Last updated: July 3, 2026
pH Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Quick Answer
The pH calculator converts between pH, pOH, [H⁺], and [OH⁻] for aqueous solutions at 25 °C. It uses pH = −log₁₀[H⁺], [H⁺] = 10^(−pH), pOH = −log₁₀[OH⁻], and pH + pOH = 14. It also estimates pH for strong acids and strong bases by treating their concentrations as [H⁺] or [OH⁻].
pH equals the negative base-ten logarithm of hydrogen ion concentration. At 25 degrees Celsius, pH plus pOH equals 14, so hydroxide concentration can also be converted to pH through pOH.
Key Takeaways
- pH = −log₁₀[H⁺], so each pH unit represents a tenfold concentration change.
- [H⁺] = 10^(−pH) converts a pH reading back to mol/L.
- At 25 °C, pH + pOH = 14 and [H⁺][OH⁻] = 1.0 × 10⁻¹⁴.
- Strong monoprotic acid concentration is approximately [H⁺]; strong monohydroxide base concentration is approximately [OH⁻].
- pH below 7 is acidic, pH 7 is neutral at 25 °C, and pH above 7 is basic.
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
pH = −log₁₀[H⁺]; [H⁺] = 10^(−pH); pOH = −log₁₀[OH⁻]; pH + pOH = 14; [H⁺][OH⁻] = Kw = 1×10⁻¹⁴ at 25 °C
Where:
- pH=Negative log₁₀ of hydrogen-ion concentration(dimensionless)
- [H⁺]=Hydrogen ion concentration(mol/L)
- pOH=Negative log₁₀ of hydroxide-ion concentration(dimensionless)
- [OH⁻]=Hydroxide ion concentration(mol/L)
- Kw=Ion product of water at 25 °C(mol²/L²)
Worked Examples
Neutral water at 25 °C
Pure water has [H⁺] = 1.0 × 10⁻⁷ M and therefore pH 7.00.
- 1Use pH = −log₁₀[H⁺].
- 2Substitute [H⁺] = 1.0 × 10⁻⁷ M.
- 3pH = −log₁₀(1.0 × 10⁻⁷) = 7.00, so the solution is neutral.
Acidic solution from hydrogen ion concentration
A solution with [H⁺] = 1.0 × 10⁻³ M is strongly acidic.
- 1pH = −log₁₀(1.0 × 10⁻³).
- 2The logarithm is −3, so pH = 3.00.
- 3Because pH is below 7, the solution is acidic.
Basic solution from very low [H⁺]
Low hydrogen ion concentration corresponds to high pH.
- 1Apply pH = −log₁₀[H⁺].
- 2pH = −log₁₀(1.0 × 10⁻¹¹) = 11.00.
- 3A pH above 7 is basic.
Strong acid: 0.01 M HCl
For monoprotic strong HCl, [H⁺] is approximately the acid concentration.
- 1Assume complete dissociation: HCl → H⁺ + Cl⁻.
- 2[H⁺] ≈ 0.010 M.
- 3pH = −log₁₀(0.010) = 2.00.
Strong base: 0.001 M NaOH
For NaOH, [OH⁻] is approximately the base concentration; pOH converts to pH.
- 1Assume complete dissociation: NaOH → Na⁺ + OH⁻.
- 2pOH = −log₁₀(0.001) = 3.00.
- 3At 25 °C, pH = 14 − pOH = 11.00.
Hydrogen ion concentration from pH 4
Invert the pH definition to convert pH back to molar [H⁺].
- 1Use [H⁺] = 10^(−pH).
- 2Substitute pH = 4.00.
- 3[H⁺] = 10⁻⁴ M, while the primary pH output remains 4.00.
Introduction
The pH calculator converts among pH, pOH, hydrogen ion concentration [H⁺], and hydroxide ion concentration [OH⁻] for aqueous solutions at 25 °C. It covers the core logarithmic definitions used in general chemistry and analytical chemistry: pH = −log₁₀[H⁺], pOH = −log₁₀[OH⁻], pH + pOH = 14, and [H⁺][OH⁻] = Kw = 1.0 × 10⁻¹⁴. Use it for direct pH conversions, quick strong acid or strong base estimates, and checking whether a solution is acidic, neutral, or basic.
What pH means
pH is the negative base-10 logarithm of hydrogen ion activity. In routine dilute aqueous calculations, concentration [H⁺] in mol/L is used as a close approximation: pH = −log₁₀[H⁺]. A one-unit change in pH means a tenfold change in hydrogen ion concentration. For example, pH 3 has ten times more [H⁺] than pH 4 and ten thousand times more [H⁺] than pH 7.
pH < 7 is acidic at 25 °C.
pH = 7 is neutral when [H⁺] = [OH⁻] = 1.0 × 10⁻⁷ M.
pH > 7 is basic because [OH⁻] exceeds [H⁺].
For weak-acid equilibrium constants, use the pKa calculator.
Converting pH back to [H⁺]
The inverse relation is [H⁺] = 10^(−pH). This is useful when a pH meter gives a number but you need a molar concentration for equilibrium or dilution work. At pH 4.00, H⁺] = 1.0 × 10⁻⁴ M; at pH 9.00, [H⁺] = 1.0 × 10⁻⁹ M. When preparing solutions from stocks, pair this conversion with the [concentration calculator.
Use scientific notation for very small concentrations; writing 1e-7 is equivalent to 1 × 10⁻⁷.
pOH, hydroxide, and Kw
Water autoionizes, so hydrogen and hydroxide concentrations are linked by [H⁺][OH⁻] = Kw. At 25 °C, Kw = 1.0 × 10⁻¹⁴ and therefore pH + pOH = 14. If [OH⁻] = 1.0 × 10⁻³ M, pOH = 3.00 and pH = 11.00. The value 14 is temperature-specific; at other temperatures pKw changes.
The formal IUPAC definition of pH uses activity rather than raw concentration; dilute educational calculations usually use concentration.
Strong acid and strong base estimates
For a fully dissociated monoprotic strong acid such as HCl, H⁺] is approximately the acid concentration, so 0.010 M HCl gives pH 2.00. For a strong base such as NaOH, [OH⁻] is approximately the base concentration, so 0.001 M NaOH gives pOH 3.00 and pH 11.00. For stoichiometric setup or dilution before calculating pH, use the [molarity calculator.
HCl, HBr, HI, HNO₃, and HClO₄ are treated as strong monoprotic acids in water.
NaOH and KOH contribute one mole of OH⁻ per mole of base.
Ca(OH)₂ can contribute up to two moles of OH⁻ per mole if fully dissolved.
Very dilute strong acids and bases require including water autoionization for high precision.
How this differs from buffer and pKa tools
This calculator is for direct pH/pOH concentration conversions and strong acid/base estimates. It does not apply the Henderson–Hasselbalch equation or solve weak-acid equilibria. If a solution contains a weak acid and its conjugate base, use the buffer pH calculator. If you need acid strength from Ka or pKa, use the pKa tool instead. Authoritative definitions are available in the IUPAC Gold Book.
Common pH reference values
The table below gives approximate values at room temperature. Real samples vary with composition, temperature, ionic strength, and calibration method. Reference discussions from LibreTexts and NIST are helpful for measurement practice.
| Solution | Approximate pH | Interpretation |
|---|---|---|
| 0.01 M HCl | 2.00 | Acidic |
| Black coffee | 5 | Acidic |
| Pure water at 25 °C | 7.00 | Neutral |
| Seawater | 8.1 | Basic |
| 0.001 M NaOH | 11.00 | Basic |
Measurement assumptions and practical tips
Calculated pH assumes ideal dilute behavior, complete dissociation for strong electrolytes, and 25 °C water. A laboratory pH meter measures electrode potential and must be calibrated with standard buffers that bracket the expected sample pH. Ionic strength, temperature compensation, junction potentials, and activity coefficients can all matter in careful analytical work such as electrochemistry with the Nernst equation calculator.
Quick Reference Card
pH — Quick Reference
Quick reference • pH Calculator
pH = −log₁₀[H⁺]; [H⁺] = 10^(−pH); pOH = −log₁₀[OH⁻]; pH + pOH = 14Valid range: Common aqueous pH range is 0–14 at 25 °C, though concentrated solutions can fall outside this range.
Common Values
⚠ Watch Out
- •The relation pH + pOH = 14 assumes water at 25 °C.
- •Strong acid/base concentration equals [H⁺] or [OH⁻] only when dissociation and stoichiometry are appropriate.
- •Weak acids, weak bases, and buffers need equilibrium equations, not direct concentration substitution.
- •At high ionic strength, activity corrections can shift measured pH.
- •Very dilute strong acids and bases may require including water autoionization.
Pro Tips
- →Enter scientific notation such as 1e-7 for small ion concentrations.
- →For base solutions, calculate pOH first, then subtract from 14 at 25 °C.
- →Calibrate pH meters with two or more buffers bracketing the expected pH.
- →Check whether the solute releases one or multiple H⁺ or OH⁻ ions per formula unit.
- →Keep temperature consistent when comparing calculated and measured pH values.
FAQs
How do I calculate pH from hydrogen ion concentration?
Use pH = −log₁₀[H⁺]. For [H⁺] = 1.0 × 10⁻³ M, log₁₀ is −3, so pH = 3.00.
How do I calculate [H⁺] from pH?
Use the inverse relation [H⁺] = 10^(−pH). For pH 4.00, [H⁺] = 1.0 × 10⁻⁴ M.
What is the relation between pH and pOH?
At 25 °C in water, pH + pOH = 14. Therefore pOH = 14 − pH and pH = 14 − pOH.
Is pH 7 always neutral?
pH 7 is neutral for pure water at 25 °C because Kw = 1.0 × 10⁻¹⁴. At other temperatures neutral pH shifts because Kw changes.
Can I use acid concentration as [H⁺]?
Yes for a fully dissociated monoprotic strong acid such as HCl at ordinary concentrations. Weak acids require equilibrium calculations rather than direct substitution.
Can I use base concentration as [OH⁻]?
Yes for strong bases such as NaOH or KOH that provide one hydroxide ion per formula unit. Then calculate pOH first and convert using pH = 14 − pOH.