pH Calculator — Calculate pH, pOH & Ion Concentrations
Enter any pH value, hydrogen ion concentration [H⁺], or pOH to instantly calculate all four related quantities. Uses the formula pH = −log₁₀[H⁺] and the relationship pH + pOH = 14. Results include the solution nature (acidic, neutral, or basic), plus a visual position on the 0–14 pH scale.
pH Calculator
Valid range: 0 to 14
Frequently Asked Questions
What is pH?
pH is a logarithmic scale used to measure the acidity or basicity of an aqueous solution. It is defined as the negative base-10 logarithm of the hydrogen ion concentration: pH = −log₁₀[H⁺]. The scale ranges from 0 to 14, where values below 7 indicate an acidic solution, pH 7 is neutral (pure water at 25 °C), and values above 7 indicate a basic (alkaline) solution. The word pH stands for 'power of hydrogen.'
How do you calculate pH from hydrogen ion concentration?
Use the formula pH = −log₁₀[H⁺], where [H⁺] is the hydrogen ion concentration in mol/L. For example, if [H⁺] = 0.001 mol/L (1 × 10⁻³), then pH = −log₁₀(0.001) = −(−3) = 3. Conversely, to find [H⁺] from pH, use [H⁺] = 10⁻ᵖᴴ. So pH 3 means [H⁺] = 10⁻³ = 0.001 mol/L.
What is the relationship between pH and pOH?
At 25 °C, pH and pOH are related by the equation: pH + pOH = 14. This comes from the water ion product constant Kw = [H⁺][OH⁻] = 1 × 10⁻¹⁴ mol²/L². Taking the negative logarithm of both sides gives pKw = pH + pOH = 14. So if the pH of a solution is 3, its pOH is 14 − 3 = 11. This relationship lets you calculate pOH from pH and vice versa instantly.
What is pOH and how is it calculated?
pOH is the negative base-10 logarithm of the hydroxide ion concentration [OH⁻]: pOH = −log₁₀[OH⁻]. It is used alongside pH to describe the basicity of a solution. A pOH of 0 means a strongly basic solution ([OH⁻] = 1 mol/L), and pOH 14 means a strongly acidic solution. Since pH + pOH = 14 at 25 °C, you can find pOH by subtracting pH from 14.
Why is pure water neutral at pH 7?
Pure water at 25 °C has a pH of exactly 7 because water partially self-ionizes: H₂O ⇌ H⁺ + OH⁻. The equilibrium constant for this reaction (Kw) equals 1 × 10⁻¹⁴ mol²/L² at 25 °C, meaning [H⁺] = [OH⁻] = 1 × 10⁻⁷ mol/L. The pH is then −log₁₀(10⁻⁷) = 7. Note that at higher temperatures Kw increases, so the neutral point shifts slightly below 7.
What does each whole number change in pH represent?
Because pH is a logarithmic scale, each whole number change represents a 10-fold (tenfold) change in hydrogen ion concentration. Moving from pH 4 to pH 3 means [H⁺] increases by 10 times, making the solution 10 times more acidic. A difference of 2 pH units represents a 100-fold change in [H⁺]. This logarithmic nature is why lemon juice (pH ≈ 2) is vastly more acidic than coffee (pH ≈ 5), even though the numbers look close.
What is the pH of common household substances?
Common pH values: battery acid ≈ 0, stomach acid ≈ 1.5–2, lemon juice ≈ 2–3, vinegar ≈ 2.5, orange juice ≈ 3–4, black coffee ≈ 5, rainwater ≈ 5.6, pure water = 7, blood ≈ 7.35–7.45, seawater ≈ 8, baking soda ≈ 8.3, milk of magnesia ≈ 10.5, ammonia ≈ 11, bleach ≈ 12–13, drain cleaner/NaOH ≈ 14. These values can vary with concentration, temperature, and purity.
How do I convert between pH and hydrogen ion concentration?
Two formulas handle the conversion: (1) From [H⁺] to pH: pH = −log₁₀[H⁺]. Example: [H⁺] = 5 × 10⁻⁴ mol/L → pH = −log₁₀(5 × 10⁻⁴) = 3.30. (2) From pH to [H⁺]: [H⁺] = 10⁻ᵖᴴ. Example: pH = 3.30 → [H⁺] = 10⁻³·³⁰ ≈ 5 × 10⁻⁴ mol/L. Our calculator handles both directions — select the appropriate input mode to start from whichever value you know.
pH Formula
pH is a logarithmic scale that measures the acidity or basicity of an aqueous solution. It is defined as the negative base-10 logarithm of the hydrogen ion concentration [H⁺]. Solutions with pH below 7 are acidic, pH 7 is neutral (pure water at 25 °C), and pH above 7 are basic (alkaline).
How to Calculate pH
pH = −log₁₀[H⁺]
[H⁺] = 10⁻ᵖᴴ
The logarithmic nature means each whole-number change in pH represents a 10× change in [H⁺]. A pH of 3 is 10 times more acidic than pH 4, and 100 times more acidic than pH 5.
pH, pOH, [H⁺], and [OH⁻] Relationships
pH + pOH = 14
pOH = −log₁₀[OH⁻]
[H⁺] × [OH⁻] = 10⁻¹⁴ (Kw at 25 °C)
At 25 °C, the ion product of water (Kw) equals 1 × 10⁻¹⁴ mol²/L². This constant ties together all four quantities — knowing any one of pH, pOH, [H⁺], or [OH⁻] determines all the others.
- pOH = 14 − pH
- [OH⁻] = 10⁻ᵖᴼᴴ = Kw / [H⁺]
pH Scale — Common Substances
The pH scale ranges from 0 (most acidic) to 14 (most basic). Here are approximate pH values for everyday substances.
| Substance | Approx. pH | Nature |
|---|---|---|
| Battery acid (H₂SO₄) | 0 | Strongly acidic |
| Gastric acid (stomach) | 1.5 – 2 | Strongly acidic |
| Lemon juice / vinegar | 2 – 3 | Acidic |
| Orange juice / soda | 3 – 4 | Acidic |
| Black coffee | 5 | Weakly acidic |
| Rainwater / urine | 5.5 – 6.5 | Weakly acidic |
| Pure water (25 °C) | 7 | Neutral |
| Blood / seawater | 7.4 – 8.3 | Weakly basic |
| Baking soda (NaHCO₃) | 8.3 | Weakly basic |
| Ammonia solution | 11 | Basic |
| Bleach (NaOCl) | 12 – 13 | Strongly basic |
| Sodium hydroxide (NaOH) | 14 | Strongly basic |
How to Use This Calculator
- Choose your input mode: pH, [H⁺] Concentration, or pOH.
- Enter the known value in the input field.
- The calculator instantly computes all four related values: pH, pOH, [H⁺], and [OH⁻].
- A color-coded badge shows whether the solution is acidic, neutral, or basic.
- The visual pH scale bar shows your value's position on the 0–14 scale.
Worked Examples
Example 1: Find [H⁺] from pH
Given: pH = 3. Find [H⁺].
[H⁺] = 10⁻³ = 0.001 mol/L
pOH = 14 − 3 = 11; [OH⁻] = 10⁻¹¹ mol/L
Example 2: Find pH from concentration
Given: [H⁺] = 2.5 × 10⁻⁵ mol/L. Find pH.
pH = −log₁₀(2.5 × 10⁻⁵) = 4.60
Example 3: Find pH from pOH
Given: pOH = 4. Find pH.
pH = 14 − 4 = 10 (basic solution)
Related Tools
- Molarity Calculator — Solve for concentration (M = n/V), moles, or volume for any aqueous solution.
- Dilution Calculator — Calculate C₁V₁ = C₂V₂ dilutions. Find concentration or volume after diluting a stock solution.