pH Calculator

About the pH Calculator

Acidity is everywhere in chemistry and biology, from titrations in the lab to blood chemistry, soil testing and swimming pools. The pH scale compresses hydrogen ion concentrations spanning more than ten orders of magnitude into a convenient range of roughly 0 to 14, but the logarithms involved make hand calculation easy to get wrong.

This calculator handles the four standard conversions and the weak acid and weak base problems that appear in general chemistry. For weak electrolytes it solves the equilibrium quadratic exactly rather than relying on the small-x approximation, then reports the percent ionisation so you can see whether the shortcut would have been acceptable. Numbers can be typed in scientific notation such as 2.5e-4 or 2.5×10^-4.

What is pH?

pH is the negative base-10 logarithm of the hydrogen ion concentration in moles per litre: $\text{pH} = -\log_{10}[\mathrm{H^+}]$ . A solution with $[\mathrm{H^+}] = 10^{-3}$ M has pH 3. Because the scale is logarithmic, a drop of one pH unit means ten times more hydrogen ions.

Water self-ionises, and at 25 °C the product of the ion concentrations is fixed: $[\mathrm{H^+}][\mathrm{OH^-}] = K_w = 1.0 \times 10^{-14}$ . Taking logarithms gives $\text{pH} + \text{pOH} = 14$ . Pure water has pH 7; acidic solutions are below 7 and basic solutions above it.

How to use the pH Calculator

Select the quantity you know from the menu.
Enter the concentration in mol/L or the pH or pOH value.
For a weak acid or base, also enter Ka or Kb.
Press Calculate pH.
Read pH, pOH, [H⁺] and [OH⁻], and for weak electrolytes the percent ionisation.

Formulas

pH

\text{pH} = -\log_{10}[\mathrm{H^+}]

Inverse

[\mathrm{H^+}] = 10^{-\text{pH}}

Water at 25 °C

[\mathrm{H^+}][\mathrm{OH^-}] = 10^{-14},\quad \text{pH} + \text{pOH} = 14

Weak acid equilibrium

K_a = \frac{x^2}{C - x}

x is the equilibrium [H⁺] produced by an acid of initial concentration C.

Worked example: [H⁺] = 1.0 × 10⁻³ M

The first example takes $[\mathrm{H^+}] = 1.0 \times 10^{-3}$ M, as in a 0.001 M solution of a strong acid such as HCl. Then $\text{pH} = -\log_{10}(10^{-3}) = 3$ , $\text{pOH} = 11$ and $[\mathrm{OH^-}] = 10^{-11}$ M.

A harder case is 0.10 M acetic acid with $K_a = 1.8 \times 10^{-5}$ . Solving $x^2 + K_a x - K_a C = 0$ gives $x \approx 1.333 \times 10^{-3}$ M, so the pH is about 2.875 and only about 1.3% of the acid molecules are ionised.

The solution below is generated by the same engine that powers the calculator above.

Final answer

\text{pH} = 3

How we read your problem

Convert between hydrogen ion concentration, hydroxide concentration, pH and pOH in water at 25 °C.

[\mathrm{H^+}] = 0.001\ \text{M}

Step-by-step solution

pH
$\text{pH} = -\log_{10}[\mathrm{H^+}] = -\log_{10}(0.001) = 3$
pOH and [OH⁻] (25 °C, Kw = 1.0 × 10⁻¹⁴)
$\text{pOH} = 14 - \text{pH} = 11,\quad [\mathrm{OH^-}] = \frac{K_w}{[\mathrm{H^+}]} = 1 \times 10^{-11}\ \text{M}$

Formulas used

pH
$\text{pH} = -\log_{10}[\mathrm{H^+}]$
Water
$\text{pH} + \text{pOH} = 14$
Weak acid
$K_a = \frac{[\mathrm{H^+}][\mathrm{A^-}]}{[\mathrm{HA}]}$

pH is a logarithmic scale: each unit is a tenfold change in hydrogen ion concentration. Below 7 the solution is acidic, above 7 it is basic, at 25 °C.

Verification

[H⁺][OH⁻] = 1×10^-14 ≈ 1.0×10^-14.
The solution is acidic.

Detailed explanation

Strong versus weak

Strong acids such as HCl, HNO₃ and HBr ionise completely in water, so for a monoprotic strong acid the hydrogen ion concentration equals the acid concentration, and you can use the [H⁺] mode directly. Strong bases such as NaOH work the same way with [OH⁻]; for Ca(OH)₂ double the concentration because each formula unit releases two hydroxide ions.

Weak acids such as acetic acid, hydrofluoric acid and carbonic acid only partly ionise. Their acid dissociation constant Ka measures how far the equilibrium lies to the right. The smaller Ka is, the weaker the acid and the higher the pH at a given concentration.

The exact quadratic and the 5% rule

Textbooks often simplify $K_a = x^2 / (C - x)$ by assuming x is much smaller than C, which gives $x \approx \sqrt{K_a C}$ . The usual test is that x must be below 5% of C. For 0.10 M acetic acid the shortcut gives $1.342 \times 10^{-3}$ M, very close to the exact value.

The approximation fails for stronger weak acids or dilute solutions. With $C = 0.010$ M and $K_a = 0.010$ , the exact answer is $x \approx 6.18 \times 10^{-3}$ M, pH about 2.209, while the shortcut would claim $x = 0.010$ M and pH 2.000, a sizeable error. The calculator always uses the exact root and tells you which side of 5% you are on.

Weak bases and temperature

For a weak base B with constant Kb, the same quadratic gives [OH⁻]. For 0.050 M ammonia with $K_b = 1.8 \times 10^{-5}$ , $[\mathrm{OH^-}] \approx 9.40 \times 10^{-4}$ M, the pOH is about 3.027 and the pH about 10.97.

The relation pH + pOH = 14 holds at 25 °C only. Kw increases with temperature, so neutral water at 50 °C has a pH near 6.6 even though it is not acidic. All results here use the standard 25 °C value, which is what nearly all textbook problems assume.

Common mistakes

Using the natural logarithm instead of the base-10 logarithm.
Forgetting the minus sign, which gives a negative pH for ordinary solutions.
Treating a weak acid's concentration as its [H⁺].
Forgetting that each Ca(OH)₂ or Ba(OH)₂ unit releases two hydroxide ions.
Applying pH + pOH = 14 at temperatures other than 25 °C.

Tips

The number of significant figures in a concentration equals the number of decimal places in its pH.
If [H⁺] is a power of ten, the pH is just the exponent without its minus sign.
A tenfold dilution of a strong acid raises the pH by one unit, until it approaches 7.
Look up Ka values in your course's data table, as sources differ slightly.
Use the molar mass calculator first if a question gives grams of acid rather than its molarity.

Frequently asked questions

How do you calculate pH from hydrogen ion concentration?

Take the negative base-10 logarithm: pH = −log₁₀[H⁺]. For example, [H⁺] = 2.5 × 10⁻⁴ M gives a pH of about 3.602.

How do you find [H⁺] from pH?

Raise ten to the power of minus the pH: [H⁺] = 10^(−pH). A pH of 3.2 corresponds to about 6.31 × 10⁻⁴ M.

What is the relationship between pH and pOH?

At 25 °C, pH + pOH = 14 because the ion product of water, [H⁺][OH⁻], equals 1.0 × 10⁻¹⁴. Knowing one immediately gives the other.

How do I find the pH of a weak acid?

Set up the equilibrium Ka = x²/(C − x), where x is [H⁺], and solve the quadratic. Then take −log₁₀ x. The calculator does this exactly when you choose weak acid and enter C and Ka.

Can pH be negative or above 14?

Yes. Very concentrated strong acids can have [H⁺] above 1 M and a negative pH, and very concentrated bases can exceed 14. In such solutions activities differ from concentrations, so these values are approximate.

Why is pure water pH 7?

Water ionises slightly into equal amounts of H⁺ and OH⁻. At 25 °C each is 1.0 × 10⁻⁷ M, and −log₁₀ of that is 7.

What is percent ionisation?

It is the fraction of weak acid or base molecules that ionise, x/C × 100%. It rises as the solution becomes more dilute, even though the pH moves closer to 7.

Find the pH of your solution

Pick what you know, enter the values above and get pH, pOH, [H⁺] and [OH⁻] together.

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