Science & Engineering · Chemistry
Formula verified
pH Calculator
Enter any one of pH, pOH, [H+] or [OH-] to get the other three, using the standard Sørensen definition and the water ion-product relation pH + pOH = 14.
Known value
On-screen number pad
Tap to type into the highlighted field
pH
4.00
Acidic
pOH
10.00
[H+] (mol/L)
1.00 × 10⁻⁴
[OH-] (mol/L)
1.00 × 10⁻¹⁰
Step-by-step proofCheck by hand
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How pH, pOH, [H+] and [OH-] relate
pH is defined as the negative base-10 logarithm of the hydrogen ion concentration, and pOH the same for hydroxide. Because water's ion product, Kw = [H+][OH-], is a fixed constant (1.0×10⁻¹⁴ at 25°C), knowing any one of these four values fixes the other three — this calculator works from whichever one you enter.
The formulas
pH = −log₁₀[H+] · pOH = −log₁₀[OH-] · pH + pOH = 14
Worked example
[H+] = 1.0×10⁻⁴ mol/L: pH = −log₁₀(1.0×10⁻⁴) = 4.00, so pOH = 14 − 4 = 10.00, and [OH-] = 10⁻¹⁰ = 1.00 × 10⁻¹⁰ mol/L — acidic.
Frequently asked questions
Why is pH a negative logarithm?
Hydrogen ion concentrations in water span many orders of magnitude — from about 1 mol/L in a strong acid down to 10⁻¹⁴ mol/L in a strong base — so a logarithmic scale compresses that huge range into small, easy-to-compare numbers. The negative sign flips the scale so that a higher concentration of H⁺ (a stronger acid) gives a lower pH, which matches how the scale is conventionally read.
Why does pH + pOH always equal 14?
It comes from water's ion product, Kw = [H+][OH-] = 1.0×10⁻¹⁴ at 25°C — a fixed constant for pure water at that temperature. Taking −log₁₀ of both sides of that equation turns the product into a sum, giving pH + pOH = 14 exactly, which is why knowing either one fixes the other.
Does the pH + pOH = 14 relationship always hold?
Only at 25°C (standard room temperature) — Kw itself changes with temperature, so the 14 constant shifts slightly at other temperatures. For everyday chemistry at room temperature it's the standard figure used, and the one this calculator assumes.
Sources and method
- IUPAC — definition of pH and the water ion product Kw at 25°C.