Enter the pH into the Calculator. The calculator will evaluate the H from pH.
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pH to H⁺ Formula
The calculator uses these core relationships, depending on which mode you select.
pH ↔ H⁺ mode
[H+] = 10^(-pH) pH = -log10([H+])
pOH / OH⁻ mode (at 25 °C)
pOH = -log10([OH-]) pH = 14 - pOH
Pure water mode
pH = pKw / 2 pKw ≈ 4471/T + 0.01706*T - 6.0875
- pH: negative base-10 log of hydrogen ion activity
- [H+]: hydrogen ion concentration in mol/L
- pOH: negative base-10 log of hydroxide ion activity
- [OH-]: hydroxide ion concentration in mol/L
- Kw: ion product of water; pKw = -log10(Kw)
- T: absolute temperature in kelvin (K = °C + 273.15)
Assumptions: dilute aqueous solution, activity treated as equal to molar concentration, and pKw = 14.00 unless you use the pure water mode. The empirical pKw formula is valid from 0 °C to 100 °C. Concentrations entered in mmol/L or μmol/L are converted to mol/L before the log is taken.
The first tab takes either pH or [H+] and returns the other using the log relation. The second tab takes pOH or [OH-], converts to pH using pH + pOH = 14, and back-calculates [H+]. The third tab estimates the neutral pH of pure water at any temperature you enter, since pKw drops as water warms and neutral pH falls below 7.
Reference Tables
Use the first table to spot-check a result. The second table shows how neutral pH changes with temperature.
| pH | [H+] mol/L | [OH-] mol/L | Example |
|---|---|---|---|
| 0 | 1.0 | 1.0 × 10⁻¹⁴ | 1 M HCl |
| 2 | 1.0 × 10⁻² | 1.0 × 10⁻¹² | Lemon juice |
| 4 | 1.0 × 10⁻⁴ | 1.0 × 10⁻¹⁰ | Tomato juice |
| 7 | 1.0 × 10⁻⁷ | 1.0 × 10⁻⁷ | Pure water (25 °C) |
| 8.1 | 7.9 × 10⁻⁹ | 1.3 × 10⁻⁶ | Seawater |
| 10 | 1.0 × 10⁻¹⁰ | 1.0 × 10⁻⁴ | Milk of magnesia |
| 13 | 1.0 × 10⁻¹³ | 0.10 | Bleach |
| Temp (°C) | pKw | Neutral pH |
|---|---|---|
| 0 | 14.94 | 7.47 |
| 10 | 14.53 | 7.27 |
| 25 | 14.00 | 7.00 |
| 37 | 13.62 | 6.81 |
| 50 | 13.26 | 6.63 |
| 100 | 12.26 | 6.13 |
Worked Examples and FAQ
Example 1: pH to [H+]
Given pH = 3.50. [H+] = 10⁻³·⁵⁰ = 3.16 × 10⁻⁴ mol/L. The solution is acidic.
Example 2: [H+] to pH
Given [H+] = 4.5 × 10⁻⁹ mol/L. pH = -log10(4.5 × 10⁻⁹) = 8.35. The solution is basic.
Example 3: From [OH-]
Given [OH-] = 2.0 × 10⁻³ mol/L at 25 °C. pOH = -log10(2.0 × 10⁻³) = 2.70. pH = 14 – 2.70 = 11.30. Then [H+] = 10⁻¹¹·³⁰ = 5.0 × 10⁻¹² mol/L.
Why is neutral pH not always 7?
Neutral means [H+] = [OH-]. That happens at pH = pKw/2. Since Kw rises with temperature, pKw shrinks and neutral pH drops. At body temperature (37 °C), neutral water has a pH near 6.81, even though the water is still neutral.
Can pH be negative or above 14?
Yes. Concentrated strong acids like 12 M HCl have a measured pH below 0, and concentrated bases can exceed 14. The calculator accepts pH values from -5 to 20 to cover these cases, but activity effects make those numbers approximate.
What if I enter [H+] in mmol/L or μmol/L?
The calculator converts to mol/L before taking the log. 1 mmol/L equals 10⁻³ mol/L and 1 μmol/L equals 10⁻⁶ mol/L.
Why use -log10 instead of natural log?
The pH definition is built on base-10 logarithms so that each unit of pH represents a tenfold change in [H+]. A drop from pH 5 to pH 4 means ten times more hydrogen ions.
