Calculate pH, H+ and OH− from concentration, pOH, or water temperature, and estimate pure water neutral pH using pKw from 0–100 °C.
Related Calculators
- HCl Dilution Calculator
- Buffer Capacity Calculator + Formula
- Molarity Calculator
- mol/L To Percentage Calculator
- All Chemistry Calculators
pH to H⁺ Formula
The calculator uses these core relationships, depending on which mode you select.
pH ↔ H⁺ mode
pOH / OH⁻ mode (at 25 °C)
Pure water mode
- 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. Pure-water mode uses an approximate piecewise linear interpolation in pKw through IAPWS 2024 Table 3 values at 0, 25, 50, 75 and 100 °C. Conditions are liquid water at 0.1 MPa below 100 °C and saturated liquid at 100 °C. This is not the full IAPWS equation; displayed digits do not establish accuracy. Molar concentration estimates use the dilute-water approximation to the molality-based reference equilibrium. Concentrations entered in mmol/L or μmol/L are converted to mol/L before the log is taken.
Choose the quantity to calculate using the Solve for menu. Hydrogen and hydroxide concentrations support mol/L, mmol/L and μmol/L. Pure-water mode estimates neutral pH from temperatures between 0 and 100 °C; neutral pH decreases as water warms.
Reference Tables
Use the first table to spot-check a result. The second table shows the interpolation used for neutral pH. The IAPWS reference knots are 0, 25, 50, 75 and 100 °C; the 10 and 37 °C rows are interpolated examples.
| 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 | 14.95 | 7.475 |
| 10 | 14.566 | 7.283 |
| 25 | 13.99 | 6.995 |
| 37 | 13.6396 | 6.8198 |
| 50 | 13.26 | 6.63 |
| 100 | 12.25 | 6.125 |
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 6.82, even though the water is still neutral.
Can pH be negative or above 14?
Yes. pH is not fundamentally limited to 0–14. The calculator accepts input pH or pOH from -5 to 20 as a numerical range, but concentration estimates in concentrated solutions can be unreliable without activity corrections.
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.
