How do I calculate pH from concentration?

Take the negative base-10 logarithm of the hydrogen ion concentration. For [H⁺] = 0.001 M, pH = −log₁₀(0.001) = 3.

How do I find [H⁺] from pH?

Raise 10 to the power of minus the pH: [H⁺] = 10^−pH. Blood at pH 7.4 has [H⁺] = 10^−7.4 = 3.98 × 10⁻⁸ M.

What is the pH of a 0.01 M NaOH solution?

NaOH is a strong base, so [OH⁻] = 0.01 M. pOH = −log₁₀(0.01) = 2, and pH = 14 − 2 = 12.

Is neutral always pH 7?

Only at 25 °C. Water's ionization changes with temperature, so pure water at 100 °C is neutral at about pH 6.1. This calculator assumes 25 °C.

pH Calculator: pH, pOH, [H⁺] and [OH⁻]

pH = −log₁₀[H⁺]. A hydrogen ion concentration of 1 × 10⁻³ M gives pH 3, which is acidic. At 25 °C, pH + pOH = 14, so its pOH is 11.

Hydrogen ion concentration [H⁺]

Use e notation for small numbers: 1e-3 means 1 × 10⁻³ M.

3.00

pOH

11.00

[H⁺]

1 × 10⁻³ M

[OH⁻]

1 × 10⁻¹¹ M

acidic

Compared with everyday substances

Battery acid	0.8
Stomach acid	1.5
Lemon juice	2.2
Vinegar	2.9
Orange juice	3.7
Black coffee	5
Milk	6.6
Pure water	7
Blood	7.4
Seawater	8.1
Baking soda solution	8.3
Household ammonia	11.6
Bleach	12.5
Drain cleaner	14

Typical values; real samples vary.

Show the math

1
pH = −log₁₀[H⁺]
−log₁₀(1 × 10⁻³) = 3.00
pH is the negative power of ten of the hydrogen ion concentration.
= pH 3.00

Read the steps as text

pH = −log₁₀[H⁺]. −log₁₀(1 × 10⁻³) = 3.00 pH is the negative power of ten of the hydrogen ion concentration.
pOH = 14 − pH. 14 − 3.00 = 11.00 At 25 °C, pH and pOH always add up to 14.
[OH⁻] = 10^−pOH. 10^−11 = 1 × 10⁻¹¹ M Check: [H⁺] × [OH⁻] = 1.0 × 10⁻¹⁴ at 25 °C.
Acidic, neutral or basic?. pH 3.00 < 7 Below 7 is acidic, 7 is neutral and above 7 is basic (alkaline). Each whole pH unit is a tenfold change in [H⁺].

How pH is calculated

pH measures how acidic a solution is through its hydrogen ion concentration, [H⁺], in moles per liter. Because those concentrations span many powers of ten, pH uses the negative logarithm: pH = −log₁₀[H⁺]. A concentration of 10⁻³ M is pH 3, and 10⁻⁹ M is pH 9.

pOH does the same for hydroxide ions: pOH = −log₁₀[OH⁻]. In water at 25 °C the two concentrations multiply to 1.0 × 10⁻¹⁴, so pH + pOH = 14. Knowing any one of the four values is enough to find the other three.

Reading the pH scale

A pH below 7 is acidic, 7 is neutral and above 7 is basic (alkaline). The scale is logarithmic, so each step of 1 is a tenfold change: lemon juice at pH 2 has about 100,000 times more hydrogen ions than pure water at pH 7.

For a strong acid like hydrochloric acid, which fully splits into ions, [H⁺] equals the acid's concentration, so 0.01 M HCl has pH 2. Weak acids such as vinegar only partly ionize, so their pH needs the acid dissociation constant (Ka) as well.

Frequently asked questions

How do I calculate pH from concentration?: Take the negative base-10 logarithm of the hydrogen ion concentration. For [H⁺] = 0.001 M, pH = −log₁₀(0.001) = 3.
How do I find [H⁺] from pH?: Raise 10 to the power of minus the pH: [H⁺] = 10^−pH. Blood at pH 7.4 has [H⁺] = 10^−7.4 = 3.98 × 10⁻⁸ M.
What is the pH of a 0.01 M NaOH solution?: NaOH is a strong base, so [OH⁻] = 0.01 M. pOH = −log₁₀(0.01) = 2, and pH = 14 − 2 = 12.
Is neutral always pH 7?: Only at 25 °C. Water's ionization changes with temperature, so pure water at 100 °C is neutral at about pH 6.1. This calculator assumes 25 °C.