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pH & pOH Engine

Enter pH, pOH, [H⁺], or [OH⁻] and instantly compute all four acid-base values. Includes a visual pH scale and acidity/basicity classification.

pH Scale

Enter one value — the other three are calculated automatically.

0 (Acid)7 (Neutral)14 (Base)

pH

7
Neutral
pOH7
[H⁺]1.0000 × 10-7 M
[OH⁻]1.0000 × 10-7 M
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What is The pH Scale: Logarithmic Measurement of Acid-Base Chemistry?

pH quantifies the concentration of hydrogen ions ([H⁺]) in a solution using a logarithmic scale from 0 to 14. Because it is logarithmic, each whole number change represents a 10× change in acidity. A solution at pH 3 is 10× more acidic than pH 4, and 100× more acidic than pH 5. The scale centers on 7 (pure water), with values below 7 being acidic and above 7 being basic (alkaline).

Mathematical Foundation

pH Definition
pH=−log⁡10[H+]\text{pH} = -\log_{10}[\text{H}^+]
pH\text{pH}= Power of hydrogen — the negative base-10 logarithm of the hydrogen ion concentration.
[H+][\text{H}^+]= Molar concentration of hydrogen ions (mol/L).
Water Autoionization Constraint
pH+pOH=14(at 25°C)\text{pH} + \text{pOH} = 14 \quad \text{(at 25°C)}
pOH\text{pOH}= The negative log of the hydroxide ion concentration, analogous to pH.
1414= The pKw constant for water at 25°C. This means knowing any one of the four values (pH, pOH, [H⁺], [OH⁻]) instantly determines the other three.

Laws & Principles

  • Logarithmic Scale: Every 1.0 unit change in pH represents a 10× change in [H⁺] concentration. Stomach acid (pH 1) has 1,000,000× more hydrogen ions than pure water (pH 7). This extreme compression is why logarithms are used — molar concentrations span 14 orders of magnitude.
  • The Kw Balance: At 25°C, [H⁺] × [OH⁻] = 1.0 × 10⁻¹⁴ (the ion product of water). This is why pH + pOH always equals 14. Increasing [H⁺] automatically decreases [OH⁻] by the same factor — they are inversely coupled.
  • Temperature Dependence: The pH + pOH = 14 rule is only exact at 25°C. At body temperature (37°C), Kw ≈ 2.4 × 10⁻¹⁴, making neutral pH ≈ 6.8 instead of 7.0. This matters in clinical chemistry and pharmaceutical formulation.

Step-by-Step Example Walkthrough

" A laboratory measures [H⁺] = 3.16 × 10⁻⁵ mol/L in a solution. Determine the complete acid-base profile. "

  1. 1. pH = -log₁₀(3.16 × 10⁻⁵) = -(-4.50) = 4.50.
  2. 2. pOH = 14 - pH = 14 - 4.50 = 9.50.
  3. 3. [OH⁻] = 10⁻⁹·⁵⁰ = 3.16 × 10⁻¹⁰ mol/L.
  4. 4. Classification: pH 4.50 → Acidic (similar to tomato juice or acid rain).
Final Result: From a single [H⁺] measurement, all four values are fully determined: pH = 4.50, pOH = 9.50, [H⁺] = 3.16 × 10⁻⁵ M, [OH⁻] = 3.16 × 10⁻¹⁰ M.

Quick Answer: How does the pH Calculator work?

Enter any one of pH, pOH, [H⁺], or [OH⁻]. Using the relationships pH = -log[H⁺] and pH + pOH = 14, the calculator instantly derives all four values and classifies the solution's acidity.

Mathematical Formulas

pH = -log₁₀[H⁺] | pOH = -log₁₀[OH⁻] | pH + pOH = 14

Where [H⁺] is hydrogen ion concentration in mol/L, and the sum constraint holds at 25°C (standard conditions).

Common Substances pH Reference

Substance pH Classification [H⁺] (mol/L)
Battery Acid~1.0Strong Acid10⁻¹
Orange Juice~3.5Weak Acid3.16 × 10⁻⁴
Pure Water7.0Neutral10⁻⁷
Baking Soda~8.3Weak Base5.0 × 10⁻⁹
Drain Cleaner (NaOH)~14.0Strong Base10⁻¹⁴

Chemistry Use Cases

Water Treatment

Municipal water treatment plants maintain drinking water between pH 6.5 and 8.5 (EPA standard). Water that is too acidic corrodes metal pipes, leaching lead and copper. Water that is too basic causes scale buildup and a bitter taste.

Blood pH Homeostasis

Human blood is tightly regulated between pH 7.35 and 7.45. Dropping below 7.35 (acidosis) or rising above 7.45 (alkalosis) triggers life-threatening symptoms. The body uses bicarbonate buffering, renal excretion, and respiratory CO₂ control to maintain this razor-thin window.

Acid-Base Best Practices (Pro Tips)

Do This

  • ✓Remember pH is logarithmic, not linear. Adjusting pool water from pH 8.0 to 7.0 requires 10× more acid than adjusting from 8.0 to 7.5. Always calculate the actual [H⁺] change needed, not the pH unit difference.

Avoid This

  • ✗Don't average pH values directly. Because pH is logarithmic, averaging pH 3 and pH 5 does NOT give pH 4. You must first convert to [H⁺], average the concentrations, then convert back to pH. The correct average is pH 3.04, not 4.0.

Frequently Asked Questions

Can pH be negative or above 14?

Yes. Concentrated strong acids can have [H⁺] greater than 1 M, giving negative pH values. Concentrated HCl at 10 M has pH ≈ -1. Similarly, very concentrated NaOH can push pH above 14. The 0-14 range is simply the range where [H⁺] falls between 1 and 10⁻¹⁴ mol/L.

Why does pH + pOH = 14?

Water autoionizes: H₂O ⇌ H⁺ + OH⁻. The equilibrium constant Kw = [H⁺][OH⁻] = 10⁻¹⁴ at 25°C. Taking -log of both sides: -log[H⁺] + (-log[OH⁻]) = -log(10⁻¹⁴) = 14. Therefore pH + pOH = pKw = 14.

Is pH 7 always neutral?

Only at 25°C. Neutral means [H⁺] = [OH⁻], which occurs at pH = pKw/2. At 37°C (body temperature), Kw ≈ 2.4 × 10⁻¹⁴, so neutral pH is about 6.8. At 100°C, Kw = 5.5 × 10⁻¹³, making neutral pH ≈ 6.1. The water is not acidic — the definition of neutrality shifts with temperature.

What is the difference between a strong and weak acid?

A strong acid (like HCl) fully dissociates in water — every molecule releases its H⁺ ion. A weak acid (like acetic acid) only partially dissociates — most molecules remain intact. This means 0.1 M HCl has pH = 1.0, but 0.1 M acetic acid has pH ≈ 2.9 despite the same molar concentration.

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Calculation Provenance & Validation Record

Method

Chemical and biological quantitative analysis derived from stoichiometric and thermodynamic formulas.