Calculate −log₁₀(x) and −ln(x) for pH, pKa, pOH, and general use. Includes pH scale interpretation, concentration ↔ pH conversion, and reference tables.
The negative logarithm −log₁₀(x) is one of the most widely used transformations in science, especially chemistry. The pH of a solution is defined as −log₁₀([H⁺]), where [H⁺] is the hydrogen-ion concentration in moles per liter. Similarly, pKa, pKb, and pOH all use the negative log to compress a huge range of concentrations (from 10⁰ to 10⁻¹⁴) into a compact 0–14 scale. Beyond chemistry, the negative log appears in signal processing (decibels), information theory (entropy), and any domain where small probabilities or concentrations need a human-readable scale. This calculator lets you enter any positive value and instantly see −log₁₀(x), −ln(x), and the corresponding pH interpretation. Switch to pH mode to enter a hydrogen-ion concentration and see the full acid/base picture: pH, pOH, [OH⁻], and whether the solution is acidic, neutral, or basic. The built-in pH color-coded scale table and concentration bars give you an immediate visual understanding of where your value falls on the scale.
Negative Log Calculator (−log x) helps you solve negative log calculator (−log x) problems quickly while keeping each step transparent. Instead of redoing long algebra by hand, you can enter your inputs once and immediately inspect −log₁₀(x), −ln(x), −log₂(x) to validate your work.
This is useful for homework checks, classroom examples, and practical what-if analysis. You keep the conceptual understanding while reducing arithmetic mistakes in multi-step calculations.
−log₁₀(x) = −(log₁₀ x). pH = −log₁₀([H⁺]). pOH = −log₁₀([OH⁻]) = 14 − pH (at 25 °C). pKa = −log₁₀(Ka). [H⁺] = 10^(−pH).
Result: −log₁₀(x) shown by the calculator
Using the preset "General: −log(x)", the calculator evaluates the negative log calculator (−log x) setup, applies the selected algebra rules, and reports −log₁₀(x) with supporting checks so you can verify each transformation.
This calculator takes the problem inputs and applies the relevant negative log calculator (−log x) relationships from your chosen method. It returns both final and intermediate values so you can audit the process instead of treating it as a black box.
Start with the primary output, then use −log₁₀(x), −ln(x), −log₂(x), x in Scientific Notation to confirm signs, magnitude, and internal consistency. If anything looks off, change one input and compare the updated outputs to isolate the issue quickly.
A strong workflow is manual solve first, calculator verify second. Repeating that loop improves speed and accuracy because you learn to spot common setup errors before they cost points on multi-step algebra problems.
Concentrations in chemistry are often very small numbers (e.g., 10⁻⁷). The negative sign flips the scale so that higher concentrations give lower pH values, which is more intuitive for the 0–14 pH scale.
Pure water at 25 °C has [H⁺] = 10⁻⁷ M, so pH = −log₁₀(10⁻⁷) = 7. Use this as a practical reminder before finalizing the result.
Yes. Very strong acids with [H⁺] > 1 M can have negative pH values. For example, [H⁺] = 10 M gives pH = −1.
At 25 °C, pH + pOH = 14 (the negative log of the water autoionization constant Kw = 10⁻¹⁴). Keep this note short and outcome-focused for reuse.
[H⁺] = 10^(−pH). For example, pH 3 corresponds to [H⁺] = 10⁻³ = 0.001 M.
In chemistry (pH, pKa), −log always means base 10. In other fields like information theory, the base may differ (base 2 for bits, base e for nats).