What is pH and what does the scale measure?

pH stands for 'potential of hydrogen' and measures how acidic or basic a solution is. It is defined as the negative base-10 logarithm of the hydrogen ion concentration: pH = −log₁₀([H⁺]). The scale typically runs from 0 (extremely acidic) to 14 (extremely basic), with 7 being neutral. Because the scale is logarithmic, each whole number change represents a 10-fold change in acidity.

How do you calculate pH from hydrogen ion concentration?

Use the formula pH = −log₁₀([H⁺]), where [H⁺] is the molar concentration of hydrogen ions in mol/L. For example, if [H⁺] = 1 × 10⁻³ M, then pH = −log₁₀(10⁻³) = 3. To reverse the calculation, use [H⁺] = 10^(−pH).

What is the difference between pH and pOH?

pH measures hydrogen ion concentration while pOH measures hydroxide ion concentration. They are related by the equation pH + pOH = pKw, where pKw = 14 at 25°C. So if you know pOH, you can find pH by subtracting from 14. A low pOH indicates a basic solution, while a high pOH indicates an acidic one.

How do you calculate the pH of a weak acid?

For a weak acid with dissociation constant Ka and initial concentration C, set up the equilibrium expression Ka = x²/(C − x), where x = [H⁺]. Rearrange to the quadratic x² + Ka·x − Ka·C = 0, then solve: x = (−Ka + √(Ka² + 4·Ka·C))/2. Finally, pH = −log₁₀(x). This calculator handles this automatically when you select 'Acid Solution' mode.

What is the Henderson-Hasselbalch equation and when do you use it?

The Henderson-Hasselbalch equation is pH = pKa + log₁₀([A⁻]/[HA]), where [A⁻] is the conjugate base concentration and [HA] is the weak acid concentration. It is used to calculate the pH of buffer solutions — mixtures of a weak acid and its conjugate base that resist pH changes. It works best when the ratio [A⁻]/[HA] is between 0.1 and 10.

Does temperature affect pH calculations?

Yes. The ion product of water (Kw = [H⁺]·[OH⁻]) changes with temperature. At 25°C, Kw = 1.0 × 10⁻¹⁴ and neutral pH = 7.0. At 37°C (body temperature), Kw ≈ 2.4 × 10⁻¹⁴ and neutral pH ≈ 6.8. At 60°C, Kw ≈ 9.6 × 10⁻¹⁴ and neutral pH ≈ 6.5. This calculator adjusts Kw for your specified temperature.

How do you calculate pH from pKa and concentration?

Given pKa and concentration C of a weak acid: first convert pKa to Ka using Ka = 10^(−pKa). Then solve the quadratic equation x² + Ka·x − Ka·C = 0 for x = [H⁺], giving x = (−Ka + √(Ka² + 4·Ka·C))/2. Finally, pH = −log₁₀(x). For a quick estimate when Ka ≪ C, you can use pH ≈ ½(pKa − log₁₀(C)), but the full quadratic is more accurate.

pH Calculator

pH of an acid at given concentration

Select Acid

CH₃COOH · pKa = 4.74

Concentration

Temperature (°C)

Affects Kw (water ion product). Default 25°C.

Calculated pH

2.8753

strongly acidic— similar to Cola

pH Scale

Your result mapped against common substances

2.88

024678101214

Similar to Cola

strongly acidic · 10,000× more H⁺ than water

Detailed Results

Ion concentrations at 25°C

pOH

11.1190

[H⁺] Concentration

1.3327e-3mol/L

[OH⁻] Concentration

7.6030e-12mol/L

Kw (Water Ion Product)

1.0132e-14

Step-by-Step Solution

Ka = [H⁺]²/(C − [H⁺])

1Acetic Acid (CH₃COOH) is a weak acid
2Ka = 1.80e-5, pKa = 4.74
3C = 0.1 M
4Solve: x² + Ka·x − Ka·C = 0
5[H⁺] = (−Ka + √(Ka² + 4·Ka·C)) / 2
6[H⁺] = 1.3327e-3 M
7pH = 2.8753

Real-World Context

What your pH result means in practice

A pH of 2.88 is strongly acidic. This is closest in acidity to Cola. Each pH unit lower means 10× more hydrogen ions — so pH 2 is 10,000× more acidic than pure water.

How to Calculate pH

Core formulas for every solution type

pH measures how acidic or basic a solution is on a logarithmic scale. The fundamental relationship is pH = −log₁₀([H⁺]), where [H⁺] is the hydrogen ion concentration in mol/L. This calculator supports six different calculation modes to handle any solution type.

Strong Acid

pH = −log₁₀(C)

Full dissociation

Weak Acid (Ka)

Ka = x² / (C − x)

Equilibrium expression

Strong Base

pH = pKw + log₁₀(C)

Via pOH conversion

Buffer (H-H)

pH = pKa + log₁₀([A⁻]/[HA])

Henderson-Hasselbalch

Example — 0.1 M Acetic Acid (Ka = 1.8 × 10⁻⁵)

Concentration

0.1

CH₃COOH

1.8×10⁻⁵

Dissociation

[H⁺]

1.34×10⁻³

Quadratic soln.

2.87

−log₁₀([H⁺])

What Is pH?

Understanding the hydrogen ion scale

pH (potential of hydrogen) quantifies the acidity or basicity of an aqueous solution. Introduced by Danish chemist S. P. L. Sørensen in 1909, it is defined as the negative logarithm of the hydrogen ion activity. In dilute solutions, activity approximates concentration, giving the practical formula pH = −log₁₀([H⁺]).

Key Relationships

pH = −log₁₀([H⁺])

pOH = −log₁₀([OH⁻])

pH + pOH = pKw = 14.00 (at 25°C)

Kw = [H⁺] × [OH⁻] = 1.0 × 10⁻¹⁴ (at 25°C)

Because the scale is logarithmic, each whole-number pH change represents a 10-fold change in hydrogen ion concentration. A solution at pH 3 has 10× more H⁺ than one at pH 4, and 100× more than pH 5.

pH vs. pOH vs. pKa vs. pKb

Understanding the “p” quantities in acid-base chemistry

Quantity	Formula	Measures	Neutral Value
pH	−log₁₀([H⁺])	Acidity of a solution	7.00 at 25°C
pOH	−log₁₀([OH⁻])	Basicity of a solution	7.00 at 25°C
pKa	−log₁₀(Ka)	Acid strength (lower = stronger)	N/A
pKb	−log₁₀(Kb)	Base strength (lower = stronger)	N/A
pKw	−log₁₀(Kw)	Water ion product	14.00 at 25°C

Temperature & pH

How Kw changes with temperature

The ion product of water (Kw) increases with temperature because the dissociation of water is endothermic. This means neutral pH shifts below 7 at higher temperatures — the water is still neutral, just with more ions.

Temperature	Kw	pKw	Neutral pH
0°C	0.114 × 10⁻¹⁴	14.94	7.47
25°C	1.01 × 10⁻¹⁴	14.00	7.00
37°C	2.42 × 10⁻¹⁴	13.62	6.81
50°C	5.47 × 10⁻¹⁴	13.26	6.63
100°C	51.3 × 10⁻¹⁴	12.29	6.14

pH of Common Substances

Real-world reference values for everyday materials

Battery acid0.5

Stomach acid1.5

Lemon juice2.0

Vinegar2.4

Cola2.5

Orange juice3.5

Tomato juice4.0

Coffee5.0

Milk6.5

Pure water7.0

Blood7.4

Sea water8.1

Baking soda8.3

Milk of magnesia10.5

Ammonia solution11.0

Bleach12.5

Drain cleaner14.0

Common Mistakes to Avoid

Frequent errors in pH calculations

Using pH = −log(C) for weak acids

This shortcut only works for strong acids that fully dissociate. Weak acids like acetic acid require the Ka equilibrium expression and quadratic formula. At 0.1 M, acetic acid has pH 2.87 — not 1.0.

Forgetting temperature effects on Kw

pH + pOH = 14 only holds at 25°C. At body temperature (37°C), pKw ≈ 13.6 and neutral pH is about 6.8 — not 7.0. Always specify or assume a temperature.

Confusing pKa with Ka

pKa = −log₁₀(Ka). A lower pKa means a stronger acid (larger Ka). Hydrochloric acid (pKa ≈ −7) is far stronger than acetic acid (pKa = 4.74). The relationship is inverse.

Assuming pH stays between 0 and 14

Concentrated strong acids can have pH below 0 (e.g., 10 M HCl → pH ≈ −1) and concentrated bases can exceed pH 14. The 0–14 range is practical, not theoretical.

Ignoring polyprotic acid steps

Acids like H₂SO₄ and H₃PO₄ donate multiple protons. The first dissociation may be complete, but subsequent ones have their own Ka values and must be calculated separately.

Using Henderson-Hasselbalch outside its range

The H-H equation gives accurate results only when [A⁻]/[HA] is between 0.1 and 10. Outside this range the approximation breaks down and the full equilibrium must be solved.

Common Acid & Base Reference

Ka, pKa, and classification of frequently used chemicals

Name	Formula	Type	pKa / pKb	pH at 0.1 M
Hydrochloric Acid	HCl	Strong acid	≈ −7	1.00
Sulfuric Acid	H₂SO₄	Strong acid	≈ −3	1.00
Phosphoric Acid	H₃PO₄	Weak acid	2.12	1.62
Acetic Acid	CH₃COOH	Weak acid	4.74	2.87
Carbonic Acid	H₂CO₃	Weak acid	6.37	3.68
Boric Acid	H₃BO₃	Weak acid	9.24	5.12
Ammonia	NH₃	Weak base	4.74	11.13
Sodium Hydroxide	NaOH	Strong base	—	13.00

Frequently Asked Questions

Common questions and detailed answers

Strong acids (like HCl, HNO₃, H₂SO₄) completely dissociate in water, so [H⁺] equals the acid concentration and pH = −log₁₀(C). Weak acids (like acetic acid, citric acid) only partially dissociate, so you must use the Ka equilibrium constant and solve a quadratic equation to find [H⁺]. At the same concentration, a weak acid will always have a higher pH (less acidic) than a strong acid.

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Last updated Apr 9, 2026