pH Calculator
Convert molarity to pH, calculate from mass & volume, mix two solutions, dilute — with full step-by-step working for every calculation.
pH Calculation Report
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pH Calculator — Complete Guide
This free pH calculator computes the pH, pOH, hydrogen ion concentration [H⁺], and hydroxide ion concentration [OH⁻] for any acid or base. Enter molarity directly, or work from mass and volume — the calculator handles strong acids, strong bases, and weak acids/bases with Ka and Kb equilibrium.
How to Use the pH Calculator
- Open the dropdown "I want to calculate the pH from…" and choose your input type.
- Concentration of an acid/base — select the substance, enter concentration and unit (M, mM, μM…), then click Calculate pH.
- Mass and volume of an acid/base — select the substance, enter the mass (with unit: g, mg, μg, kg) and the volume of solution (L, mL, μL). The calculator converts mass → moles → molarity → pH automatically.
- [H⁺], [OH⁻], or pOH — choose what you know from the sub-dropdown, type the value, and get all other quantities instantly.
- Two solutions mixer — enter pH and volume for each solution; the calculator works out excess H⁺ or OH⁻ after neutralisation.
- Dilution — enter initial pH and volume, then final volume; new pH is found by diluting [H⁺] with M₁V₁ = M₂V₂.
- Read the step-by-step working below the result to understand every formula used.
- Download as PDF, share, or print for lab reports.
Tip for mass/volume mode: Make sure you select the correct unit for both mass and volume. For example, if you dissolve 3.65 g of HCl in 1000 mL of water, set mass = 3.65 g and volume = 1000 mL. The calculator will compute molarity = 0.1 M, then pH = 1.00.
The pH Scale
The pH scale is a dimensionless number that runs from 0 to 14 (and technically beyond, for very concentrated solutions). It was introduced by Danish chemist Søren Peder Lauritz Sørensen in 1909 at the Carlsberg Laboratory.
| pH Range | Classification | Examples | [H⁺] (M) |
|---|---|---|---|
| 0 – 2 | Strongly Acidic | Battery acid, gastric acid | 1 – 0.01 |
| 2 – 5 | Weakly Acidic | Lemon juice, vinegar, coffee | 0.01 – 10⁻⁵ |
| 5 – 7 | Mildly Acidic | Rainwater, milk, urine | 10⁻⁵ – 10⁻⁷ |
| 7 | Neutral | Pure water at 25°C | 10⁻⁷ |
| 7 – 9 | Mildly Basic | Blood (7.4), seawater, eggs | 10⁻⁷ – 10⁻⁹ |
| 9 – 12 | Weakly Basic | Baking soda, antacids | 10⁻⁹ – 10⁻¹² |
| 12 – 14 | Strongly Basic | Bleach, drain cleaner, NaOH | 10⁻¹² – 10⁻¹⁴ |
Because the scale is logarithmic, each unit change represents a 10-fold change in [H⁺]. A solution at pH 3 is 10× more acidic than pH 4, and 100× more acidic than pH 5.
Definitions of an Acid and a Base
Three different theories define acids and bases, each useful in different contexts:
1. Arrhenius Definition (1884)
- Acid: A substance that produces H⁺ ions in aqueous solution. Example: HCl → H⁺ + Cl⁻
- Base: A substance that produces OH⁻ ions in aqueous solution. Example: NaOH → Na⁺ + OH⁻
- Limitation: Only works in water.
2. Brønsted–Lowry Definition (1923)
- Acid: A proton (H⁺) donor.
- Base: A proton (H⁺) acceptor.
- Works in non-aqueous solvents. Every acid has a conjugate base, and every base has a conjugate acid.
- Example: NH₃ + H₂O ⇌ NH₄⁺ + OH⁻ (water acts as acid, donating H⁺ to ammonia)
3. Lewis Definition (1923)
- Acid: An electron pair acceptor.
- Base: An electron pair donor.
- Most general definition — includes reactions without any proton transfer at all.
- Example: BF₃ (Lewis acid) + NH₃ (Lewis base) → F₃B–NH₃
For pH calculations in aqueous solutions (like this calculator), the Brønsted–Lowry definition is most commonly used. Strong acids donate 100% of their protons; weak acids donate only a fraction, governed by Ka.
How to Find pH — The pH Formula
The pH formula is one of the most important equations in chemistry. Introduced by Sørensen, it is defined as the negative base-10 logarithm of the hydrogen ion concentration:
And its inverse — to convert pH back to [H⁺]:
Related formulas at 25°C:
pOH = −log₁₀ [OH⁻][OH⁻] = 10−pOHpH + pOH = 14.00 (at 25°C)Kw = [H⁺][OH⁻] = 1.0 × 10−14 (at 25°C)pKw = −log₁₀(Kw) = 14.00 (at 25°C)
When working from mass and volume, first calculate molarity:
How to Calculate pH — Step by Step
Case 1: Strong Acid (e.g. 3.65 g HCl in 1000 mL)
- Molar mass of HCl = 36.46 g/mol
- Moles of HCl = 3.65 ÷ 36.46 = 0.1001 mol
- Volume = 1000 mL = 1.000 L
- Molarity = 0.1001 mol ÷ 1.000 L = 0.1001 M
- HCl is a strong acid → dissociates completely: [H⁺] = 0.1001 M
pH = −log₁₀(0.1001) = 1.00pOH = 14.00 − 1.00 = 13.00[OH⁻] = 10⁻¹³ = 1.0 × 10⁻¹³ M
Case 2: Weak Acid (e.g. 0.1 M Acetic Acid, Ka = 1.8 × 10⁻⁵)
- Equilibrium: CH₃COOH ⇌ H⁺ + CH₃COO⁻
- Ka = [H⁺][CH₃COO⁻] / [CH₃COOH] = x² / (0.1 − x) = 1.8 × 10⁻⁵
- Rearrange to quadratic: x² + (1.8 × 10⁻⁵)x − (1.8 × 10⁻⁶) = 0
- Solve: x = [H⁺] = [−Ka + √(Ka² + 4KaC)] / 2
- [H⁺] = 1.33 × 10⁻³ M
pH = −log₁₀(1.33 × 10⁻³) = 2.88- Degree of dissociation = 1.33 × 10⁻³ / 0.1 = 1.33%
Case 3: Strong Base (e.g. 4.00 g NaOH in 1000 mL)
- Molar mass of NaOH = 40.00 g/mol
- Moles = 4.00 ÷ 40.00 = 0.1 mol
- Volume = 1.000 L → Molarity = 0.1 M
- NaOH is a strong base → [OH⁻] = 0.1 M
pOH = −log₁₀(0.1) = 1.00pH = 14.00 − 1.00 = 13.00[H⁺] = 10⁻¹³ = 1.0 × 10⁻¹³ M
Case 4: Dilution (pH 2.0 HCl diluted 10× )
- Initial [H⁺] = 10⁻² = 0.01 M; initial volume V₁
- Final volume = 10 × V₁ (10× dilution)
- Using M₁V₁ = M₂V₂ on [H⁺]: [H⁺]₂ = 0.01 / 10 = 0.001 M
pH = −log₁₀(0.001) = 3.00— increased by exactly 1 unit- Rule: 10× dilution of a strong acid → pH increases by 1
The Mind Behind the pH Calculator
The concept of pH was invented by Søren Peder Lauritz Sørensen (1868–1939), a Danish biochemist who worked at the Carlsberg Laboratory in Copenhagen. In 1909, while studying the effect of ion concentrations on enzyme activity in brewing, he found it inconvenient to work with very small numbers like 0.000001 M.
Sørensen introduced a logarithmic scale and the notation "p" (from the German Potenz, meaning power) combined with "H" for hydrogen. His original notation used a superscript: pᴴ. The modern notation pH became standard after 1920.
In 1924, Sørensen and his wife Margrethe Høyrup Sørensen revised the pH scale to be based on electrochemical measurements rather than concentrations, producing the modern operational definition still used today by IUPAC.
Fun fact: The "p" in pH stands for the German word Potenz (power). The "H" stands for Hydrogen. So pH literally means "the power of hydrogen" — a logarithmic measure of hydrogen ion activity in solution.
Today, pH is measured using glass electrodes connected to a pH meter, which measures the electrical potential difference between a reference electrode and a measuring electrode immersed in the solution. Indicator strips provide a quick visual estimate using dyes that change colour at specific pH values.