pH Calculator
Enter either the hydrogen ion concentration to find the pH, or the pH to find the concentration, using pH = −log₁₀[H⁺]. Two 3D diagrams compare a strongly acidic and a strongly basic solution, and charts show the logarithmic relationship between pH and concentration.
Reviewed by the ToolNestr Editorial Team — July 2026
Acidic vs basic solutions
1. Strongly acidic solution
A dense cloud of H⁺ ions (red) — a low pH means a high concentration of hydrogen ions.
2. Strongly basic solution
A sparse scattering of H⁺ ions (blue-tinted) — a high pH means very few free hydrogen ions remain.
pH graphs
How it works
The core idea in one line: pH compresses an enormous range of hydrogen ion concentrations into a small, manageable number line by taking a logarithm — so a seemingly small pH difference always hides a much larger difference in actual acidity.
pH = −log₁₀[H⁺]
pH from hydrogen ion concentration, [H⁺] in mol/L
[H⁺] = 10^(−pH)
the inverse conversion — concentration from pH
pH + pOH = 14 (at 25°C)
from the ion product of water, Kw = [H⁺][OH⁻] = 1.0×10⁻¹⁴
Because pH is defined as −log₁₀[H⁺], every one-unit decrease in pH corresponds to a tenfold increase in hydrogen ion concentration. Taking 10 to the power of −pH reverses the operation, recovering [H⁺] directly. At 25°C, water's own self-ionization sets [H⁺]=[OH⁻]=1.0×10⁻⁷ M, which is exactly why pH 7 is the neutral midpoint of the scale, and why the ion product Kw=[H⁺][OH⁻]=1.0×10⁻¹⁴ links pH and pOH through pH+pOH=14.
Worked example 1 — pH from a known concentration
Given: A solution has [H⁺] = 2.5 × 10⁻⁴ mol/L. Find the pH and classify the solution.
The corresponding hydroxide concentration is [OH⁻] = 1.0×10⁻¹⁴ / 2.5×10⁻⁴ = 4.0×10⁻¹¹ M, confirming the solution is strongly acidic.
Worked example 2 — concentration from a known pH
Given: A solution is measured at pH = 9.5. Find the hydrogen ion concentration and classify it.
A pH of 9.5 is mildly basic — for comparison, baking soda solution sits around pH 8.3 and household ammonia around pH 11.
The pH of common substances
Each whole-number pH step represents a tenfold change in hydrogen ion concentration — a small pH difference hides a large concentration difference.
| Substance | Approx. pH | Classification |
|---|---|---|
| Battery acid | 0.5 | Strongly acidic |
| Vinegar | 2.5 | Strongly acidic |
| Pure water ★ | 7.0 | Neutral |
| Baking soda solution | 8.3 | Weakly basic |
| Ammonia | 11.5 | Strongly basic |
★ Reference point. Pure water at 25°C has [H⁺] = 1.0×10⁻⁷ M, exactly matching [OH⁻], which is what defines neutral pH.
Where pH actually matters
🌱 Environmental water quality monitoring
Scientists measure the pH of rivers, lakes, and groundwater to detect acid rain effects and track pollution impacts on aquatic ecosystems and drinking water safety.
👩🔬 Buffer preparation in the lab
Lab technicians prepare buffer solutions at specific pH values for experiments and instrument calibration, often using the Henderson-Hasselbalch equation to calculate the needed acid-to-base ratio.
🍎 Food science and preservation
Controlling pH is essential in food preservation, fermentation, and beverage production — canned foods must stay below pH 4.6 to prevent the growth of Clostridium botulinum.
🩺 Blood pH regulation
The human body tightly regulates blood pH within a very narrow range (about 7.35–7.45) — even small deviations outside this range indicate serious medical conditions requiring immediate attention.
Common misconceptions
"A pH of 3 is only slightly more acidic than a pH of 5."
Because pH is logarithmic, a solution at pH 3 is actually 100 times more acidic (has 100× the hydrogen ion concentration) than one at pH 5 — the scale hides how dramatically concentration changes with each pH step.
"For any acid, [H⁺] equals the labeled concentration."
This only holds for strong acids like HCl, which fully dissociate. Weak acids only partially dissociate, so their actual [H⁺] is much lower than the nominal concentration — the full dissociation assumption in this calculator applies only to strong acids and bases.
"pH 7 is always neutral, at any temperature."
pH 7 is only neutral at 25°C — the ion product of water (Kw) changes with temperature, so neutral pH shifts to about 7.47 at 0°C and about 6.51 at 60°C, even though [H⁺] still equals [OH⁻] in each case.
"Negative pH values are impossible."
Extremely concentrated strong acids can actually have pH values below 0 — the pH scale of 0–14 is a common convenient range, not a hard mathematical limit, since pH is simply −log₁₀[H⁺] for any positive concentration.
Formula sources & further reading
The formulas here are standard, traceable to:
- • OpenStax, Chemistry 2e — Chapter 14, "Acid-Base Equilibria" (free, peer-reviewed). openstax.org
- • Brown, LeMay & Bursten, Chemistry: The Central Science — Chapter 16, Acid-Base Equilibria.
- • Zumdahl & Zumdahl, Chemistry — pH and the pH scale.
pH = −log₁₀[H⁺]; [H⁺] = 10^(−pH); pH+pOH=14 at 25°C. Assumes complete dissociation (valid for strong acids/bases). Results are rounded for display.
How to use this calculator
Choose the direction
"pH from [H⁺]" calculates pH from concentration; "[H⁺] from pH" finds concentration from a known pH.
Enter your value
Type the concentration in mol/L (scientific notation supported) or the pH value.
See the classification
The solution is classified from strongly acidic to strongly basic, with a visual pH scale reference.
Related tools
Frequently asked questions
What is pH?
pH is a measure of the acidity or basicity of a solution, defined as the negative logarithm of the hydrogen ion concentration: pH = −log₁₀[H⁺]. A pH of 7 is neutral, below 7 is acidic, above 7 is basic.
What is the pH scale?
The pH scale typically runs from 0 to 14. A strong acid like HCl has pH near 0, pure water is pH 7, and a strong base like NaOH has pH near 14. Each whole-number step represents a tenfold change in [H⁺].
What does pOH mean?
pOH is the negative log of hydroxide concentration [OH⁻]. In water at 25°C, pH + pOH = 14, a relationship that comes from the ion product of water, Kw = [H⁺][OH⁻] = 1.0×10⁻¹⁴.
How do I find the pH of a weak acid?
Weak acids do not fully dissociate. Use the acid dissociation constant Ka and the initial concentration: [H⁺] ≈ √(Ka×C). This calculator assumes complete dissociation, so it is accurate for strong acids and strong bases.
Does temperature affect pH?
Yes — the ion product of water Kw changes with temperature, shifting neutral pH away from exactly 7 (about 7.47 at 0°C, about 6.51 at 60°C). A specific solution's pH also shifts with temperature because dissociation constants themselves vary.