pH / Acid-Base Calculator

Move the slider or enter a concentration to convert between pH, pOH, [H⁺], and [OH⁻], and see where a solution falls on the acid-base scale.

Worked example — pH / Acid-Base Calculator

pH	7.00
pOH	7.00
[OH-]	1.00×10⁻⁷ mol/L

These are the values the calculator shows when the page opens. Change any input above to recompute them.

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Three pH units is a factor of a thousand 🖖

Because pH is a logarithmic measure, each single unit represents a tenfold change in hydrogen-ion concentration — a solution of pH 3 is not "twice as acidic" as pH 6, it holds a thousand times the H⁺ — three units, three factors of ten. This is why a shift of just 0.1 pH units in ocean water, or a swing from pH 7.4 to 7.35 in human blood, represents a real and significant change in ion concentration even though the numbers look small. The scale exists because [H⁺] in everyday solutions spans more than 14 orders of magnitude — from about 10⁻¹⁴ mol/L in strong bases to 10⁰ mol/L in strong acids — and a logarithm compresses that enormous range into a single easy-to-read number from 0 to 14.

pH is really an ion count 🖖

At heart, pH just reports how crowded the free hydrogen ions (H⁺) are in a water-based liquid — the more crowded, the more acidic. Pure water splits slightly into equal amounts of H⁺ and OH⁻ (about 10⁻⁷ mol/L of each at room temperature), which is why neutral lands at pH 7. Since pH + pOH always adds to 14, knowing any one of pH, pOH, [H⁺], or [OH⁻] pins down the other three — which is exactly what this tool does.

Neutral isn't always pH 7 🖖

The neat rules that neutral means pH 7 and that pH + pOH = 14 hold only at 25°C. Water self-ionizes more readily when it is hot, so its ion product K_w grows with temperature: pure water is neutral at about pH 6.8 at body temperature (37°C) and near pH 6 close to boiling. The water is still perfectly neutral — equal H⁺ and OH⁻ — so the famous 7 is really just a room-temperature coincidence.

Problem solved in full

Pure water at pH 7 and a small pH change 5 steps
Pure water is pH 7. Show why, and then work out what a "small" pH change actually means.
1. Water self-ionises, and at 25 °C the product of the two ion concentrations is fixed. In pure water the two are equal by symmetry, so each is the square root of 10⁻¹⁴.
  
  $K_{w} = [H^{+}] [O H^{-}] = 1.0 \times 1 0^{- 14} at 2 5^{\circ} C$
2. pH is minus the base-ten logarithm of that concentration. The logarithm is the whole design: concentrations here span fourteen orders of magnitude, and a linear scale would be unusable.
  
  $pH = - lo g_{10} [H^{+}] = 7.00 \Rightarrow [H^{+}] = 1.0 \times 1 0^{- 7} mol/L$
3. Since the product is fixed, the two p-values must sum to 14. The calculator above prints both, and neutrality means equal — not "7" as such. At 50 °C neutral water is pH 6.63, because K_w is temperature-dependent.
  
  $pH + pOH = 14 \Rightarrow pOH = 7.00, [O H^{-}] = 1.00 \times 1 0^{- 7} mol/L$
4. Now read the scale properly. A drop of three pH units is not a 43% change; each unit is a factor of ten.
  
  $\frac{[ H ^{+} ] _{pH 4}}{[ H ^{+} ] _{pH 7}} = \frac{1 0 ^{- 4}}{1 0 ^{- 7}} = 1000$
5. Apply that to something with a narrow tolerance. Human blood is held between 7.35 and 7.45.
  
  $blood 7.4 \to 7.0 : \frac{1 0 ^{- 7.0}}{1 0 ^{- 7.4}} = 1 0^{0.4} = 2.5 \times$
Answer

pH 7.00, pOH 7.00, both ions at 1.00 × 10⁻⁷ mol/L. pH 7 to pH 4 is a thousandfold increase in acidity, which is why "slightly acidic rain" is not a slight thing. And blood falling from 7.4 to 7.0 — a change that looks like 5% — is a 2.5-fold rise in hydrogen-ion concentration and is fatal. Every intuition about "how much" fails on this scale unless you undo the logarithm first.

$pH = - lo g_{10} [H^{+}] Δ pH = 1 ⟺ 10 \times$

References (1)

The logarithmic definition and why one unit is a factor of ten: D. C. Harris, Quantitative Chemical Analysis, 9th ed., ch. 8. W. H. Freeman, 2015. ISBN 978-1-4641-3538-5.

By the 42Math team · Updated 2026-06-08

Reviewed against published sources. Corrections welcome. Editorial policy · Corrections

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Example problems

Stomach acid - Stomach acid pH 1.5: [H⁺] = 0.032 mol/L — about 320,000 times more acidic than water
Coffee - Coffee pH 5.0: [H⁺] = 1.0×10⁻⁵ mol/L — 100 times more acidic than water
Pure water - Pure water pH 7.0: [H⁺] = [OH⁻] = 1.0×10⁻⁷ mol/L — perfectly neutral
Bleach - Bleach pH 12.5: [OH⁻] = 0.032 mol/L — strongly basic