Article — pH Calculator
pH Calculator: Hydrogen Ion Concentration, pOH, and the 0–14 Scale
pH is the negative base-10 logarithm of the hydrogen-ion concentration in mol/L. Pure water at 25 °C has [H+] = 10−7 M, giving pH = 7. The pH scale runs from 0 (most acidic) to 14 (most basic), with each unit representing a 10× change in acidity. S. P. L. Sørensen introduced the scale at the Carlsberg Laboratory in 1909.
The pH calculator on this page converts in four directions: from [H+] to pH, from [OH−] to pH, from pH back to ion concentrations, and from pOH to pH. All four reuse the same logarithmic identity.
What pH measures
pH quantifies acidity by tracking hydrogen-ion activity in solution. The lower the pH, the higher the hydrogen-ion concentration, and the more acidic the solution. A change of one pH unit means a tenfold change in [H+].
The scale is calibrated for water-based solutions at 25 °C. The neutral point sits at pH 7 because pure water self-ionizes weakly: a small fraction of molecules dissociate into H+ and OH−, and at room temperature the equilibrium concentration of each ion is 10−7 M.
The pH formula in detail
The core definition is one line:
pH = −log10[H+] concentration to pH[H+] = 10−pH pH to concentrationpH + pOH = 14 at 25 °CThe pH calculator uses these three equations to convert between any pair of inputs. The negative sign in the definition is what makes acidic solutions, which have high [H+], correspond to low pH numbers. Without the negative sign, the scale would run backward.
pH versus pOH and the water constant
Water dissociates: H2O ↔ H+ + OH−. The equilibrium constant is Kw = [H+][OH−] = 1.0 × 10−14 at 25 °C. Taking the negative log of both sides gives pH + pOH = 14. The 14 is temperature-dependent: at 60 °C, Kw rises to about 10−13, and the "neutral pH" drops to roughly 6.5.
pOH is calculated the same way as pH but with hydroxide concentration: pOH = −log10[OH−]. Most chemistry uses pH because the hydrogen-ion concentration is what matters for biological systems, indicator dyes, and titrations. pOH is mostly a bookkeeping tool for working with bases.
The pH scale was invented for beer. Søren Peter Lauritz Sørensen developed pH at the Carlsberg Laboratory in Copenhagen in 1909, where he was studying protein behavior and brewing quality control. The "p" comes from the German Potenz (power or exponent). What started as a way to optimize fermentation became the universal language of acid-base chemistry.
pH of everyday substances
Knowing typical pH values builds intuition. Battery acid sits at 0–1, lemon juice at 2–3, vinegar at 2.4, coffee around 5, milk near 6.7, blood around 7.4, sea water 8.2, baking soda 8.3, household ammonia 11–13, and concentrated drain cleaner up to 14.
Living organisms are picky about pH. Human blood is buffered to stay between 7.35 and 7.45; drops below 7.0 or rises above 7.8 are life-threatening. Stomach acid runs at pH 1.5–3.5, while the small intestine is around pH 6–7. Soil pH affects plant nutrient availability: most crops thrive between pH 6 and 7.5, while blueberries and azaleas prefer 4.5–5.5.
Why pH is logarithmic
Ion concentrations in solution span an enormous range: from about 1 M in concentrated acid to 10−14 M in concentrated base. Plotting these linearly is hopeless; the logarithm compresses the range into a friendly 0–14 scale.
The logarithmic nature has consequences. A drop from pH 7 to pH 4 is not three units of acidity but a thousandfold increase in [H+]. A jump from pH 8 to pH 5 makes a solution one thousand times more acidic. Ocean acidification, where pH has fallen from about 8.2 to 8.1 over the past 200 years, corresponds to a 25% increase in hydrogen-ion concentration — a much larger biological impact than the pH numbers suggest at a glance.
Measuring pH in practice
Three methods dominate lab work. pH paper (indicator strips) costs pennies and gives accuracy of about 0.5 unit. Color-comparator kits do a bit better, around 0.2 unit. Glass electrode pH meters reach 0.01 unit with proper two-point or three-point calibration against buffer standards.
Calibrate pH meters daily with two buffer standards bracketing the expected range — usually pH 4.01 and 7.00 for acidic samples, or 7.00 and 10.01 for basic ones. The electrode glass membrane drifts as it ages, and uncalibrated meters can read 0.2–0.5 units off without warning.
Common pH calculation mistakes
Common slips: dropping the negative sign in pH = −log[H+], using natural log instead of base-10 log, plugging in concentration in mmol/L instead of mol/L, and confusing pH with pOH. If your calculated pH for a strong acid comes out around 3 when you expected 1, check whether you converted the concentration units correctly.
- Negative pH is real — 12 M HCl has pH about −1.1; the 0–14 range is convention, not a strict limit
- Each pH unit = 10× change in [H+]; pH 4 to pH 7 means 1000× less acidic
- Temperature matters — Kw rises with heat, so neutral pH shifts below 7 at warmer temperatures
- Strong acids dissociate fully — 0.01 M HCl gives pH 2 (ignoring activity corrections)
- Weak acids dissociate partially — 0.01 M acetic acid gives pH about 3.4, not 2
- Buffers resist change — adding small amounts of acid or base barely shifts pH inside the buffer range
Buffers and the Henderson-Hasselbalch equation
A buffer holds pH near a target value by combining a weak acid with its conjugate base. The Henderson-Hasselbalch equation predicts the pH: pH = pKa + log10([A−] / [HA]). When the acid and conjugate base are in equal amounts, the log term is zero and pH equals the pKa.
Biological systems are full of buffers. Blood pH stays at 7.4 thanks to the bicarbonate/carbonic-acid system. Intracellular pH is buffered by phosphates and proteins. Laboratory buffers cover specific ranges: acetate near pH 4–6, phosphate near pH 7, Tris near pH 8–9, and carbonate above 9.