Dosage calculation: the four formulas
Four formula plates stacked vertically, each with its equation in variables only and a leader-lined key defining every symbol, with a selector rail branching to the right.
Formula 1 · Desired over have
Amount to administer = (Desired dose ÷ Dose on hand) × Quantity. Desired dose is what the order asks for. Dose on hand is the strength printed on the label. Quantity is the volume or number of units that strength is contained in. The answer comes out in that same quantity unit.
Formula 2 · Ratio and proportion
Dose on hand : Quantity on hand = Desired dose : Unknown amount. Set the known concentration equal to the unknown as two ratios, then solve the cross product. The units in each position must match before you cross-multiply, or the proportion is meaningless.
Formula 3 · Dimensional analysis
Ordered quantity × conversion factor × conversion factor = answer in the unit asked for. Arrange each factor so that every unit cancels except the one the question wants. Because unit conversion is absorbed into the setup rather than handled beforehand, this is the most defensible method under exam pressure.
Formula 4 · Weight-based dosing
Total dose = Prescribed amount per kilogram × Patient weight in kilograms. Convert pounds to kilograms before the multiplication, never inside it. The result is a dose, which then usually feeds one of the first three formulas to become a volume.
Which one, when
One concentration and one unit throughout: formula 1. Any unit change anywhere in the problem: formula 3. A patient weight in the stem: formula 4 first, then one of the others to get to what you will actually draw up.
The safety check that is not arithmetic
An answer requiring an implausible number of tablets or an implausible volume is a signal to recheck the setup, not to draw it up. Write leading zeros. Never write trailing zeros after a decimal point.
Margin noteset it up so the units cancel and the math gets boring.
Watch outa calculated pediatric dose is verified against the safe dose range before it is given, every time.
Takeawaythe formula is chosen from the shape of the problem, and choosing right is most of the work.
Every worked example → BOOK 06 · P3.