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pH Calculator

Convert between pH, pOH, hydrogen ion concentration and hydroxide ion concentration, or find the pH of a strong acid or base from how much is dissolved.

Level: Grades 10–12

  • Common Core standard HSF.BF.B.5(+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.
Printable worksheet

pH Calculator

Know the answer you need? Pick an input to work backward.

Inputs

Molar concentration. Use e-notation for small values: 2.5e-4 is 2.5 × 10⁻⁴.

Result

pH

3.6021

pH 3.6021 and pOH 10.3979, with [H⁺] = 2.5 × 10⁻⁴ mol/L and [OH⁻] = 4 × 10⁻¹¹ mol/L (acidic).

pOH
10.3979
Hydroxide ion concentration [OH⁻]
4e-11 mol/L4 × 10⁻¹¹ mol/L
The solution is
AcidicCompared with neutral water at 25 °C (pH 7).

See the step-by-step solution ↓

Step-by-step solution

  1. Find pH: take the base-10 logarithm of the hydrogen ion concentration (its power of ten) and flip the sign

    pH=−log₁₀(2.5 × 10⁻⁴)=3.60206

  2. Find pOH: at 25 °C, pH + pOH always equals 14, so subtract pH from 14

    pOH=14−3.60206=10.39794

  3. Find the hydroxide concentration. In water, [H⁺] × [OH⁻] always equals Kw, so divide Kw by [H⁺]

    [OH⁻]=1 × 10⁻¹⁴2.5 × 10⁻⁴=4 × 10⁻¹¹ mol/L

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

What this calculator does

Find the pH of a solution, or turn a pH into the amount of acid it stands for. pH is a short way to write how many hydrogen ions are in a water-based solution. Those amounts are measured in mol/L (moles per litre, a standard count of particles in each litre).

They range hugely, from about 1 mol/L in strong acid down to around 10⁻¹⁴ mol/L in strong base. That's why chemists take the negative logarithm, which turns them into a tidy scale that usually runs from 0 to 14. pOH does the same for hydroxide ions. At 25 °C, pH and pOH always add up to 14.

This calculator links all four quantities. Enter whichever one you know: pH, pOH, [H⁺] or [OH⁻]. The square brackets mean 'the concentration of'. It returns the other three and tells you whether the solution is acidic, neutral or basic. It also finds the pH of a strong acid or strong base from its concentration. That includes very dilute solutions, where the ions from the water itself start to matter.

Where it's used

Why this math matters outside the classroom:

  • Swimming pools. Pool owners keep water near pH 7.4 and know a drop to 6.4 means ten times the hydrogen ion concentration.
  • Garden soil. Gardeners test soil because many vegetables grow best in slightly acidic soil around pH 6 to 7.
  • Strong acids. A 0.01 M solution of hydrochloric acid has [H⁺] = 10⁻² M, so its pH is 2.
  • Aquariums. Aquarium keepers track pH because different fish species are adapted to different ranges of acidity.
  • Using pOH. Students use pH + pOH = 14 at 25 °C, so a solution at pH 9 has a pOH of 5.

Grade level and standards: Grades 10–12; Common Core State Standards for Mathematics HSF.BF.B.5. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. Choose what you know: a concentration, pH, pOH, or the molarity (concentration in mol/L) of a strong acid or base.
  2. Enter the value. You can type small concentrations in e-notation, so 2.5 × 10⁻⁴ mol/L is 2.5e-4.
  3. For a strong acid or base, also enter how many H⁺ or OH⁻ ions each formula unit releases (2 for Ba(OH)₂). A formula unit is one 'piece' of the substance, as its chemical formula shows.
  4. Read pH, pOH and both ion concentrations, with each conversion shown in the working.

What the inputs mean

[H⁺]
The concentration of hydrogen ions in mol/L. Strictly speaking, these are hydronium ions, H₃O⁺.
[OH⁻]
The concentration of hydroxide ions in mol/L.
pH
Most solutions fall between 0 and 14; very concentrated ones can go slightly beyond.
Concentration
The molarity of the acid or base as you made it up. The calculator assumes it dissociates completely, meaning it all breaks apart into ions. That's true only for strong acids and bases.
H⁺ or OH⁻ released per formula unit
Ions released per formula unit. Hydrochloric acid releases one H⁺; calcium hydroxide releases two OH⁻.

Formula and method

pH = −log₁₀[H⁺]        [H⁺] = 10^(−pH)
pOH = −log₁₀[OH⁻]      [OH⁻] = 10^(−pOH)
Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25 °C, so pH + pOH = 14
Strong acid: [H⁺] = n × C (or (C + √(C² + 4Kw)) ÷ 2 when C < 10⁻⁶ mol/L)

[H⁺] is the hydrogen ion concentration and [OH⁻] is the hydroxide ion concentration, both in mol/L. C is the concentration of the acid or base you dissolved, and n is how many ions each formula unit releases. Kw is a fixed number for water, explained below.

The 'p' in pH means 'the negative base-10 logarithm of'. A base-10 logarithm counts powers of ten, so log₁₀(1000) = 3. Each step of one pH unit is a tenfold change in hydrogen ions. So pH 3 has ten times more H⁺ than pH 4, and a thousand times more than pH 6.

Water always splits slightly into H⁺ and OH⁻. Multiply the two concentrations and you get a fixed number at a given temperature, called Kw. This calculator uses Kw = 1.0 × 10⁻¹⁴, its value at 25 °C. That's what makes pH + pOH equal exactly 14.

For a strong acid at ordinary concentrations, the acid supplies nearly all the H⁺. Below about 10⁻⁶ mol/L, water's own 10⁻⁷ mol/L becomes significant. So the calculator solves the charge balance exactly, making sure the positive and negative charges even out. That's why 10⁻⁸ M hydrochloric acid has a pH of about 6.98, not 8. (M is short for mol/L.)

Worked example

A sample has a hydrogen ion concentration of 2.5 × 10⁻⁴ mol/L. What are its pH, pOH and hydroxide concentration?

  1. pH = −log₁₀(2.5 × 10⁻⁴) = 3.6021.
  2. pOH = 14 − 3.6021 = 10.3979.
  3. [OH⁻] = 1.0 × 10⁻¹⁴ ÷ 2.5 × 10⁻⁴ = 4 × 10⁻¹¹ mol/L.

Result: The sample has a pH of 3.6021 and is acidic, with pOH 10.3979 and [OH⁻] = 4 × 10⁻¹¹ mol/L.

Understanding the result

At 25 °C, a solution below pH 7 is acidic, above 7 it's basic, and at 7 it's neutral. The scale counts powers of ten. So a change from pH 5 to pH 3 is a hundredfold increase in acidity, not a small shift.

pH values below 0 or above 14 are possible. A 2 mol/L strong acid has a pH of about −0.3. At such high concentrations, though, the simple formulas become less accurate (see the limitations).

Assumptions and limitations

  • The temperature is 25 °C, where Kw = 1.0 × 10⁻¹⁴. At other temperatures Kw changes, and so does the pH of neutral water.
  • Concentrations stand in for activities, the 'effective' concentrations chemists use. That's a good approximation in dilute solutions.
  • In the strong acid and base modes, the dissolved substance breaks apart completely and releases the number of ions you enter.
  • This tool doesn't handle weak acids or bases, which only partly break apart. For a mix of a weak acid and its conjugate base (the form left after it gives up H⁺), use the Henderson–Hasselbalch calculator.
  • In concentrated solutions (above roughly 0.1 mol/L), real pH readings drift from these ideal values. That's because the ions start to interact with each other.
  • Polyprotic acids, which can give up more than one H⁺, such as sulfuric acid, don't release their second one fully. So entering 2 for them overstates [H⁺].

Frequently asked questions

Why do pH and pOH add up to 14?

Take the negative logarithm of Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴, and you get pH + pOH = 14. The value 14 holds at 25 °C. In warmer water Kw is larger, so the sum is smaller and neutral water has a pH below 7.

Can pH be negative?

Yes. Any hydrogen ion concentration above 1 mol/L gives a negative pH, which happens in concentrated strong acids. The number is real, though measured values at that strength stray from the simple formula.

Why isn't the pH of a very dilute acid above 7?

Adding acid can never make water less acidic. Pure water already holds 1 × 10⁻⁷ mol/L of H⁺. So a tiny amount of acid only nudges the pH a little below 7. The calculator accounts for this automatically below 10⁻⁶ mol/L.

What's the difference between [H⁺] and [H₃O⁺]?

In water, a free hydrogen ion (a proton) attaches to a water molecule to form hydronium, H₃O⁺. Chemists use the two symbols interchangeably for pH, because each hydronium ion stands for one hydrogen ion.

How this calculator is checked

Method: Definitions pH = −log₁₀[H⁺] and pOH = −log₁₀[OH⁻]; ion product of water Kw = 1.0 × 10⁻¹⁴ at 25 °C; exact charge balance [H⁺] = (C + √(C² + 4Kw))/2 for dilute strong acids. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

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