Ka to pKa Equation: Formula, Conversion & Examples

This calculator converts an acid dissociation constant (Ka) into its corresponding pKa value, or vice versa. You enter either the Ka or the pKa, and the calculator returns the other value using the standard relationship between them. The result is the missing quantity, rounded to a sensible number of decimal places.

Formula

The equation linking Ka and pKa is:

pKa = -log�₀(Ka)

and its inverse:

Ka = 10^(-pKa)

Where:

• Ka is the acid dissociation constant (unitless, typically expressed in mol/L but often reported without units).
• pKa is the negative base-10 logarithm of Ka (unitless).

The pKa scale is a convenient way to express the strength of an acid: the lower the pKa, the stronger the acid. For example, acetic acid has a Ka of about 1.8 × 10��, which gives a pKa of about 4.74.

Worked Example

Using the default values from the calculator above, let’s convert a Ka of 1.8 × 10�� to pKa:

1. Start with the formula: pKa = -log�₀(Ka)
2. Plug in the value: pKa = -log�₀(1.8 × 10��)
3. Calculate the logarithm: log�₀(1.8 × 10��) ≈ -4.7447
4. Apply the negative sign: pKa ≈ 4.7447
5. Rounded to two decimal places: pKa ≈ 4.74

So a Ka of 1.8 × 10�� corresponds to a pKa of 4.74, matching the calculator’s output.

Why pKa Instead of Ka?

Ka values often span many orders of magnitude—from about 10�¹� for very weak acids to 10� for strong acids in water. Working with such numbers directly is cumbersome and error-prone. Taking the negative logarithm compresses this range into a more manageable scale, typically from about -7 to 15 for aqueous acids. This is analogous to the pH scale, which is simply -log�₀[H�]. In fact, pKa is defined in exactly the same way, but for the equilibrium constant of acid dissociation.

Another reason pKa is preferred is that it makes comparisons easier. An acid with pKa 3 is ten times stronger than one with pKa 4, because each unit change in pKa corresponds to a tenfold change in Ka. This logarithmic relationship is intuitive once you get used to it.

How to Use the Calculator

To use the calculator, enter a positive number in either the Ka field or the pKa field. The calculator will automatically compute the other value. If you enter values in both fields, it will use the Ka field and ignore the pKa field (to avoid confusion). If you enter a Ka of 0 or a negative number, the calculator will fall back to converting the pKa you entered, since log of a non-positive number is undefined.

For example:

• Enter Ka = 1.0 × 10â�»â�· → pKa = 7.00
• Enter pKa = 2.00 → Ka = 1.0 × 10â�»Â²
• Enter Ka = 4.5 × 10â�»â�´ → pKa = 3.35

The result is displayed with four decimal places, which is more than enough for most chemical work. You can use scientific notation (like 1.8e-5) in the Ka field.

Common Mistakes and Misconceptions

One frequent error is forgetting the negative sign. The formula is pKa = -log�₀(Ka), not log�₀(Ka). Since Ka is always less than 1 for weak acids, log�₀(Ka) is negative, so pKa ends up positive. If you forget the minus, you’ll get a negative pKa, which would incorrectly suggest a very strong acid.

Another mistake is confusing pKa with pH. They are related but not the same. pH is the -log of the hydrogen ion concentration in a solution, while pKa is a property of a specific acid under defined conditions (usually 25°C in water). The pH of a solution depends on the acid’s concentration and the presence of other species; pKa does not change with concentration.

A third issue is unit handling. Ka has units of concentration (mol/L) in its formal definition, but because it is a ratio of concentrations (products over reactants), the units cancel and Ka is typically reported as dimensionless. When you take the log, the units must cancel, so always use the numerical value without units.

Finally, be careful with significant figures. The number of decimal places in a pKa should match the number of significant figures in the Ka. For example, if Ka = 1.8 × 10�� (two significant figures), the pKa should be reported as 4.74 (two decimal places). The calculator gives four decimals, so you may need to round appropriately for your work.

Limitations and Context

The Ka-to-pKa conversion is straightforward, but the underlying Ka value itself is not universal. Ka depends on temperature, solvent, and ionic strength. Most tabulated values are for dilute aqueous solutions at 25°C. If you are working at a different temperature or in a non-aqueous solvent, the Ka will differ, and so will the pKa.

Also, for polyprotic acids (like phosphoric acid, H₃PO₄), there are multiple Ka values (Ka�, Ka₂, Ka₃), each with its own pKa. Make sure you are using the correct one for the proton transfer you are considering. The calculator works for any single Ka value, but you must know which dissociation step it corresponds to.

For strong acids, Ka is very large (often > 1), and pKa becomes negative. The formula still works, but the concept of pKa is less commonly used for strong acids because they are essentially fully dissociated in water. In such cases, the pKa is more of a theoretical value.

Frequently Asked Questions

What is the difference between Ka and pKa?

Ka is the acid dissociation constant, a measure of how completely an acid donates a proton to water. Larger Ka means a stronger acid. pKa is simply -log�₀(Ka), which converts the often unwieldy Ka values into a more manageable scale. Lower pKa means a stronger acid.

How do I convert pKa to Ka without a calculator?

Use the inverse formula: Ka = 10^(-pKa). For example, if pKa = 4.74, then Ka = 10^(-4.74) ≈ 1.8 × 10��. You can do this with a scientific calculator using the 10^x function (often labeled as “10^x� or “inv log�).

Can pKa be negative?

Yes. If Ka is greater than 1, then -log�₀(Ka) is negative. This happens for very strong acids like hydrochloric acid (Ka ≈ 10�, pKa ≈ -6). In practice, strong acids are often considered to have pKa values below about -1.74 (the pKa of the hydronium ion).

Why is pKa used instead of Ka in biochemistry?

Biochemical systems often involve weak acids and bases with Ka values ranging from 10�² to 10�¹². pKa values (2 to 12) are easier to compare and to relate to physiological pH (around 7.4). For example, the pKa of the amino acid side chain of histidine is about 6.0, which is close to physiological pH, making it an important buffer.

Does the calculator work for bases?

For bases, you can use the same formula if you have the Kb (base dissociation constant) and want pKb. However, to relate pKa and pKb for a conjugate acid-base pair, you need the relationship pKa + pKb = 14 (at 25°C in water). This calculator only converts Ka ↔ pKa, not Kb ↔ pKb.

What if I enter both Ka and pKa?

The calculator prioritizes the Ka field. If both are filled, it uses the Ka to compute pKa and ignores the pKa input. To convert from pKa to Ka, leave the Ka field empty (or set it to 0) and enter the pKa value.

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in ka | Ka value | - | 1.8e-5 | 0
in pka | pKa value | - | 4.74 | 0
out result | Converted value | - | (ka > 0 ? -log10(ka) : pka) | 4