pH Calculator
Calculate pH, pOH, and ion concentrations
Understanding pH
pH is a logarithmic scale used to measure the acidity or basicity of a solution. It ranges from 0 (strongly acidic) to 14 (strongly basic), with 7 being neutral. The pH equals the negative log base 10 of the hydrogen ion concentration: pH = -log[H+].
This calculator can determine pH from a known acid or base concentration, or calculate all related values (pOH, [H+], [OH-]) from a given pH value.
The pH Scale
Because the pH scale is logarithmic, each whole number change represents a tenfold difference in hydrogen ion concentration. A solution with pH 3 is ten times more acidic than pH 4, and one hundred times more acidic than pH 5. This makes pH a powerful way to express the wide range of acidity found in chemical and biological systems.
- pH 0–2: Strongly acidic (e.g., battery acid, stomach acid)
- pH 3–6: Weakly acidic (e.g., vinegar, coffee, rain water)
- pH 7: Neutral (pure water at 25°C)
- pH 8–11: Weakly basic (e.g., baking soda, soap, ammonia)
- pH 12–14: Strongly basic (e.g., bleach, drain cleaner)
Key Relationships
At 25°C, the ion product of water is Kw = [H+][OH-] = 1.0 × 10¹&sup4;. This means pH + pOH = 14 for any aqueous solution. When you know the pH, the calculator uses these relationships to determine pOH, the hydrogen ion concentration [H+], and the hydroxide ion concentration [OH-].
These calculations are essential in analytical chemistry for titration analysis, buffer preparation, and environmental water quality monitoring.
Worked example: 0.010 M hydrochloric acid
Hydrochloric acid is a strong acid, which means it dissociates completely in water. That assumption is what makes this calculation a single logarithm.
- Because dissociation is complete, the hydrogen ion concentration equals the acid concentration, so [H+] is 0.010 M.
- Apply the definition. pH is the negative base ten logarithm of [H+], so pH equals minus log of 0.010, which is 2.00.
- Find pOH from the water relationship. At 25 degrees Celsius, pH plus pOH equals 14.00, so pOH is 12.00.
- Find the hydroxide concentration. [OH-] is ten to the power of minus pOH, which is 1.0 times ten to the minus twelve molar.
Answer. The solution has pH 2.00, pOH 12.00, and a hydroxide concentration of 1.0 times ten to the minus twelve molar. Note that the two decimal places in the pH correspond to the two significant figures in the concentration.
Common mistakes
These are the errors that come up most often, and each one changes the answer rather than merely looking untidy.
Treating a weak acid as though it were strong
Acetic acid at 0.010 M does not give pH 2. Only a small fraction of it dissociates, so the real pH is closer to 3.4. Using the strong acid shortcut on a weak acid is the single most common pH error, and it is always wrong in the same direction, making the solution look more acidic than it is.
Counting significant figures in the wrong part of the number
In a logarithm, only the digits after the decimal point are significant. A pH of 2.00 carries two significant figures, not three. The 2 before the point records the order of magnitude, not a measured digit.
Assuming pH must lie between 0 and 14
It need not. Concentrated strong acids can give a negative pH and concentrated bases can exceed 14. The familiar range simply covers the dilute aqueous solutions met in most teaching laboratories.
Ignoring temperature
The relationship that pH plus pOH equals 14 holds at 25 degrees Celsius because that is where the ion product of water has the value used. At 50 degrees Celsius the sum is closer to 13.3, and neutral water has a pH below 7 while remaining exactly neutral.
Frequently asked questions
Can pH be negative or greater than 14?
Yes. A 10 molar solution of a strong acid has a hydrogen ion concentration well above 1 molar, which gives a negative pH. The 0 to 14 scale is a convention that covers ordinary dilute solutions, not a physical limit.
Why does neutral water have pH 7?
Because at 25 degrees Celsius the ion product of water is 1.0 times ten to the minus fourteen, so in pure water both the hydrogen and hydroxide concentrations are ten to the minus seven molar. Neutrality means those two concentrations are equal, and it happens to fall at 7 only at that temperature.
How do I handle a weak acid?
You need the acid dissociation constant, Ka, and must solve an equilibrium expression rather than take a direct logarithm. For a weak acid of concentration c, the hydrogen ion concentration is approximately the square root of Ka times c, provided dissociation is small relative to c.
What is the difference between pH and pOH?
They are two ways of describing the same solution. pH measures hydrogen ion concentration and pOH measures hydroxide ion concentration, and at 25 degrees Celsius they always add to 14. Which one you use is usually a matter of whether the problem is framed around an acid or a base.