pH Calculator from Hydrogen Ion Concentration [H⁺]
pH measures how acidic or basic an aqueous solution is. It is defined as the negative base-10 logarithm of the hydrogen ion concentration: pH = −log₁₀[H⁺], where [H⁺] is expressed in mol per liter (M). The scale runs from 0 (very acidic) to 14 (very basic), with 7 as neutral — corresponding to pure water at 25 °C. Because the scale is logarithmic, each unit represents a tenfold change in hydrogen ion concentration: pH 4 is 100 times more acidic than pH 6. This calculator handles two directions. Enter the pH to get [H⁺], pOH, and [OH⁻]. Enter the [H⁺] concentration to compute pH from molarity. Use the result to classify the solution as acidic (pH < 7), neutral (pH ≈ 7), or basic/alkaline (pH > 7). The calculator assumes water at 25 °C, where the ion product Kw = [H⁺][OH⁻] = 10⁻¹⁴, so pH + pOH = 14 always holds. The pH scale was introduced by Danish chemist Søren Sørensen in 1909 at the Carlsberg Laboratory and is now fundamental in chemistry, biology, medicine, agriculture, environmental science, aquariums, and swimming pools.
pH = −log₁₀[H⁺]. If [H⁺] = 0.001 M (10⁻³ mol/L), then pH = 3 (acidic). At 25 °C, pH + pOH = 14. pH < 7 is acidic, pH = 7 is neutral, pH > 7 is basic.
When to use this calculator
- General chemistry student computing the pH of a 0.001 M HCl solution: [H⁺] = 10⁻³ M → pH = 3 (acidic).
- Pool owner checking whether water (target pH 7.2–7.6) is in safe range: [H⁺] = 6.3 × 10⁻⁸ M → pH = 7.2.
- Aquarium hobbyist verifying that tank water for tropical freshwater fish stays between pH 6.5 and 7.5.
- Soil scientist interpreting a soil test result of pH 5.5 to decide whether to add lime for tomatoes (ideal pH 6.0–6.8).
- Biology student calculating pOH from blood pH = 7.4: pOH = 14 − 7.4 = 6.6, so [OH⁻] = 2.5 × 10⁻⁷ M.
- Brewery quality control measuring wort acidity, where target pH is 5.2–5.6 for optimal enzyme activity.
- Wastewater treatment engineer confirming effluent pH between 6.0 and 9.0 for regulatory compliance.
- Pharmacist preparing a buffered eye drop solution at pH 7.4 to match physiological tear fluid.
Worked Example: [H⁺] = 10⁻³ M → pH
- Given: [H⁺] = 0.001 M = 10⁻³ mol/L (e.g., dilute HCl solution).
- pH formula: pH = −log₁₀(10⁻³) = −(−3) = 3.
- pOH: 14 − 3 = 11, so [OH⁻] = 10⁻¹¹ M.
- Classification: acidic — similar in acidity to diluted vinegar (pH ≈ 2.8).
- Check: [H⁺] × [OH⁻] = 10⁻³ × 10⁻¹¹ = 10⁻¹⁴ ✓ (equals Kw at 25 °C).
How it works
2 min readThe pH Formula
pH = −log₁₀[H⁺] where [H⁺] is the hydrogen ion concentration in mol/L (molarity).
To go the other direction: [H⁺] = 10^(−pH)
At 25 °C: pH + pOH = 14 (from Kw = [H⁺][OH⁻] = 10⁻¹⁴)
Conversion Table: [H⁺] ↔ pH
| [H⁺] (mol/L) | pH | Classification |
|---|---|---|
| 1.0 × 10⁰ = 1 M | 0 | Strongly acidic |
| 1.0 × 10⁻¹ = 0.1 M | 1 | Strongly acidic |
| 1.0 × 10⁻² = 0.01 M | 2 | Strongly acidic |
| 1.0 × 10⁻³ = 0.001 M | 3 | Acidic |
| 1.0 × 10⁻⁴ | 4 | Acidic |
| 1.0 × 10⁻⁵ | 5 | Weakly acidic |
| 1.0 × 10⁻⁶ | 6 | Weakly acidic |
| 1.0 × 10⁻⁷ | 7 | Neutral |
| 1.0 × 10⁻⁸ | 8 | Weakly basic |
| 1.0 × 10⁻⁹ | 9 | Basic |
| 1.0 × 10⁻¹⁰ | 10 | Basic |
| 1.0 × 10⁻¹¹ | 11 | Strongly basic |
| 1.0 × 10⁻¹² | 12 | Strongly basic |
| 1.0 × 10⁻¹³ | 13 | Strongly basic |
| 1.0 × 10⁻¹⁴ | 14 | Strongly basic |
pH of Common Substances
| Substance | pH Value |
|---|---|
| Battery acid | 0 |
| Gastric acid | 1.5–3.5 |
| Lemon juice | 2.5 |
| Vinegar | 2.8 |
| Coffee | 5 |
| Normal rain | 5.6 |
| Pure water | 7.0 |
| Human blood | 7.35–7.45 |
| Seawater | 8.1 |
| Baking soda solution | 9 |
| Ammonia | 11.5 |
| Bleach | 12.5 |
| Drain cleaner | 13–14 |
Key Relationships
Common Mistakes
Frequently asked questions
What is pH and how do you calculate it?
pH measures how acidic or basic a solution is using the formula pH = −log₁₀[H⁺], where [H⁺] is the hydrogen ion concentration in mol/L. The scale goes from 0 (very acidic) to 14 (very basic), with 7 being neutral (pure water at 25 °C).
How do you find pH from hydrogen ion concentration?
Use the formula pH = −log₁₀[H⁺]. For example, if [H⁺] = 10⁻³ M (0.001 M), then pH = −log(10⁻³) = 3 (acidic). If [H⁺] = 5 × 10⁻⁵ M, then pH = −log(5 × 10⁻⁵) ≈ 4.30.
What is pOH and how does it relate to pH?
pOH is the negative logarithm of hydroxide ion concentration: pOH = −log[OH⁻]. At 25 °C, pH + pOH = 14 always. So if pH = 3, then pOH = 11, and [OH⁻] = 10⁻¹¹ M.
What's the difference between acidic and basic?
pH 0–6: acidic (more H⁺ ions than OH⁻). pH 7: neutral (equal H⁺ and OH⁻). pH 8–14: basic/alkaline (more OH⁻ than H⁺). Each pH unit represents a 10× difference in hydrogen ion concentration.
Can pH be negative?
Yes. In very concentrated strong acids, pH can go below 0. For example, 10 M hydrochloric acid has pH ≈ −1. This is rare in everyday applications but occurs in industrial chemistry and some volcanic hydrothermal vents.
What is the pH of human blood?
Normal human arterial blood pH is 7.35–7.45 (slightly basic). The body tightly regulates this with bicarbonate and protein buffer systems. pH below 7.35 (acidosis) or above 7.45 (alkalosis) requires medical attention.
How do strong vs. weak acids differ in pH calculation?
Strong acids (HCl, H₂SO₄, HNO₃) dissociate 100% in water, so [H⁺] equals the molar concentration directly. A 0.1 M HCl solution has pH = 1. Weak acids (acetic acid, citric acid) only partially dissociate. A 0.1 M acetic acid solution gives pH ≈ 2.87 because its Ka ≈ 1.8 × 10⁻⁵. For weak acids use the Henderson-Hasselbalch equation: pH = pKa + log([A⁻]/[HA]).
Does temperature affect pH?
Yes. The ion product of water (Kw) depends on temperature. At 25 °C, Kw = 10⁻¹⁴ and pH + pOH = 14. At 37 °C (body temperature), neutral pH is 6.81, not 7. At 100 °C, neutral pH is 6.14. High-precision labs always report temperature with pH and use automatic temperature compensation (ATC) meters.
Why is the pH scale logarithmic?
Because pH = −log₁₀[H⁺] compresses the enormous range of hydrogen ion concentrations (from 1 M to 10⁻¹⁴ M) into a 0–14 scale. This means pH 4 is 100 times more acidic than pH 6 (10² = 100), and pH 2 is 100,000 times more acidic than pH 7.
What pH is safe for drinking water?
WHO and the U.S. EPA recommend drinking water pH between 6.5 and 8.5. Outside this range water is not necessarily unsafe but may taste metallic (low pH) or cause pipe scaling (high pH). Most bottled spring waters fall between pH 7.0 and 8.0.
How do you measure pH in a lab?
Three main methods: pH meter (glass electrode, most precise, ±0.01 pH units), pH indicator paper/strips (color comparison, ±0.5 units), and liquid indicators like phenolphthalein (turns pink above pH 8.2) or methyl orange (red below pH 3.1). Digital pH meters require regular calibration with buffer solutions (pH 4, 7, 10).
What is the pH of common substances?
Battery acid: ~0 | Gastric acid: 1.5–3.5 | Lemon juice: 2.5 | Vinegar: 2.8 | Coffee: 5 | Rain: 5.6 | Pure water: 7.0 | Blood: 7.35–7.45 | Seawater: 8.1 | Baking soda solution: 9 | Ammonia: 11.5 | Bleach: 12.5 | Drain cleaner: 13–14.