 10⁻³ | Acidic |
| Orange juice | 3.5 | 3.16 × 10⁻⁴ | Acidic |
| Coffee | 5.0 | 1.0 × 10⁻⁵ | Weakly acidic |
| Milk | 6.5 | 3.16 × 10⁻⁷ | Slightly acidic |
| Pure water | 7.0 | 1.0 × 10⁻⁷ | Neutral |
| Blood | 7.4 | 3.98 × 10⁻⁸ | Slightly basic |
| Baking soda | 8.3 | 5.01 × 10⁻⁹ | Basic |
| Ammonia | 11.0 | 1.0 × 10⁻¹¹ | Basic |
| Bleach | 12.5 | 3.16 × 10⁻¹³ | Strongly basic |
Frequently Asked Questions
What does pH stand for?
The "p" in pH stands for "power" or "potential" (from the German "Potenz"), and "H" represents the hydrogen ion. So pH literally means "power of hydrogen." It quantifies the activity of hydrogen ions in a solution on a logarithmic scale, providing a convenient measure of acidity or basicity without dealing with very small numbers in scientific notation.
Can pH be negative or greater than 14?
Yes, pH can be negative or exceed 14 in extreme cases. Concentrated strong acids like 10 M HCl have a pH of approximately -1, and concentrated strong bases like 10 M NaOH have a pH of approximately 15. The 0-14 range applies to dilute aqueous solutions at 25°C where [H⁺] ranges from 1 M to 10⁻¹⁴ M.
How is pH measured in a laboratory?
pH is measured using a pH meter with a glass electrode, which generates a voltage proportional to the H⁺ activity in solution. The meter is calibrated using standard buffer solutions (typically pH 4, 7, and 10). pH indicator papers and universal indicator solutions provide approximate measurements through color changes but are less precise than electronic meters.
What is the relationship between pH and pOH?
At 25°C, pH + pOH = 14. This relationship comes from the water autoionization equilibrium: Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴. Taking the negative logarithm of both sides gives pKw = pH + pOH = 14. If you know either pH or pOH, you can immediately calculate the other by subtraction from 14.
Why is blood pH maintained at 7.4?
Blood pH is maintained at 7.35-7.45 through buffer systems (primarily bicarbonate/carbonic acid), respiratory regulation (CO₂ exhalation), and renal regulation (H⁺ excretion). Even small deviations can be life-threatening: pH below 7.35 (acidosis) or above 7.45 (alkalosis) impairs enzyme function, oxygen transport, and cellular metabolism. The body has multiple overlapping mechanisms to maintain this narrow range.
How does temperature affect pH?
Temperature affects pH in two ways: it changes the ion product of water (Kw), and it affects the dissociation of weak acids and bases. At 25°C, neutral pH is 7.0, but at 37°C it is about 6.8, and at 60°C it is about 6.5. This does not mean hot water is acidic — it means the neutral point shifts. pH meters have temperature compensation to account for this effect during measurement.
Understanding pH in Chemistry and Biology
The pH scale is one of the most widely used measurements in all of science. From environmental monitoring to pharmaceutical manufacturing, from agriculture to food processing, pH plays a critical role in determining the behavior of chemical and biological systems. Understanding pH is essential for anyone working in chemistry, biology, medicine, environmental science, or engineering.
In biological systems, pH regulation is a matter of life and death. Enzymes, the protein catalysts that drive virtually all biochemical reactions, have optimal pH ranges outside of which they lose their three-dimensional structure and become inactive. Pepsin in the stomach works best at pH 2, while trypsin in the small intestine requires pH 8. The blood buffering system maintains arterial pH at 7.4 with remarkable precision, and even a shift of 0.3 units can be fatal.
In environmental science, pH determines the health of aquatic ecosystems. Most freshwater fish thrive in water with pH between 6.5 and 8.5. Acid rain, with pH values as low as 4.2, has devastated lakes and forests in industrialized regions. Soil pH affects nutrient availability for plants: most crops prefer slightly acidic to neutral soil (pH 6.0-7.0), while acid-loving plants like blueberries thrive at pH 4.5-5.5.
Industrial applications of pH control are vast. Water treatment plants adjust pH to optimize coagulation and disinfection. The food industry monitors pH to ensure product safety and quality — botulism bacteria cannot grow below pH 4.6, which is why acidic foods like pickles and tomato sauce are safer from this pathogen. Swimming pools are maintained at pH 7.2-7.8 for effective chlorine disinfection and swimmer comfort.
In analytical chemistry, pH buffers are essential for maintaining constant conditions during experiments. A buffer solution resists changes in pH when small amounts of acid or base are added. Common buffer systems include acetate buffers (pH 3.7-5.8), phosphate buffers (pH 5.8-8.0), and Tris buffers (pH 7.0-9.0). The Henderson-Hasselbalch equation (pH = pKa + log([A⁻]/[HA])) is used to calculate the pH of buffer solutions and to design buffers with specific pH values.