pH Calculator
Example 1
A student prepares a solution of hydrochloric acid with a concentration of 0.010 M. Since HCl is a strong acid that dissociates completely, the pH calculation is straightforward.
Solution
HCl is a strong acid that dissociates completely in water: HCl → H⁺ + Cl⁻. The hydrogen ion concentration equals the acid concentration, so [H⁺] = 0.010 M = 1.0 × 10⁻² M.
The pH is defined as the negative base-10 logarithm of the hydrogen ion concentration:
Applying the formula:
Answer
pH = 2.00
A 0.010 M HCl solution has pH 2.00, which is strongly acidic. For comparison, lemon juice has a pH of about 2.2.
A 0.010 M HCl solution has pH 2.00, which is strongly acidic. For comparison, lemon juice has a pH of about 2.2.
Source: IUPAC Gold Book - pH
Example 2
A biochemist prepares a 0.100 M solution of acetic acid (CH₃COOH) for use as a buffer component. Since acetic acid is a weak acid, the pH must be calculated using the acid dissociation constant.
Solution
Acetic acid is a weak acid with Kₐ = 1.8 × 10⁻⁵. Because Kₐ is much smaller than 1, the hydrogen ion concentration can be approximated using:
Substituting the values:
The pH is then:
Answer
pH = 2.87
A 0.100 M acetic acid solution has a pH of 2.87, which is less acidic than HCl at the same concentration because incomplete dissociation leaves most acetic acid molecules intact.
A 0.100 M acetic acid solution has a pH of 2.87, which is less acidic than HCl at the same concentration because incomplete dissociation leaves most acetic acid molecules intact.
Source: LibreTexts CK-12 Foundation
Example 3
A molecular biologist needs a phosphate buffer at pH 7.4. The buffer contains 0.10 M NaH₂PO₄ and 0.15 M Na₂HPO₄. The pKₐ of the H₂PO₄⁻/HPO₄²⁻ pair is 7.21.
Solution
The buffer contains 0.10 M NaH₂PO₄ (the weak acid, HA) and 0.15 M Na₂HPO₄ (the conjugate base, A⁻), with pKₐ = 7.21 for the H₂PO₄⁻/HPO₄²⁻ pair. The Henderson-Hasselbalch equation gives the pH of a buffer:
Substituting the values:
Answer
pH = 7.39
This buffer is very close to the target of 7.4. The Henderson-Hasselbalch equation shows how the ratio of base to acid determines the pH of a buffer system.
This buffer is very close to the target of 7.4. The Henderson-Hasselbalch equation shows how the ratio of base to acid determines the pH of a buffer system.
Source: IUPAC Gold Book - pH
Example 4
Calculate the pH of a 0.010 M sodium hydroxide (NaOH) solution at 25°C. Verify that the pOH and pH sum to 14.00.
Solution
NaOH is a strong base that dissociates completely: [OH⁻] = 0.010 M.
The pOH is defined as the negative base-10 logarithm of the hydroxide concentration:
Substituting the value:
Using the ion product of water at 25°C, pH and pOH are related by:
Therefore, pH = 14.00 − 2.00 = 12.00 and [H⁺] = 10⁻¹² = 1.0 × 10⁻¹² M. The [H⁺] is 10¹² times smaller than [OH⁻], confirming the solution is strongly basic.
Answer
pH = 12.00, pOH = 2.00
The pH lies well above 7, consistent with a strong base at this concentration. A 0.010 M strong acid (HCl) would give the mirror image: pH = 2.00.
The pH lies well above 7, consistent with a strong base at this concentration. A 0.010 M strong acid (HCl) would give the mirror image: pH = 2.00.
Source: IUPAC Gold Book - pH
Published:
Updated:
References
- [1]IUPAC, IUPAC Gold Book - pH, 2019. https://goldbook.iupac.org/terms/view/P04524
- [2]Pearson, Vogel's Textbook of Quantitative Chemical Analysis, 6th Ed., 2000.
- [3]CRC Press, CRC Handbook of Chemistry and Physics, 105th Ed., 2024.
Glossary
- pH – A logarithmic measure of the acidity or basicity of an aqueous solution, defined as the negative base-10 logarithm of the hydrogen ion concentration: pH = −log₁₀[H⁺]. The pH scale typically ranges from 0 to 14 at 25 °C.
- pOH – The negative base-10 logarithm of the hydroxide ion concentration: pOH = −log₁₀[OH⁻]. In aqueous solution at 25 °C, pH + pOH = 14.00, providing a direct relationship between the two measures.
- Acid – A substance that donates hydrogen ions (H⁺) to a solution, increasing the hydrogen ion concentration and lowering the pH. Strong acids such as HCl dissociate completely, while weak acids such as CH₃COOH dissociate only partially.
- Base – A substance that accepts hydrogen ions or donates hydroxide ions (OH⁻) to a solution, decreasing the hydrogen ion concentration and raising the pH. Strong bases such as NaOH dissociate completely in water.
- Ion product of water (Kw) – The equilibrium constant for the self-ionisation of water, equal to [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25 °C. Kw is temperature-dependent, increasing to approximately 5.5 × 10⁻¹⁴ at 100 °C.
- Hydrogen ion concentration [H⁺] – The molar concentration of hydrogen ions in solution, expressed in mol/L. It is the primary determinant of pH and ranges from > 1 mol/L (strongly acidic) to < 10⁻¹⁴ mol/L (strongly basic).
- Hydroxide ion concentration [OH⁻] – The molar concentration of hydroxide ions in solution, expressed in mol/L. It is inversely related to [H⁺] through the ion product of water Kw.
- Strong acid – An acid that dissociates completely in water, releasing all available hydrogen ions. Common examples are hydrochloric acid (HCl), nitric acid (HNO₃), and sulfuric acid (H₂SO₄). Strong acids have pH values approaching 0 at high concentrations.
- Weak acid – An acid that dissociates only partially in water, establishing an equilibrium between the undissociated acid and its ions. Acetic acid (CH₃COOH) and carbonic acid (H₂CO₃) are common examples with Ka values less than 1.
- Neutralisation – The reaction between an acid and a base to form water and a salt. For a strong acid and strong base, the net ionic equation is H⁺ + OH⁻ → H₂O, and the resulting solution has pH = 7 at 25 °C.
- Buffer solution – A solution that resists changes in pH when small amounts of acid or base are added. Buffers contain a weak acid and its conjugate base (or a weak base and its conjugate acid) in comparable concentrations.
- Acid-base indicator – A substance that changes colour over a specific pH range due to structural changes in its molecule. Phenolphthalein (colourless to pink, pH 8.2–10.0) and bromothymol blue (yellow to blue, pH 6.0–7.6) are commonly used in titrations.
How to Use?
- 1
Select your input type
Choose [H⁺] concentration, [OH⁻] concentration, or direct pOH value from the dropdown. The visible input fields adjust automatically based on your selection.
- 2
Enter the concentration value
For [H⁺] or [OH⁻], type the coefficient (e.g., 1.0) in the first field. Optionally enter the base-10 exponent (e.g., -5 for 10⁻⁵) in the second field. The calculator combines them as coefficient × 10^exponent. You can also enter the full decimal directly and leave the exponent blank.
- 3
Review the calculated results
The results panel displays pH (4 decimal places), pOH, and the solution type: acidic (pH < 7), neutral (pH = 7), or basic (pH > 7). A warning indicator highlights acidic results for quick visual reference.
- 4
Cross-check using a different input mode
Switch the dropdown to another input type and verify that you get the same combined result. For example, if you entered [H⁺] = 1.0 × 10⁻³ and got pH = 3.00, switch to pOH mode and enter 11.00 – you should get pH = 3.00 again. This confirms internal consistency.
- 5
Apply your results in context
Use the calculated pH for buffer preparation, titration analysis, environmental monitoring, or recipe formulation. The calculator assumes 25 °C standard temperature (K<em>w</em> = 1.0 × 10⁻¹⁴). For work at other temperatures, adjust the pH+pOH sum using the known pK<em>w</em> at your temperature.
Frequently Asked Questions
pH stands for "potential of hydrogen." It is defined as the negative base-10 logarithm of the hydrogen ion activity (approximately the concentration in dilute solutions): pH = −log₁₀[H⁺]. A lower pH means higher acidity, a higher pH means higher alkalinity. Each unit change represents a tenfold change in hydrogen ion concentration.
In aqueous solutions at 25 °C, pH + pOH = 14. This relationship comes from the autoionization constant of water: K_w = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴. Taking negative logarithms of both sides gives pH + pOH = pK_w = 14.00. This calculator uses this relationship to convert between pH, pOH, [H⁺], and [OH⁻] in all three input modes.
The relationship pH + pOH = 14 is only valid at 25 °C because K_w is temperature-dependent. At 0 °C, pK_w = 14.95 (neutral pH = 7.47). At 100 °C, pK_w = 12.26 (neutral pH = 6.14). This calculator assumes 25 °C. For accurate pH at other temperatures, you need to use the appropriate pK_w value and adjust the pH + pOH sum accordingly.
Strong acids (HCl, HNO₃, H₂SO₄, HClO₄) dissociate completely in water, so [H₊] equals the acid concentration. Weak acids (acetic acid, citric acid, carbonic acid) dissociate only partially, so [H₊] is much lower than the acid concentration. For example, 0.1 M HCl gives pH = 1.00, while 0.1 M acetic acid (K_a = 1.8 × 10⁻⁵) gives pH = 2.87. This calculator accepts the actual [H₊] you enter, so you must use the correct free ion concentration for your specific acid or base.
The calculator assumes water-based solutions at 25 °C where K_w = 1.0 × 10⁻¹⁴. For non-aqueous solvents or mixed-solvent systems, the ion product constant is entirely different (e.g., for ethanol, the equivalent constant is about 10⁻¹⁹µ), and the conventional pH scale does not apply. For such systems, use non-aqueous pH measurement methods and appropriate reference standards.
Many pH-relevant concentrations are expressed in scientific notation, such as 1.0 × 10⁻⁷ M for pure water. Splitting the input into a coefficient field and an optional exponent field lets you enter values exactly as they appear in textbooks and lab data. You can also enter the full decimal (e.g., 0.0000001) directly in the coefficient field and leave the exponent blank.
Use the Henderson–Hasselbalch equation: pH = pK_a + log([A⁻]/[HA]). For example, a buffer containing 0.1 M acetic acid (pK_a = 4.76) and 0.2 M sodium acetate gives pH = 4.76 + log(0.2/0.1) = 5.06. This calculator works with the final [H₊] concentration. If you know the buffer’s exact [H₊], enter it directly. For preparing buffer stock solutions, use the Stock Solution Calculator.
Calibrate your pH meter daily for routine use and before every critical measurement series. Use at least two buffer solutions bracketing your expected sample pH (typically pH 4.00, 7.00, and 10.00). Replace buffers monthly and always use fresh aliquots to avoid contamination. If you notice slow response or drifting readings, clean the electrode and recalibrate. For high-precision work (< ±0.02 pH), calibrate immediately before each measurement.
Pure water undergoes autoionization: H₂O ⇌ H⁺ + OH⁻. At 25 °C, the equilibrium constant K_w = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴. Since pure water has equal concentrations of H⁺ and OH⁻, [H⁺] = [OH⁻] = 1.0 × 10⁻⁷ M. Taking the negative logarithm: pH = −log(1.0 × 10⁻⁷) = 7.00. Pure water exposed to air absorbs CO₂ and forms carbonic acid, lowering its pH to about 5.5–6.0.
The calculator is most accurate for dilute solutions (below 0.1 M) where activity coefficients are close to 1. For concentrated acids above 1 M, the actual (measured) pH differs from −log[H⁺] because activity coefficients deviate significantly from 1. For example, 10 M HCl has an activity-based pH of about −1.0, but the direct calculation gives −log(10) = −1.0. For concentrated solutions, experimental measurement with a properly calibrated pH meter is recommended.
Normal arterial blood pH is 7.35–7.45, tightly regulated by the bicarbonate buffering system and respiratory control of CO₂ levels. Venous blood pH is slightly lower at 7.31–7.41. Blood pH below 7.35 is acidosis, and above 7.45 is alkalosis. Life-threatening conditions occur when blood pH falls below 6.8 or rises above 7.8. The bicarbonate system (H₂CO₃/HCO₃⁻, pK_a = 6.35) maintains this narrow range through the equilibrium: CO₂ + H₂O ⇌ H₂CO₃ ⇌ H⁺ + HCO₃⁻.
CO₂ dissolves in water to form carbonic acid (H₂CO₃), which dissociates to release H⁺: CO₂ + H₂O ⇌ H₂CO₃ ⇌ H⁺ + HCO₃⁻. This is why open containers of pure water or dilute buffers have pH 5.5–6.0 rather than 7.0. The same process causes ocean acidification: atmospheric CO₂ dissolves in seawater, lowering pH from 8.2 to 8.1 since the Industrial Revolution. In laboratory measurements, minimize sample exposure to air for accurate pH readings of unbuffered solutions.
pH test strips and indicator solutions provide semi-quantitative pH estimates.
Universal indicator changes color across the full pH range (red at pH 0–3, orange/yellow at pH 4–6, green at pH 7, blue at pH 8–10, purple at pH 11–14).
For specific ranges, single indicators are more precise: phenolphthalein (colorless at pH < 8.3, pink at pH > 10.0), bromothymol blue (yellow at pH < 6.0, blue at pH > 7.6).
Litmus paper gives only a binary acid/base classification.
Test strips typically have ±0.5 pH unit accuracy.
Universal indicator changes color across the full pH range (red at pH 0–3, orange/yellow at pH 4–6, green at pH 7, blue at pH 8–10, purple at pH 11–14).
For specific ranges, single indicators are more precise: phenolphthalein (colorless at pH < 8.3, pink at pH > 10.0), bromothymol blue (yellow at pH < 6.0, blue at pH > 7.6).
Litmus paper gives only a binary acid/base classification.
Test strips typically have ±0.5 pH unit accuracy.
The calculator flags results for quick interpretation: a warning indicator appears for acidic solutions (pH < 7), and a neutral or basic result shows an ok indicator. This is a visual helper designed for rapid scanning of results, especially useful when processing multiple samples in a laboratory or educational setting.
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