All calculatorsHydrogen Ion Concentration Calculator
Compute [H⁺] from pH or pH from [H⁺]. Includes scientific notation, optional temperature-based pure water estimate via Kw, step-by-step working, and a mini gauge showing the acid–neutral–base range (0–14).
Background
pH and hydrogen ion concentration are related by:
[H⁺] = 10−pH and pH = −log₁₀[H⁺].
Pure water at 25 °C has [H⁺] = 1.0×10⁻⁷ M (pH = 7).
How to use this calculator
- Enter either pH or [H⁺] (M). Leave the other blank.
- Check “Use Kw” to auto-compute [H⁺] of pure water at any T.
- Toggle scientific notation or mini gauge as desired.
Formula & Equation Used
[H⁺] from pH: [H⁺] = 10−pH
pH from [H⁺]: pH = −log₁₀[H⁺]
Pure water at T: Kw(T) ≈ 1.0×10⁻¹⁴ (25 °C). [H⁺] = √Kw.
Example Problems & Step-by-Step Solutions
Example 1 — pH 3.50
[H⁺] = 10−3.50 = 3.16×10⁻⁴ M.
Example 2 — [H⁺] = 1.0×10⁻⁵ M
pH = −log₁₀(1.0×10⁻⁵) = 5.00.
Frequently Asked Questions
Q: Should I enter both pH and [H⁺]?
No. Enter only one and the calculator will compute the other.
Q: Why use scientific notation for [H⁺]?
[H⁺] values are often very small; scientific notation makes them easier to read and compare.
Q: What does the mini gauge show?
It places your result on the pH scale (0–14), highlighting acidic, neutral, or basic.
