Alligation Calculator

Alligation is a compact method for finding how much of two ingredients with different strengths must be combined to reach a concentration between them. It is widely used in pharmacy compounding, laboratory solution preparation, food production, beverage blending, and any process where two known concentrations create one target concentration. This calculator implements alligation alternate, the form used to determine a mixing ratio. It does not change units, so all three concentration values must use the same basis, such as percent by mass, percent by volume, grams per liter, or milligrams per milliliter. The calculation starts by subtracting the target concentration from the higher concentration. That difference gives the number of parts of the lower-strength solution. Next, the lower concentration is subtracted from the target. That difference gives the number of parts of the higher-strength solution. Therefore the lower-to-higher mixing ratio is (high minus target) : (target minus low). If a total batch amount is supplied, each side of the ratio is divided by the sum of both parts and multiplied by the total. The two calculated amounts always add back to the requested batch size. For example, mixing a 5 percent solution and a 20 percent solution to obtain 12 percent gives 8 parts of the lower solution and 7 parts of the higher solution. For a 1,000 mL batch, that becomes approximately 533.33 mL and 466.67 mL. A weighted-average check confirms the final strength: the concentration contributed by each portion, divided by total volume, equals 12 percent. The target must lie strictly between the two source concentrations. A target outside that interval cannot be reached by combining only those two materials, while a target equal to one source requires none of the other source. Real mixtures can also change volume or density when combined, so this arithmetic assumes additive quantities and compatible concentration definitions. For regulated pharmacy or analytical work, use appropriately calibrated equipment, account for purity and density where required, and follow the governing preparation procedure. Used with consistent units and realistic inputs, alligation provides a fast, transparent way to plan a two-component blend and independently verify its proportions.