pH Calculator
Convert between pH, pOH, hydrogen ion concentration, and hydroxide ion concentration. You can also work out the pH of a strong acid, a strong base, or a weak acid from its concentration.
What pH is measuring
pH is a compact way of writing how many hydrogen ions are floating around in a solution. Those concentrations are awkward numbers, often somewhere near 0.0000001 mol/L, so chemists take the negative logarithm instead.
pH = −log10[H+] and [H+] = 10−pH
The square brackets mean "concentration in moles per liter." Because it is a logarithm, each whole step on the scale is a tenfold change. A solution at pH 3 has ten times more hydrogen ions than one at pH 4, and a hundred times more than one at pH 5. That is why a small pH shift in a river or in blood is a big deal.
The minus sign means the scale runs backwards from what you might expect. More hydrogen ions gives a lower pH.
pH, pOH, and the number 14
Water constantly splits into hydrogen and hydroxide ions in a process called autoionization. At 25 °C the two concentrations multiply to a fixed value:
[H+] × [OH−] = 1.0 × 10−14
Take the negative logarithm of both sides and you get the familiar shortcut:
pH + pOH = 14.00
This is where the 0 to 14 scale comes from. It is worth knowing that 14 only applies at 25 °C. Warm the water and it splits more readily, so the product grows and the sum shrinks. At 100 °C neutral water sits at about pH 6.14, not 7. The water is still neutral, because hydrogen and hydroxide are still equal. Neutral means the two are balanced, not that pH equals 7.
pH can also fall outside 0 to 14. Concentrated acids reach negative pH values and concentrated bases go above 14.
Strong acids and bases
A strong acid gives up essentially all of its hydrogen ions, so the hydrogen ion concentration simply equals the acid concentration.
For 0.010 M hydrochloric acid:
[H+] = 0.010 mol/L, so pH = −log(0.010) = 2.00
Strong bases work the same way through pOH. For 0.010 M sodium hydroxide:
[OH−] = 0.010, so pOH = 2.00 and pH = 14.00 − 2.00 = 12.00
One trap: some bases release more than one hydroxide per unit. Calcium hydroxide, Ca(OH)2, gives two, so a 0.010 M solution is 0.020 M in hydroxide.
Weak acids
A weak acid only partly dissociates. Vinegar is about 0.8 M acetic acid, but almost all of it stays intact as whole molecules. To find the pH you need the acid dissociation constant, Ka.
Most textbooks use the approximation [H+] = √(Ka × C), which is accurate as long as very little of the acid dissociates. This calculator solves the exact quadratic instead:
[H+] = (−Ka + √(Ka2 + 4·Ka·C)) ÷ 2
It also reports what percent of the acid broke apart. The usual rule is that the simple square root shortcut is fine below about 5 percent dissociation. Above that it starts to overestimate the acidity, and the exact answer is worth using.
Ka and pKa for common weak acids
| Acid | Ka (25 °C) | pKa |
|---|---|---|
| Phosphoric (first proton) | 7.1 × 10−3 | 2.15 |
| Citric (first proton) | 7.4 × 10−4 | 3.13 |
| Hydrofluoric | 6.8 × 10−4 | 3.17 |
| Formic | 1.8 × 10−4 | 3.75 |
| Lactic | 1.4 × 10−4 | 3.86 |
| Benzoic | 6.3 × 10−5 | 4.20 |
| Acetic | 1.8 × 10−5 | 4.76 |
| Carbonic (first proton) | 4.5 × 10−7 | 6.35 |
| Hypochlorous | 2.9 × 10−8 | 7.54 |
| Ammonium | 5.6 × 10−10 | 9.25 |
A smaller Ka means a weaker acid. Because pKa is the negative logarithm, a larger pKa means a weaker acid.
The pH of everyday things
| Substance | Approximate pH |
|---|---|
| Stomach acid | 1.5 to 3.5 |
| Lemon juice | 2.0 |
| Vinegar | 2.5 |
| Black coffee | 5.0 |
| Rain, unpolluted | 5.6 |
| Milk | 6.7 |
| Pure water at 25 °C | 7.0 |
| Human blood | 7.35 to 7.45 |
| Seawater | 8.1 |
| Baking soda solution | 8.3 |
| Household bleach | 12.5 |
Unpolluted rain is mildly acidic because carbon dioxide from the air dissolves into it and forms carbonic acid. Acid rain is a separate problem caused by sulfur and nitrogen oxides.
Mistakes worth avoiding
- Assuming neutral always means 7. That holds at 25 °C. Neutral really means hydrogen and hydroxide are equal.
- Treating a weak acid like a strong one. A 0.10 M acetic acid solution is pH 2.88, not pH 1.00.
- Forgetting multiple hydroxides. Ca(OH)2 releases two per formula unit.
- Counting decimals wrong. In a pH, only the digits after the decimal point are significant. A concentration with two significant figures gives a pH like 2.00, not 2.
- Adding pH values. Mixing a pH 3 and a pH 5 solution does not give pH 8. Convert to concentrations, combine those, then convert back.
Frequently asked questions
What is the formula for pH?
pH is the negative base-10 logarithm of the hydrogen ion concentration: pH = -log[H+]. To go the other way, [H+] = 10 raised to the power of negative pH.
How do I find pH from concentration?
For a strong acid the hydrogen ion concentration equals the acid concentration, so take the negative logarithm directly. A 0.010 M solution of hydrochloric acid gives pH 2.00. For a weak acid you also need the Ka value.
Why does pH plus pOH equal 14?
Water splits into hydrogen and hydroxide ions, and at 25 degrees Celsius the two concentrations always multiply to 1.0 x 10 to the power of -14. Taking negative logarithms of both sides turns that product into a sum of 14. The value shifts at other temperatures.
Can pH be negative or above 14?
Yes. The 0 to 14 range covers ordinary dilute solutions, but concentrated strong acids can have a negative pH and concentrated strong bases can go above 14.
How do I calculate the pH of a weak acid?
Use the acid dissociation constant. The exact result comes from solving Ka = x squared divided by (C minus x) for x, which is the hydrogen ion concentration. The common shortcut, the square root of Ka times C, is accurate when less than about 5 percent of the acid dissociates.
Is pure water always pH 7?
Only at 25 degrees Celsius. Water splits more readily as it warms, so hot pure water has a lower pH. At 100 degrees Celsius neutral water is about pH 6.14, and it is still perfectly neutral because hydrogen and hydroxide ions remain equal.
Related terms
Next: the molarity calculator converts grams into the mol/L figure this tool needs.