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pH Calculator: Fast pH, pOH & Concentration Converter

Aniruddh

September 13, 2025

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pH Calculator — instant pH, pOH, [H⁺] and [OH⁻]

This pH calculator lets you move quickly between pH, pOH, hydrogen-ion concentration, and hydroxide-ion concentration. You can calculate pH from molarity for strong or weak acids and bases. You can also convert a known pH back to concentration in a heartbeat. Everything here follows accepted chemistry practice at 25 °C which means the results match classroom problems and most lab situations.

How to use the pH Calculator

Choose the path that matches your data. If you know a concentration then select acid or base and enter the molarity. If you only know mass and solution volume then switch to the mass-and-volume mode. If you already know pH or pOH then pick the direct mode and enter a single value. The calculator fills the rest automatically.

• Concentration mode. Enter solution type then concentration. For weak species add Ka or Kb or use pKa or pKb.
• Mass & volume. Enter solute mass, molar mass, and final solution volume. The tool converts to molarity then computes pH.
• Direct conversions. Enter exactly one of pH, pOH, [H⁺], or [OH⁻]. The others update instantly.
• Reset & export. Use the Reset button to clear inputs. Copy or download CSV from the results panel.

What is pH

pH measures the acidity or basicity of an aqueous solution on a logarithmic scale. It is defined as the negative base-10 logarithm of the hydrogen ion activity. In practice you can use the molar concentration of H⁺ for dilute solutions.

Formal definition from the IUPAC Gold Book: pH = −log₁₀ a_H⁺. At 25 °C pure water undergoes auto-ionization which sets the ionic product K_w ≈ 1.0×10⁻¹⁴. That relationship links pH and pOH since pH + pOH = 14 for dilute aqueous systems at this temperature.

Core formulas & quick conversions

You can get very far with four short equations. These appear in every general chemistry syllabus and they power this pH calculator.

Featured snippet-ready conversions

1. Given pH → [H⁺]: [H⁺] = 10^−pH M
2. Given pOH → [OH⁻]: [OH⁻] = 10^−pOH M
3. Given [H⁺] → pH: pH = −log₁₀[H⁺]
4. Given [OH⁻] → pH: pH = 14 − (−log₁₀[OH⁻])

Strong vs weak acids and bases

Strong acids and strong bases dissociate almost completely in water. Weak species dissociate partially which means equilibrium matters. The calculator handles both cases with the appropriate equations.

Strong acids

For a monoprotic strong acid of concentration C the hydrogen ion concentration is not simply C at very low levels because auto-ionization of water starts to matter. The more robust expression is

[H⁺] = ½ ( C + √(C² + 4K_w) )

This reduces to [H⁺] ≈ C when C ≫ 10⁻⁶ M which covers most practical cases.

Strong bases

Symmetry saves you here. For a strong base of concentration C

[OH⁻] = ½ ( C + √(C² + 4K_w) ) then [H⁺] = K_w / [OH⁻].

Weak acids and weak bases

You have two useful approaches. The square-root approximation works when C is much larger than Ka or Kb. The exact solution uses the mass balance and charge balance relationships and solves a single variable with a safe root-finding method.

The calculator uses the exact method by default which remains accurate when the approximation breaks down. That prevents surprises near the boundaries where Ka and C have similar magnitudes.

Worked examples you can copy

1) pH of a 0.10 M strong acid

Input concentration C = 0.10 M. For a strong acid [H⁺] ≈ C. You get pH ≈ −log₁₀(0.10) = 1.00. The exact expression gives pH = 1.000 because K_w is tiny at this concentration.

2) pH of a weak acid with Ka

Consider benzoic acid where Ka ≈ 6.3×10⁻⁵. For C = 1.0×10⁻³ M the square-root estimate gives [H⁺] ≈ √(6.3×10⁻⁵ × 1.0×10⁻³) = 7.94×10⁻⁴ M so pH ≈ 3.10. The exact solution will match closely because C is much larger than Ka.

3) pH from a mass and volume

Dissolve 0.500 g of acetic acid (M_r ≈ 60.052 g·mol⁻¹) in 250 mL of solution. Moles = 0.500/60.052 = 8.33×10⁻³ mol. Molarity = 8.33×10⁻³/0.250 = 0.0333 M. Use Ka = 1.8×10⁻⁵. The exact weak-acid calculation gives pH ≈ 2.64. The square-root shortcut gives √(1.8×10⁻⁵ × 0.0333) = 7.75×10⁻⁴ so pH ≈ 3.11 which is worse because C is not huge relative to Ka. The exact method wins.

4) Convert pH to [H⁺] and pOH

If pH = 5.00 then [H⁺] = 10⁻⁵ M. pOH = 9.00 at 25 °C because pH + pOH = 14.

Weak acid and weak base methods

The equilibrium model below mirrors what textbooks present. It produces results that hold for dilute aqueous solutions at 25 °C.

Weak acid HA ⇌ H⁺ + A⁻

• Mass balance: C = [HA] + [A⁻]
• Charge balance: [H⁺] = [A⁻] + [OH⁻]
• Autoprotolysis: [H⁺][OH⁻] = K_w
• Equilibrium: K_a = [H⁺][A⁻]/[HA]

Substitute [A⁻] = [H⁺] − [OH⁻] and [HA] = C − ([H⁺] − [OH⁻]). You arrive at a single equation in h = [H⁺]:

F(h) = K_a(C − (h − K_w/h)) − h(h − K_w/h) = 0.

Solve F(h) = 0 over a sensible bracket and you get the physically meaningful root. The calculator uses a safe bisection routine which guarantees convergence when a root is bracketed.

Weak base B + H₂O ⇌ BH⁺ + OH⁻

• Mass balance: C = [B] + [BH⁺]
• Charge balance: [OH⁻] = [BH⁺] + [H⁺]
• Autoprotolysis: [H⁺][OH⁻] = K_w
• Equilibrium: K_b = [BH⁺][OH⁻]/[B]

Replace [BH⁺] with [OH⁻] − [H⁺] and solve for y = [OH⁻]:

G(y) = K_b(C − (y − K_w/y)) − y(y − K_w/y) = 0 then [H⁺] = K_w/y and pH follows.

When the approximation is fine

If C ≥ 100·Ka then [H⁺] ≈ √(Ka·C) gives a quick answer with minimal error. If C ≥ 100·Kb then use √(Kb·C) for bases. You might use this for hand checks then compare with the exact value from the calculator.

Units, significant figures, and rounding

• Units. Use molarity for [H⁺] and [OH⁻] which is moles per liter (M). The calculator supports mM, µM, nM, pM, and fM for convenience.
• Sig figs. The number of digits after the decimal in pH equals the number of significant figures in the hydrogen ion concentration. If [H⁺] = 1.8×10⁻⁵ M then pH = 4.744.
• Rounding. Present at most 6 significant figures for concentrations and 2–3 decimals for pH unless your measurement precision demands more.

Accuracy, temperature, and activity

pH depends on temperature because K_w changes with T. The relationship pH + pOH = 14 holds at 25 °C. At other temperatures the sum shifts slightly. For rigorous work use a temperature-corrected K_w value and apply activity coefficients in concentrated or ionic solutions.

• At 25 °C K_w ≈ 1.0×10⁻¹⁴ (autoprotolysis of water).
• At 37 °C K_w is larger which reduces neutral pH below 7 by a small margin.
• High ionic strength affects activity which shifts the effective concentration.

Helpful constants & typical values

Short answers to common questions

What does a pH value tell you

Values less than 7 indicate acidic solutions. Values equal to 7 indicate a neutral solution at 25 °C. Values greater than 7 indicate basic solutions. The further from 7 the stronger the acidity or basicity.

Can pH be negative

Yes. Very concentrated acids can have pH values below 0 because [H⁺] can exceed 1 M in strong acid media. The calculator reports the correct value when you enter those concentrations.

Does distilled water always have pH 7

Freshly prepared pure water at 25 °C sits at pH 7. Exposure to air dissolves CO₂ which forms carbonic acid and nudges the pH downward. This is normal in open containers.

How is pH measured in the lab

Two common methods are used. Color indicators give a rough range which works for quick checks. Glass electrodes connected to a calibrated pH meter provide accurate values. Calibrate with buffer solutions that bracket your expected pH to keep drift in check. Guides from instrument makers and validated methods from standards bodies cover practical steps in depth.

Further reading

• IUPAC Gold Book — pH definition
• Autoprotolysis of water and K_w
• Acetic acid data (PubChem)
• Henderson–Hasselbalch equation

A reliable pH calculator saves time and reduces mistakes. It converts among pH, pOH, [H⁺], and [OH⁻] in seconds. It also handles strong and weak acids and bases with the right level of chemistry under the hood. Use it for lab prep, class assignments, or quick checks between experiments. Keep temperature and activity in mind when you need high-precision work then verify with a calibrated meter.