How do you calculate pH from concentration?

Take the negative logarithm (base 10) of the hydronium concentration in mol/L. [H₃O⁺] = 0.001 M: −log(0.001) = 3, so pH 3. For 2.5 × 10⁻⁴ M, −log = 3.60. Enter the concentration and the page shows the log.

How do you find the concentration from pH?

Raise 10 to the negative pH: [H₃O⁺] = 10^(−pH). pH 4.5 gives 10⁻⁴·⁵ = 3.16 × 10⁻⁵ mol/L. Choose 'pH' as the known value and the page gives both [H₃O⁺] and [OH⁻].

What is pOH and how is it related to pH?

pOH is −log[OH⁻], the hydroxide equivalent of pH. At 25 °C, pH + pOH = 14, so a solution with pOH 3 has pH 11. Given either concentration the page reports both values.

Is a pH of 3 ten times or a thousand times more acidic than pH 6?

A thousand times: each pH unit is a factor of ten in hydronium concentration, and three units is 10³. The page's last line states the factor relative to pure water.

What is the pH of a 0.01 M solution of a strong acid?

2: a strong acid such as HCl ionises completely, so [H₃O⁺] = 0.01 = 10⁻², and −log(10⁻²) = 2. Each tenfold dilution raises the pH by one, until it nears 7.

Does pH + pOH always equal 14?

Only at 25 °C, where water's ion product is 1.0 × 10⁻¹⁴. At body temperature, 37 °C, it is about 2.4 × 10⁻¹⁴, so the sum is about 13.6 and neutral water has a pH near 6.8.

pH Calculator (from [H₃O⁺], [OH⁻] or pH)

pH and pOH from a hydronium or hydroxide concentration, or both concentrations from a pH, with the working.

Inputs

I know the

[H₃O⁺] concentration(mol/L)

0 mol/L10 mol/L

[OH⁻] concentration(mol/L)

0 mol/L10 mol/L

014

Include CalculateEveryday mark

2.9208

2.92

Acidic

AcidicNeutralBasic

Working: pH = −log(1.20e-3) = 2.9208
[H₃O⁺] (mol/L): 1.2000e-3
pOH: 11.0792
[OH⁻] (mol/L): 8.3333e-12
At 25 °C: acidic — 1.20e+4× the [H₃O⁺] of pure water

Use this calculator on your own site

Free embed

Two lines of HTML, unlimited views
Shows a small CalculateEveryday bar, with a credit link under the calculator

What each pH input means

I know the: Start from the hydronium (H₃O⁺) concentration, the hydroxide (OH⁻) concentration, or a pH.
[H₃O⁺] concentration: Hydronium-ion concentration in mol/L. For a strong acid such as HCl, it equals the acid's molarity.
[OH⁻] concentration: Hydroxide-ion concentration in mol/L. For a strong base such as NaOH, it equals the base's molarity.
pH: A pH value, to find the concentrations it stands for.

pH formula

pH = −log₁₀[H₃O⁺] · pOH = −log₁₀[OH⁻] · pH + pOH = 14.00 at 25 °C · [H₃O⁺] = 10^(−pH)

\text{pH} = -\log_{10}[\text{H}_3\text{O}^+], \qquad \text{pH} + \text{pOH} = 14.00

pH compresses hydronium-ion concentrations that span fourteen powers of ten into a number from 0 to 14: it is the negative logarithm of [H₃O⁺] in mol/L, so a concentration of 10⁻³ M is pH 3 and each unit of pH is a tenfold change. pOH does the same for hydroxide, and because water's ion product is 10⁻¹⁴ at 25 °C the two always add to 14. Neutral water has [H₃O⁺] = [OH⁻] = 10⁻⁷ M, pH 7. The page works from whichever quantity you have — hydronium concentration, hydroxide concentration or the pH itself — and returns the other three, with the logarithm or power of ten written out.

pH worked example

OpenStax's stomach-acid example: [H₃O⁺] = 1.2 × 10⁻³ M. pH = −log(1.2 × 10⁻³) = −(−2.92) = 2.92, so pOH = 14 − 2.92 = 11.08 and [OH⁻] = 10⁻¹¹·⁰⁸ = 8.3 × 10⁻¹² M. That is 12,000 times the hydronium concentration of pure water. From a hydroxide concentration of 10⁻⁵ M the route is the reverse: pOH 5, pH 9, basic.

More pH examples

0.002 M sodium hydroxide gives [OH⁻] = 0.002: pOH = −log(0.002) = 2.699, so pH = 14 − 2.699 = 11.301 — basic, with 20,000 times less hydronium than pure water.

A pH of 8.3, about that of a baking-soda solution: [H₃O⁺] = 10⁻⁸·³ = 5.0 × 10⁻⁹ mol/L and [OH⁻] = 2.0 × 10⁻⁶. The headline repeats it as 8.3, with pOH 5.7.

Where the pH calculator can give the wrong answer

The 14.00 relation holds at 25 °C. Water's ion product rises with temperature, so at 37 °C neutral pH is about 6.8, and pH + pOH is a little under 14; the page assumes 25 °C.
These formulas take the concentration of H₃O⁺ actually present. For a weak acid, that is not the acid's concentration — acetic acid at 0.1 M is only about 1.3% ionised, pH 2.9 not 1 — and an equilibrium calculation with Kₐ comes first.
Strictly pH uses ion activity rather than concentration; in dilute solutions the two are close, in concentrated or salty ones they are not, which is why a meter and this arithmetic can disagree by a few tenths.
pH below 0 and above 14 exist (concentrated strong acids and bases) but the page's pH input is limited to 0–14, the range that concentrations up to 1 M cover.
Enter concentrations in mol/L. A 1% or 1 ppm figure has to be converted to molarity first.

Spotted a mistake? Tell us

pH reference table

pH, hydronium and hydroxide concentrations at 25 °C
pH	[H₃O⁺] (mol/L)	[OH⁻] (mol/L)	pOH
0	1	10⁻¹⁴	14
2	10⁻²	10⁻¹²	12
4	10⁻⁴	10⁻¹⁰	10
6	10⁻⁶	10⁻⁸	8
7 (neutral)	10⁻⁷	10⁻⁷	7
8	10⁻⁸	10⁻⁶	6
10	10⁻¹⁰	10⁻⁴	4
12	10⁻¹²	10⁻²	2
14	10⁻¹⁴	1	0

Source: OpenStax Chemistry 2e, §14.2: pH = −log[H₃O⁺], pOH = −log[OH⁻], pH + pOH = 14.00 at 25 °C

pH FAQ

: Take the negative logarithm (base 10) of the hydronium concentration in mol/L. [H₃O⁺] = 0.001 M: −log(0.001) = 3, so pH 3. For 2.5 × 10⁻⁴ M, −log = 3.60. Enter the concentration and the page shows the log.
: Raise 10 to the negative pH: [H₃O⁺] = 10^(−pH). pH 4.5 gives 10⁻⁴·⁵ = 3.16 × 10⁻⁵ mol/L. Choose 'pH' as the known value and the page gives both [H₃O⁺] and [OH⁻].
: pOH is −log[OH⁻], the hydroxide equivalent of pH. At 25 °C, pH + pOH = 14, so a solution with pOH 3 has pH 11. Given either concentration the page reports both values.
: A thousand times: each pH unit is a factor of ten in hydronium concentration, and three units is 10³. The page's last line states the factor relative to pure water.
: 2: a strong acid such as HCl ionises completely, so [H₃O⁺] = 0.01 = 10⁻², and −log(10⁻²) = 2. Each tenfold dilution raises the pH by one, until it nears 7.
: Only at 25 °C, where water's ion product is 1.0 × 10⁻¹⁴. At body temperature, 37 °C, it is about 2.4 × 10⁻¹⁴, so the sum is about 13.6 and neutral water has a pH near 6.8.