Learn & Understand

Why Mixing 21% and 15% Doesn't Give You 18%

The gas mixing calculator finds the concentration that results when two gas streams merge, and it insists the answer is a flow-weighted average, not the simple midpoint of the two concentrations. This is a place where intuition reliably misleads: mixing a stream at 21% with one at 15% does not generally give 18%. The result depends on how much of each stream you have. Understanding why reveals the difference between a simple average and a weighted one, a distinction that trips people up far beyond gas mixing.

The Seductive Wrong Answer

Faced with two concentrations, most people instinctively split the difference: halfway between 21% and 15% is 18%, so surely the mixture is 18%. This is correct only in one special case, when you have exactly equal amounts of the two streams. The moment the two flows differ in size, the simple midpoint becomes wrong, because the larger stream contributes more to the mixture and pulls the result toward its own concentration. Intuition assumes equal influence; reality weights by quantity.

The Bigger Stream Has the Bigger Vote

The correct principle is that each stream influences the final concentration in proportion to how much of it there is. A large stream at 15% mixed with a small stream at 21% produces a mixture much closer to 15%, because most of the molecules in the blend came from the larger stream. The concentration is really a vote among all the molecules, and the stream contributing more molecules gets more votes. This is a weighted average: each value weighted by its share of the total.

Why This Matters Beyond Gases

The weighted-average trap is not unique to gases, it appears everywhere quantities of different sizes are combined. A student's overall grade weighted by credit hours, a portfolio's average return weighted by how much is invested in each holding, a population's average weighted by group size: all of them punish the naive midpoint. Wherever the parts being averaged come in different amounts, the simple average is a mistake, and only weighting by quantity gives the truth. Gas mixing is one clean, physical instance of a very general principle.

Why the Calculator Weights by Flow

This is exactly why the calculator multiplies each stream's concentration by its flow rate before combining, and divides by the total flow. It is computing the weighted average correctly, letting each stream's contribution scale with how much of it there is. The formula looks more complicated than "add and halve," but it is the only version that respects reality. When two gas streams merge, the result belongs to whichever stream brought the most gas, and the calculator honors that by weighting, not guessing.

When modeling flue gas recirculation, combine this with the Gas Mixture Molar Mass Calculator; for a blend's heating value, the Gas Mixture Heating Value Calculator.