Answer first
What this calculator tells you
Calculate pH and pOH from a hydrogen ion concentration. Read an acid or base concentration on the scale used in labs and pools. Formula: pH = −log₁₀[H⁺]; pOH = 14 − pH at 25 °C, with [H⁺] = a × 10⁻ⁿ mol/L. At the worked-example inputs, the ph is 3.5. Holding every other input steady, moving coefficient (a) from 2.6 to 3.8 moves the result from 3.4 to 3.6.
Transparent method
The formula
Read an acid or base concentration on the scale used in labs and pools.
Worked example
Example inputs
How to interpret the result
The pH scale is a logarithm of hydrogen ion concentration, so each step is a tenfold change. A concentration of 3.2 times ten to the minus four gives a pH near 3.5, and pH 3 is ten times more acidic than pH 4. At room temperature pH and pOH add to 14, which is why the second output mirrors the first around 7.
At the worked-example inputs the ph is 3.5. It rises with exponent (n) and falls as coefficient (a) increases.
These are exact physics and chemistry formulas. Real-world results add tolerances from component quality, temperature and measurement error that this calculator does not model.
Before you rely on it
What to check
Enter the concentration in moles per liter. A value in millimoles or micromoles needs converting first, or the pH lands several units off.
The common error
Where people go wrong with ph value calculator
Reading pH as a linear scale. A drop of one pH unit is ten times the acidity, and a drop of two is a hundred times.
Sensitivity evidence
How coefficient (a) changes the ph
Holding every other input at the worked-example value, moving coefficient (a) from 2.6 to 3.8 moves the ph from 3.4 to 3.6: a spread of 0.165, or 5% of the worked-example result.
| Coefficient (a) | pH | pOH |
|---|---|---|
| 2.6 | 3.6 | 10.4 |
| 2.9 | 3.5 | 10.5 |
| 3.2worked example | 3.5 | 10.5 |
| 3.5 | 3.5 | 10.5 |
| 3.8 | 3.4 | 10.6 |
Every input, tested
Which input moves the ph most
Of the 2 inputs, exponent (n) moves the ph most (2 across the range tested) and coefficient (a) moves it least (0.082).
| Input | Tested from | To | pH at each end | Swing |
|---|---|---|---|---|
| Exponent (n) | 3 | 5 | 2.5 to 4.5 | 2 (57%) |
| Coefficient (a) | 2.9 | 3.5 | 3.5 to 3.5 | 0.082 (2.3%) |
Two variables at once
pH by coefficient (a) and exponent (n)
Across the grid the ph runs from 1.4 to 5.6. Moving coefficient (a) from 2.6 to 3.8 shifts it by 0.165 at the middle column, and moving exponent (n) from 2 to 6 shifts it by 4 at the middle row, so exponent (n) is the bigger lever here.
| Coefficient (a) \ Exponent (n) | 2 | 4 | 6 |
|---|---|---|---|
| 2.6 | 1.6 | 3.6 | 5.6 |
| 2.9 | 1.5 | 3.5 | 5.5 |
| 3.2 | 1.5 | 3.5 | 5.5 |
| 3.5 | 1.5 | 3.5 | 5.5 |
| 3.8 | 1.4 | 3.4 | 5.4 |
The highlighted cell is the worked example: 3.5.
Step by step
The worked example, input by input
| Input | Value used | What it means |
|---|---|---|
| Coefficient (a) | 3.2 | The number in front of the power of ten. |
| Exponent (n) | 4 | Enter 4 for 10⁻⁴. The concentration is a × 10⁻ⁿ mol/L. |
| pH | 3.5 | |
| pOH | 10.5 | |
Inputs, definitions and assumptions
Coefficient (a)
The number in front of the power of ten. The prefilled worked-example value is 3.2.
Exponent (n)
Enter 4 for 10⁻⁴. The concentration is a × 10⁻ⁿ mol/L. The prefilled worked-example value is 4.
How to use this calculator
- 1Verify the inputs. Gather coefficient (a) and exponent (n) from your own documents; the prefilled values are examples.
- 2Save a baseline. The worked example puts the ph at 3.5. Store your own version of it as Scenario A.
- 3Test one change. Start with exponent (n), the input with the biggest effect here: moving exponent (n) from 3 to 5 takes the ph from 2.5 to 4.5, a swing of 57% of the worked-example figure.
- 4Check the extremes. At half the example exponent (n) (2) the ph is 1.5; at double (8) it is 7.5.
People also ask
Frequently asked questions
How do you calculate ph value?
pH = −log₁₀[H⁺]; pOH = 14 − pH at 25 °C, with [H⁺] = a × 10⁻ⁿ mol/L. At the worked-example inputs the ph is 3.5.
What does the ph value result mean?
Read an acid or base concentration on the scale used in labs and pools. At the worked-example inputs the ph is 3.5. It rises with exponent (n) and falls as coefficient (a) increases.
How much does coefficient (a) change the ph?
Holding every other input at the worked-example value, moving coefficient (a) from 2.6 to 3.8 moves the ph from 3.4 to 3.6, a spread of 0.165.
What are the limits of this ph value calculator?
These are exact physics and chemistry formulas. Real-world results add tolerances from component quality, temperature and measurement error that this calculator does not model. The tables on this page test coefficient (a) only from 2.6 to 3.8; a value outside that range is not tabulated here.
Which input moves the ph most in the ph value calculator?
Ranked by how far each moves the ph across the range tested: exponent (n) (2, 57%) and coefficient (a) (0.082, 2.3%).
If I double exponent (n) in the ph value calculator, does the ph double?
Doubling it from 4 to 8 takes the ph from 3.5 to 7.5, which is 2.14 times the worked-example figure. So the result grows faster than the input does. Halving it to 2 gives 1.5.
How much does exponent (n) matter in the ph value calculator?
The worked example uses 4. Holding every other input at its worked-example value, moving exponent (n) from 3 to 5 takes the ph from 2.5 to 4.5, a swing of 57% of the worked-example figure.
Which inputs change the poh in the ph value calculator?
At the worked-example inputs it is 10.5. Coefficient (a) takes it from 10.5 to 10.5 and exponent (n) takes it from 11.5 to 9.5.
What does a voltage divider do?
It uses two resistors in series to drop a voltage to a fraction of the input. It suits signals and sensor inputs, and it is a poor way to power anything because it wastes energy and sags under load.
Why do motors draw more current than their wattage suggests?
A motor's power factor is below 100 percent, so it draws extra current that does no useful work. Starting a motor can also draw several times the running current for a moment.
Sources and evidence
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