How this instrument works
pH is defined as the negative base-10 logarithm of the hydrogen ion concentration: pH = -log10([H+]), where [H+] is measured in moles per litre. Danish chemist Søren Sørensen introduced the scale in 1909 specifically because hydrogen ion concentrations in everyday solutions are inconveniently small and span many orders of magnitude — from about 1 mol/L in strong acid down to roughly 10^-14 mol/L in strong base. Taking the negative log compresses that whole range into a tidy scale running roughly from 0 to 14.
Because the relationship is logarithmic, each single step of pH represents a tenfold change in [H+], not a proportional or additive one. A solution at pH 4 doesn't have '3 units more acid' than one at pH 7 — it has a hydrogen ion concentration 1,000 times greater, since the 3-unit gap means a factor of 10^3. This is the single most common source of confusion when reasoning about pH informally, and it is exactly what this instrument's underlying formula makes precise.
pH 7 marks neutral, corresponding to pure water's own [H+] of 1 x 10^-7 mol/L at 25 degrees C. Values below 7 are acidic (higher [H+]), values above 7 are basic or alkaline (lower [H+]). This instrument works in the direction most lab measurements actually start from — a known or measured hydrogen ion concentration, converted into the pH figure that's easier to communicate and compare.
- Enter the solution's hydrogen ion concentration, in moles per litre, into Hydrogen ion concentration [H+] (mol/L).
- Read pH directly beneath the field — the instrument computes the negative base-10 logarithm automatically.
- Enter the concentration as a plain decimal or in scientific notation (e.g. 0.0001 or 1e-4) — both represent the same value.
- [H+] must be greater than zero; a concentration of exactly zero has no defined logarithm, so the instrument requires a positive value.
- Need to go the other direction, from a known pH back to [H+]? Use this site's hydrogen ion concentration calculator instead.
Worked example — [H+] = 0.0001 mol/L
Enter 0.0001 into Hydrogen ion concentration [H+] (mol/L) — one ten-thousandth of a mole of hydrogen ions per litre. pH reads 4.0, since -log10(0.0001) = -log10(1x10^-4) = 4 exactly.
A pH of 4.0 places this solution solidly in the acidic range, three full units below neutral pH 7 — meaning its hydrogen ion concentration is 10^3, or 1,000 times, greater than that of neutral water, even though '4' and '7' look like nearby numbers on the page.
Questions
Why is pH defined using a negative logarithm?
Because [H+] values in real solutions span an enormous range of small numbers — from about 1 mol/L down to roughly 10^-14 mol/L — which is unwieldy to write and compare directly. Taking -log10 turns that huge multiplicative range into a compact additive scale running roughly 0 to 14, and the negative sign flips the naturally negative exponents (like -4 in 10^-4) into the positive, easy-to-read numbers chemists actually use.
Does a pH of 4 mean twice the acidity of a pH of 8?
No — it means 10,000 times the hydrogen ion concentration, not twice. Each single pH unit corresponds to a tenfold change in [H+] because the scale is logarithmic base 10, so a 4-unit gap between pH 4 and pH 8 means a factor of 10^4 = 10,000 in [H+], one of the most common misreadings of the pH scale.
What [H+] corresponds to neutral pH 7?
1 x 10^-7 mol/L, at 25 degrees C. That figure comes from pure water's own autoionization equilibrium (2 H2O <=> H3O+ + OH-), where hydrogen and hydroxide ion concentrations are exactly equal at 10^-7 mol/L each — which is also why pH 7 is defined as the neutral point rather than some other value.
How is this different from the hydrogen ion concentration calculator?
This instrument goes from [H+] to pH, using pH = -log10([H+]) — enter a concentration, get the log-scale number. This site's hydrogen ion concentration calculator runs the identical relationship in reverse, [H+] = 10^(-pH), taking a pH value and returning the actual molar concentration it represents. Use whichever one matches the quantity you already have.
Can pH be negative or above 14?
Yes, in sufficiently concentrated strong acid or base — for example, [H+] = 10 mol/L gives pH = -log10(10) = -1. The formula pH = -log10([H+]) has no built-in floor or ceiling; the familiar 0-14 range is simply where most dilute aqueous solutions in practice fall, not a hard mathematical limit on the formula itself.
Is this the same relationship used in the Henderson-Hasselbalch equation?
It's the same logarithmic pH definition underneath, but a different formula for a different situation. This calculator converts a known [H+] straight into pH; the Henderson-Hasselbalch equation instead estimates a buffer's pH from its acid's pKa and the ratio of conjugate base to weak acid concentration, without needing [H+] measured directly. Both ultimately rest on the same -log10 relationship that defines pH and pKa alike.