Chemistry calculator
pH Calculator
Convert hydrogen ion concentration to pH or pH to concentration, showing pOH at 25 °C.
pH
7
Two modes: concentration to pH or pH to concentration
The calculator operates in two distinct modes, selectable via a dropdown. In the first mode, you enter hydrogen ion concentration [H+] in moles per liter and the tool computes pH using the logarithmic definition. Concentration must be a positive number and may be entered in scientific notation such as 1e-7 or 1.5e-3. The calculator rejects zero or negative concentrations because the logarithm of such values is undefined.
In the second mode, you enter a pH value directly and the calculator solves for the implied hydrogen ion concentration using the inverse function. The pH field accepts values from 0 to 14, a practical range for dilute aqueous solutions at 25 degrees Celsius. The result displays concentration in scientific notation, making it easy to compare very small or large concentrations side by side. Both modes also compute pOH using the relationship pOH = 14 minus pH, which holds at 25 °C and becomes less accurate at other temperatures.
Worked calculation from concentration to pH
Pure water at 25 °C contains hydrogen ions at a concentration of 1 × 10⁻⁷ mol/L (0.0000001 M). Taking the base-10 logarithm of this concentration: log₁₀(1 × 10⁻⁷) = log₁₀(10⁻⁷) = -7. Applying the pH formula, pH = -(-7) = 7. This is neutral pH, the reference point at which [H+] and [OH⁻] are equal in aqueous solution.
Once pH is known, pOH follows immediately: pOH = 14 - 7 = 7. The sum pH plus pOH always equals 14 at 25 °C because the ion product of water, Kw, equals 1 × 10⁻¹⁴ at that temperature. Both pH and pOH measure 7 at neutrality, both increase in basic solution (pOH decreases), and both decrease in acidic solution (pOH increases).
Calculating concentration from pH
Suppose a solution has a measured pH of 3. The hydrogen ion concentration is found by inverting the logarithm: [H+] = 10^−pH = 10⁻³ = 0.001 mol/L or 1.0 × 10⁻³ M. This is the concentration in a solution of a strong acid like hydrochloric acid diluted to pH 3. The calculator displays this in scientific notation as 1.000000 × 10⁻³ M for clarity. Entering pH 3 on the tab also yields pOH = 14 - 3 = 11, confirming that the solution is acidic.
Conversely, a basic solution with pH 11 contains [H+] = 10⁻¹¹ M, which is 1 × 10⁻¹¹ or 0.00000000001 mol/L. The pOH is 14 - 11 = 3, meaning hydroxide ions [OH⁻] are at 10⁻³ M. This inversion between hydrogen and hydroxide ion concentrations across the pH scale reflects the constraint that their product must equal Kw. Strong acids and bases lie at the extremes; mild acids and bases cluster around pH 3 to 5 and pH 9 to 11 respectively.
pH scale examples and practical implications
- Gastric acid (pH 1.5): [H+] ≈ 3 × 10⁻² M, one of the most acidic environments in biology, strong enough to denature dietary proteins and kill many ingested microbes.
- Lemon juice (pH 2): [H+] = 1 × 10⁻² M, acidic enough to taste sour and to corrode calcium in teeth or eggshells over time.
- Pure water (pH 7): [H+] = 1 × 10⁻⁷ M, the neutral midpoint where acidic and basic character balance; real tap water often reads pH 6–7 due to dissolved carbon dioxide.
- Household ammonia (pH 11): [H+] = 1 × 10⁻¹¹ M, basic enough to denature proteins and effective as a cleaning agent, though caustic to skin.
- Alkaline seawater (pH 8.1): [H+] ≈ 8 × 10⁻⁹ M, slightly basic from dissolved carbonate minerals, supporting coral and shellfish development.
Frequently asked questions
What does scientific notation like 1e-7 mean?
1e-7 is shorthand for 1 × 10⁻⁷ = 0.0000001. The exponent tells you how many places to move the decimal point to the left (for negative exponents) or right (for positive exponents).
Why is zero concentration rejected?
Log₁₀(0) is undefined. A concentration of zero would require an infinite pH, which has no physical meaning. The tool requires a strictly positive concentration.
Does pH plus pOH always equal 14?
The sum equals 14 at 25 °C in aqueous solution because the ion product of water (Kw) is 1 × 10⁻¹⁴ at that temperature. At higher or lower temperatures, Kw changes and the sum shifts accordingly.
Can I enter a pH greater than 14?
The calculator rejects pH values outside 0–14 to prevent nonsensical results. Extremely concentrated acidic or basic solutions can fall outside this range in specialized settings, but they are rare in typical chemistry courses.
Does this pH formula work for non-aqueous systems?
No. The formula pH = -log₁₀[H+] and the relationship pH + pOH = 14 apply only to aqueous solutions near 25 °C. In organic solvents, molten salts, or extreme temperatures, the equilibrium and definition of pH change.
Why does a strong acid like HCl at 10 M give a negative pH?
At very high concentrations, [H+] exceeds 1 M, so -log₁₀ of a number greater than 1 is negative. Negative pH is rare but mathematically valid and appears in concentrated industrial solutions.