pH Calculator
Convert between pH, pOH, [H⁺] and [OH⁻], or find the pH of a strong acid or base, or of a weak acid or base from its Ka or Kb. Weak solutions are solved exactly and compared with the quadratic and the √(K·C) shortcut, so you can see when the 5 % rule holds. All values are at 25 °C. Runs entirely in your browser. Free, no sign-up.
Scientific notation works: 2.5e-4 or 2.5 × 10^-4.
Results
3.60
pH
10.40
pOH
2.5 × 10⁻⁴
[H⁺] (mol/L)
4.0 × 10⁻¹¹
[OH⁻] (mol/L)
This solution is acidic: pH below 7 at 25 °C.
All values are at 25 °C, where Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ and pH + pOH = 14.00. Kw changes with temperature, and so does neutral pH.
pH and pOH are shown with as many decimal places as the concentration has significant figures, the usual convention.
The working
pH = −log₁₀[H⁺] = −log₁₀(2.5e-4) = 3.60
pH + pOH = 14.00, so pH = 3.60 and pOH = 10.40
[H⁺] × [OH⁻] = 1.0 × 10⁻¹⁴
How to Use the pH Calculator
- 1. Choose the job. Convert turns any one of pH, pOH, [H⁺] or [OH⁻] into the other three. Strong acid or base handles fully dissociated solutes. Weak acid or base uses a Ka or Kb.
- 2. Enter what you know. Concentrations are in mol/L and accept scientific notation such as 2.5e-4. For a weak solute, pick it from the list or type its Ka, Kb or pK.
- 3. Read the four values. pH, pOH, [H⁺] and [OH⁻] appear together with a note on whether the solution is acidic, neutral or basic.
- 4. Follow the working. Each result comes with the formulas and numbers behind it; weak solutions also show three methods side by side.
The Definitions
pH
pH = −log₁₀[H⁺]
pOH
pOH = −log₁₀[OH⁻]
Water
Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25 °C
Sum
pH + pOH = 14.00
The value 1.0 × 10⁻¹⁴ is the textbook ion product of water at 25 °C. It rises with temperature, so pure water is neutral at pH 7.00 only at 25 °C; at other temperatures the neutral point moves, and so does the pH + pOH total. Everything in this calculator assumes 25 °C and uses concentrations in place of activities, which is the standard general-chemistry treatment.
| Solution | pH at 25 °C |
|---|---|
| Acidic | Less than 7 |
| Neutral | Exactly 7 |
| Basic | Greater than 7 |
Strong Acids and Bases
A strong acid or base dissociates completely, so the ion concentration is the solute concentration times the number of ions per formula unit. For 0.050 M HCl, [H⁺] = 0.050 M and pH = 1.30. For 0.0050 M Ca(OH)₂, which gives two hydroxide ions, [OH⁻] = 0.010 M, so pOH = 2.00 and pH = 12.00. Sulfuric acid is strong only for its first proton, so do not enter 2 for it.
Very dilute strong acids
A 1.0 × 10⁻⁸ M solution of HCl is not basic. Water supplies about 10⁻⁷ M of H⁺ on its own, and the exact calculation, which includes it, gives pH 6.98. Naively taking −log(10⁻⁸) gives 8.00, which would make an acid a base. The calculator warns when water matters (below about 10⁻⁶ M).
Weak Acids and Bases: the Quadratic and the 5 % Rule
A weak acid HA only partly ionises, so Ka = x² ÷ (C − x), where x is the [H⁺] produced and C the starting concentration. Rearranged, x² + Ka·x − Ka·C = 0, whose positive root is x = (−Ka + √(Ka² + 4·Ka·C)) ÷ 2. A weak base works the same way with Kb and [OH⁻].
When x is small beside C, C − x ≈ C and the equation shortens to x ≈ √(Ka·C). The 5 % rule says that shortcut is acceptable when the x it gives is below 5 % of C. For 0.100 M acetic acid (Ka = 1.8 × 10⁻⁵) the quadratic gives x = 1.33 × 10⁻³ M, so pH 2.88 with 1.3 % ionised; the shortcut gives 2.87, and passes. For 0.0010 M hydrofluoric acid (Ka = 6.4 × 10⁻⁴) the quadratic gives pH 3.27, the shortcut gives 3.10, and the shortcut value of x is 80 % of C, so it fails.
The "exact" row in the table goes one step further than the textbook quadratic by also counting water's ions. It matters only for extremely dilute or very weak solutions. Ka and Kb values are from OpenStax Chemistry 2e, Appendices H and I, at 25 °C.
Frequently Asked Questions
- How do you calculate pH from the hydrogen ion concentration?
- Take the negative base-10 logarithm of [H⁺] in mol/L. For [H⁺] = 2.5 × 10⁻⁴ M, pH = −log(2.5 × 10⁻⁴) = 3.60. The calculator gives the pOH (10.40) and [OH⁻] (4.0 × 10⁻¹¹ M) at the same time.
- How do you find the pH of a weak acid?
- Write Ka = x² ÷ (C − x), solve for x with the quadratic formula, then take pH = −log x. If x comes out under 5 % of C you can use x ≈ √(Ka·C) instead. The calculator shows the exact, quadratic and shortcut answers together.
- What is the 5 % rule in equilibrium problems?
- It is a test for whether you may treat the starting concentration as unchanged. If the x you get by ignoring it is less than 5 % of that concentration, the error is small enough that the shortcut stands. If not, solve the quadratic instead.
- How do you convert pOH to pH?
- Subtract from 14.00: pH = 14.00 − pOH, valid at 25 °C. A pOH of 3.20 means pH 10.80. For a base you usually find [OH⁻] first, then pOH, then pH.
- Can pH be negative or above 14?
- Yes. A 2.0 M strong acid has a calculated pH of −0.30, and a 2.0 M strong base 14.30. In concentrated solutions the activities differ noticeably from the concentrations, so measured values can differ from the calculated ones.
- How many decimal places should a pH have?
- As many as the concentration has significant figures. A concentration of 2.5 × 10⁻⁴ M has two, so write pH 3.60, with two decimal places. The digits before the decimal point only locate the power of ten, so they are not counted.