pH Calculator – Calculate pH from H⁺ Concentration
Determine the pH of any solution instantly with our pH calculator. Input the hydrogen ion concentration [H⁺] or pH value to convert between them. Great for chemistry students, teachers, and lab professionals.
pH measures how acidic or basic a solution is. The scale runs from 0 to 14. Seven is neutral – pure water sits right in the middle. Below 7 is acidic. Above 7 is basic (alkaline). The "p" stands for power or potential, and "H" is hydrogen. So pH literally means "power of hydrogen."
Here's what makes pH tricky: it's logarithmic, not linear. A pH of 5 isn't twice as acidic as pH 6 – it's ten times more acidic. pH 4 is 100× more acidic than pH 6. This is why small pH changes in your blood (normally 7.35-7.45) can be life-threatening.
The pH Formula
pH = -log₁₀[H⁺]
Where [H⁺] is the hydrogen ion concentration in moles per liter
| pH | Substance | Category | [H⁺] (mol/L) |
|---|---|---|---|
| 0 | Battery Acid | Strong Acid | 1.0e+0 |
| 1 | Stomach Acid | Strong Acid | 1.0e-1 |
| 2 | Lemon Juice | Acid | 1.0e-2 |
| 3 | Vinegar | Acid | 1.0e-3 |
| 4 | Tomato Juice | Acid | 1.0e-4 |
| 5 | Black Coffee | Weak Acid | 1.0e-5 |
| 6 | Urine/Milk | Slightly Acidic | 1.0e-6 |
| 7 | Pure Water | Neutral | 1.0e-7 |
| 8 | Sea Water | Slightly Basic | 1.0e-8 |
| 9 | Baking Soda | Weak Base | 1.0e-9 |
| 10 | Milk of Magnesia | Base | 1.0e-10 |
| 11 | Ammonia | Base | 1.0e-11 |
| 12 | Soapy Water | Strong Base | 1.0e-12 |
| 13 | Bleach | Strong Base | 1.0e-13 |
| 14 | Drain Cleaner | Strong Base | 1.0e-14 |
| Body Fluid | Normal pH Range | Function |
|---|---|---|
| Blood | 7.35-7.45 | Oxygen transport, enzyme function |
| Stomach Acid | 1.5-3.5 | Protein digestion, pathogen destruction |
| Saliva | 6.2-7.6 | Initial digestion, tooth protection |
| Urine | 4.5-8.0 | Waste excretion, pH balance |
| Pancreatic Juice | 7.5-8.8 | Neutralizes stomach acid in intestines |
| Cerebrospinal Fluid | 7.3-7.4 | Brain/spinal cord protection |
Blood pH outside 7.35-7.45 causes acidosis or alkalosis – both potentially fatal. Your body tightly regulates this through breathing and kidney function.
Example 1: Strong Acid
Problem: What is the pH of a solution with [H⁺] = 1 × 10⁻³ mol/L?
pH = -log₁₀(1 × 10⁻³) = -(-3) = 3
Answer: pH = 3 (acidic – similar to vinegar or orange juice)
Example 2: Finding [H⁺] from pH
Problem: What is [H⁺] when pH = 8.5?
[H⁺] = 10^(-pH) = 10^(-8.5) = 3.16 × 10⁻⁹ mol/L
Answer: [H⁺] = 3.16 × 10⁻⁹ mol/L (basic – similar to sea water)
Example 3: Neutral Water
Problem: Pure water has [H⁺] = 1 × 10⁻⁷ mol/L. What's the pH?
pH = -log₁₀(1 × 10⁻⁷) = -(-7) = 7
Answer: pH = 7 (neutral)
Can pH be negative or above 14?
Yes, but it's rare. Concentrated acids like 10M HCl have pH = -1. Concentrated bases like 10M NaOH have pH = 15. The 0-14 scale applies to dilute aqueous solutions. Industrial chemicals can exceed these bounds.
Why is pH logarithmic?
Hydrogen ion concentrations vary enormously – from 1 mol/L in strong acids to 10⁻¹⁴ mol/L in strong bases. A logarithmic scale compresses this 14-order-of-magnitude range into manageable 0-14 numbers. It's the same reason we use logarithmic scales for earthquakes (Richter) and sound (decibels).
What's the difference between pH and acidity?
pH measures hydrogen ion concentration. Acidity refers to the total amount of acid present, including both dissociated and undissociated forms. A weak acid solution can have high acidity (lots of acid molecules) but relatively high pH (few H⁺ ions) because the acid doesn't fully dissociate.
How do I measure pH?
Three main methods: pH paper (litmus strips) – cheap but imprecise (±0.5 pH); liquid indicators like phenolphthalein – good for titrations; pH meters – most accurate (±0.01 pH) but require calibration. For precise work, always use a calibrated pH meter.
What happens when pH changes by 1 unit?
A 1-unit pH change means a 10× change in hydrogen ion concentration. Going from pH 7 to pH 6 means 10× more H⁺ ions. From pH 7 to pH 5 means 100× more. This is why ocean acidification – a drop from 8.2 to 8.1 – represents a 26% increase in acidity and threatens marine ecosystems.
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