Free pH Calculator
This pH calculator converts between pH and the hydrogen ion concentration [H+] of an aqueous solution, and also reports the matching pOH and hydroxide ion concentration [OH-]. Enter EITHER a pH value OR a hydrogen ion concentration in moles per litre (mol/L), and the calculator fills in the other three quantities for you. It uses the defining relationship pH = -log10[H+] together with [H+] = 10^(-pH), and the 25 °C water relationship pOH = 14 - pH, so you can move freely between concentration and the logarithmic pH scale without doing the logs by hand. The pH scale runs roughly from 0 (very acidic) through 7 (neutral) to 14 (very basic), and every whole-number step represents a tenfold change in [H+].
pH = −log₁₀[H⁺] and [H⁺] = 10^(−pH). pOH = 14 − pH and [OH⁻] = 10^(−pOH), at 25 °C where the water ion product Kw = 1×10⁻¹⁴. Concentrations are in moles per litre (mol/L).
Quick answer
pH is the negative base-10 logarithm of the hydrogen ion concentration: pH = -log10[H+], and conversely [H+] = 10^(-pH), with [H+] in moles per litre (mol/L). At 25 °C the related basic measures are pOH = 14 - pH and [OH-] = 10^(-pOH). For example, a solution with [H+] = 0.01 mol/L has pH = 2, pOH = 12, and [OH-] = 1×10^-12 mol/L.
Formula & method
pH = -log₁₀[H⁺] • [H⁺] = 10^(-pH) • pOH = 14 - pH • [OH⁻] = 10^(-pOH)
- pH — Acidity on the logarithmic pH scale (typically 0-14)
- [H⁺] — Hydrogen (hydronium) ion concentration in mol/L
- pOH — Basicity measure; pH + pOH = 14 at 25 °C
- [OH⁻] — Hydroxide ion concentration in mol/L
Valid for dilute aqueous solutions at 25 °C, where the water ion product Kw = [H⁺][OH⁻] = 1×10⁻¹⁴, so pH + pOH = 14. [H⁺] must be greater than 0.
Examples
- Input
- pH = 7
- Result
- [H⁺] = 1×10⁻⁷ mol/L, pOH = 7, [OH⁻] = 1×10⁻⁷ mol/L
- Why
- From [H⁺] = 10^(-pH) = 10^(-7) = 1×10⁻⁷ mol/L. Then pOH = 14 - 7 = 7, so [OH⁻] = 10^(-7) = 1×10⁻⁷ mol/L. Equal hydrogen and hydroxide concentrations are exactly what 'neutral' means at 25 °C.
- Input
- [H⁺] = 0.01 mol/L (1×10⁻²)
- Result
- pH = 2, pOH = 12, [OH⁻] = 1×10⁻¹² mol/L
- Why
- pH = -log10(0.01) = -log10(10^(-2)) = 2. Then pOH = 14 - 2 = 12, so [OH⁻] = 10^(-12) = 1×10⁻¹² mol/L. This is roughly the acidity of stomach-strength dilute hydrochloric acid.
- Input
- pH = 3
- Result
- [H⁺] = 1×10⁻³ mol/L (0.001), pOH = 11, [OH⁻] = 1×10⁻¹¹ mol/L
- Why
- [H⁺] = 10^(-3) = 0.001 mol/L. pOH = 14 - 3 = 11, so [OH⁻] = 10^(-11) = 1×10⁻¹¹ mol/L. Note that pH 3 has ten times more H⁺ than pH 4 and a hundred times more than pH 5.
- Input
- [H⁺] = 4.0×10⁻⁹ mol/L
- Result
- pH ≈ 8.40, pOH ≈ 5.60, [OH⁻] ≈ 2.5×10⁻⁶ mol/L
- Why
- pH = -log10(4.0×10⁻⁹) = -(log10 4 - 9) = -(0.602 - 9) = 8.398 ≈ 8.40. Then pOH = 14 - 8.40 = 5.60, and [OH⁻] = 1×10⁻¹⁴ / 4.0×10⁻⁹ = 2.5×10⁻⁶ mol/L, confirming the solution is slightly basic (pH > 7).
When to use this tool
- Converting a measured or known hydrogen ion concentration [H⁺] into a pH value, or going the other way from pH back to [H⁺].
- Finding pOH and the hydroxide concentration [OH⁻] of a solution once you know its pH or [H⁺].
- Checking chemistry homework, lab reports, or titration calculations that involve the pH scale at 25 °C.
- Building intuition for how acidic or basic a solution is, and how big a tenfold (one pH unit) change in concentration really is.
Common mistakes
- Entering [H⁺] in the wrong units. The formula expects concentration in moles per litre (mol/L), not millimoles, grams per litre, or percent. Convert to mol/L first, or the pH will be off by orders of magnitude.
- Using a zero or negative [H⁺]. The logarithm of zero or a negative number is undefined, so [H⁺] must be strictly greater than 0. A truly neutral or basic solution still has a small positive [H⁺] (for example 1×10⁻⁷ at pH 7).
- Forgetting that pH is logarithmic. Each whole pH unit is a tenfold change in [H⁺], so pH 4 is ten times more acidic than pH 5 and one hundred times more acidic than pH 6 — the scale is not linear.
- Assuming pH + pOH = 14 always holds. That relationship is specific to 25 °C, where the water ion product Kw is 1×10⁻¹⁴. At other temperatures Kw changes, so the neutral point and the 14 constant shift slightly.
- Mixing up [H⁺] and pH when reading the result. A small concentration like 1×10⁻⁹ mol/L corresponds to a large pH (about 9), because the minus sign in -log10 flips the order.
Frequently asked questions
What is the formula for pH?
pH is defined as the negative base-10 logarithm of the hydrogen ion concentration: pH = -log10[H+], where [H+] is in moles per litre (mol/L). To reverse it, raise 10 to the negative pH: [H+] = 10^(-pH). For example, [H+] = 0.001 mol/L gives pH = 3, and pH = 3 gives [H+] = 10^(-3) = 0.001 mol/L.
How do I convert [H+] concentration to pH?
Take the base-10 logarithm of the concentration in mol/L and change the sign. So pH = -log10[H+]. If [H+] is 2.5×10⁻⁴ mol/L, then log10(2.5×10⁻⁴) ≈ -3.60, and pH ≈ 3.60. This calculator does the logarithm for you when you choose to enter [H+].
What are pOH and [OH-], and how are they related to pH?
pOH measures basicity the same way pH measures acidity: pOH = -log10[OH-]. At 25 °C the water ion product Kw = [H+][OH-] = 1×10⁻¹⁴, which gives the handy rule pH + pOH = 14. So once you know pH you can get pOH = 14 - pH and then [OH-] = 10^(-pOH).
What does a pH of 7 mean?
A pH of 7 is neutral at 25 °C: the hydrogen ion concentration equals the hydroxide ion concentration, both at 1×10⁻⁷ mol/L. Pure water at room temperature has pH 7. Values below 7 are acidic (more H+), and values above 7 are basic or alkaline (more OH-).
Can pH be negative or above 14?
Yes. The 0-14 range is just the convenient span for everyday dilute solutions. Very concentrated strong acids can have [H+] greater than 1 mol/L, giving a negative pH, and very concentrated strong bases can push pH above 14. The formula pH = -log10[H+] still applies; only the familiar 0-14 bounds are exceeded.
Why is the pH scale logarithmic instead of linear?
Hydrogen ion concentrations in real solutions span an enormous range, from about 1 mol/L down to 10⁻¹⁴ mol/L. A logarithmic scale compresses those many orders of magnitude into a readable 0-14 span. The trade-off is that each whole pH unit represents a tenfold change in [H+], so the difference between pH 2 and pH 5 is a factor of 1000, not 3.
Sources & references
External references open in a new tab. We are independent and not affiliated with these organizations.
- ✓ Free to use
- ✓ No sign-up required
- ✓ Runs entirely in your browser — nothing is uploaded.
- ✓ Formula and method shown above
Provided “as is” for general information only — results may be inaccurate, so verify before you rely on them. No warranty; use at your own risk.
Built and reviewed by HIFreeTools against the formula shown above and any authoritative references cited on this page. See our methodology and editorial standards.
Related tools
- Molarity CalculatorScience & Engineering
- Ideal Gas Law CalculatorScience & Engineering
- Scientific CalculatorScience & Engineering
- Density CalculatorScience & Engineering
- Percentage CalculatorCalculators
Embed this tool on your site
Free to embed, no sign-up. Paste this code where you want the ph calculator to appear: