Chemists use negative logarithms to turn tiny concentrations into convenient numbers: a hydrogen ion concentration of 0.0000001 mol/L becomes pH 7. The same trick gives pKa, pOH and pKw.
How to use the Negative Log Calculator
- Number b
- Base a
Results update as you type, and everything is calculated in your browser.
How it works
Enter the number b and the base a (10 for pH-type scales).
Inputs explained
| Field | What to enter |
|---|---|
| Number b | A number |
| Base a | A number |
What each result means
- −log_a(b) = -ln([Number b])÷ln([Base a])
- log_a(b) = ln([Number b])÷ln([Base a])
Example values
How the main result changes when Number b changes and everything else stays at the example values above:
| Number b | −log_a(b) |
|---|---|
| 5.0000e-8 | 7.301 |
| 7.5000e-8 | 7.1249 |
| 1.0000e-7 | 7 |
| 1.2500e-7 | 6.9031 |
| 1.5000e-7 | 6.8239 |
| 2.0000e-7 | 6.699 |
Formula
−log_a(b) = −ln b / ln a (pH = −log₁₀[H⁺])
Worked example
Inputs — Number b: 1e-07; Base a: 10.
Results — −log_a(b) = 7; log_a(b) = -7.
Key terms
- pH
- −log₁₀ of the hydrogen ion concentration.
Frequently asked questions
What is the pH of 10⁻⁷ mol/L H⁺?
7.
Why use a negative log?
Concentrations are usually below 1, so their logs are negative; the minus sign makes the scale positive.
What is the pH of 0.01 M HCl?
2.
Does a lower pH mean more acid?
Yes – each unit is ten times more H⁺.