Desired over have formula: how D/H × Q works in dosage calculations

The desired over have formula is D ÷ H × Q = x, often written D/H × Q.

• D is the dose desired: the dose in the order, with its unit.
• H is the dose on hand: the strength printed on the label, such as the milligrams in one tablet or in a stated volume.
• Q is the quantity that holds the dose on hand: one tablet or capsule, or the volume the label's strength refers to.
• x is the amount to give. It comes out in Q's unit: tablets, capsules or milliliters.

StatPearls counts the formula method, also called desired over have, as one of three primary methods for calculating doses, with dimensional analysis and ratio and proportion. It writes the formula as the desired dose over the amount on hand, times the quantity, equals x. Bergen Community College's module sets out the steps: know the formula, place each value from the problem in its position with its unit, check that the dose ordered and the dose on hand are in the same unit, calculate, then label the answer in the form or unit the drug comes in.

The formula divides one dose by another, so both have to be measured in the same unit before you divide. StatPearls is direct about it: units of measurement must match, or they are converted to like units first. Bergen's module makes the unit check a step of its own before the arithmetic, and Mercer County Community College's guidelines say to convert all items to equal units before working the problem.

The usual case is an order in milligrams against tablets labeled in micrograms. Convert one of the two with 1,000 mcg in 1 mg, then divide. Bergen's module converts the order into the unit on hand, which leaves the label's numbers as printed. The conversion chart lists the factors.

If the conversion is skipped, nothing in the formula warns you. D ÷ H still gives a number, and between milligrams and micrograms it is a thousand times too large or too small.

The formula is one of three ways to write the same arithmetic. Each sets the dose desired against the dose on hand and scales by the quantity; only the notation differs.

StatPearls shows the link with ratio and proportion. Written in colon form as H : V :: D : x, with V for the quantity, multiplying the means and the extremes gives H × x = D × V, and x = D × V ÷ H is the formula. In dimensional analysis, the unit of D cancels against the unit of H, which is the same-unit rule built into the chain.

The worked example in this guide sets one tablet problem out in all three notations, and the line of arithmetic is the same in each; the ratio and proportion guide sets out the proportion in full. StatPearls describes these methods as useful for checking the accuracy of one another, a double or triple check. Mercer County Community College's guidelines state that no method is preferred and any is acceptable if the right answer is reached. Use the notation your program teaches; the dimensional analysis guide compares the three.

For a tablet, Q is one tablet. For a liquid or an injection, H and Q come from the concentration on the label, read as a pair: so many milligrams in so many milliliters. Q is the volume in that pair, and it is not always 1 mL. Bergen's module works one liquid problem from a label strength per 5 mL, with 5 mL as Q.

The second worked example in this guide is a subcutaneous injection from a multidose vial labeled per 5 mL, so Q is 5 mL. Where an answer needs rounding, round once, at the end, under your program's rule; the rounding rules guide compares published rules.

Bergen's module notes that formulas vary with the type of calculation and gives D ÷ H × Q for basic dosage calculations. Three kinds of problem need something else, or a step first.

• A rate from a volume and a time. A volume divided by a time is not a dose desired over a dose on hand, so a pump rate is the volume over the hours, and drops per minute have their own formula, which the IV drip rate guide works through.
• A rate from a dose per hour. An order written as so many milligrams or units per hour does fit: the hourly dose is D, the drug in the bag is H and the bag's volume is Q, and the answer is in milliliters per hour. Bergen's module works an hourly order this way, beside a proportion and a chain.
• A weight-based order. A dose per kilogram is not D yet. Work D out first, the weight in kilograms (pounds ÷ 2.2) times the dose per kilogram, then put it over H. Open RN's multi-step example does the same, converting the weight and multiplying it by the per-kilogram order before setting up the rest.

For critical care drips, Bergen's module suggests dimensional analysis may be the simplest approach, and the formula it gives for those problems is a longer one. The formulas guide lists one formula for each kind of problem.

DoseReady writes each worked solution in the notation your program teaches where the problem allows it. It offers the formula method on 95 of its 180 problems, the ones it fits, and in every one of them the dose desired and the dose on hand are already in the same unit. When an order and a label are in different units, such as milligrams against micrograms, the app shows that problem as a dimensional analysis chain, where the conversion is one more fraction, and does not set the formula out for it; converting the order to the label's unit first and then dividing gives the same answer.

Each of the tablet and capsule practice problems is worked in every notation that fits it, with the answer under a stated rounding rule.

1. 1

   Conversion skipped: The order and the label are in different units and D goes over H as printed. Between milligrams and micrograms the answer is a thousand times off, and the formula gives no warning, so check the units of D and H before you divide.

2. 2

   Conversion factor inverted: H and Q trade places, so the answer is D × H ÷ Q instead of D × Q ÷ H. In the tablet example in this guide that gives thousands of tablets, an answer no order means.

3. 3

   Decimal point one place out: The digits are right and the point is not, which is easiest to miss on an injection under 1 mL. Write the leading zero and ask whether the volume is a plausible amount for one injection.

4. 4

   Rounded to the wrong precision: The working is right and the answer is rounded to a different place than the rule asks, for example to the tenth where the program wants the hundredth for a dose under 1 mL.

Tablet and capsule dosage calculation practice problems→

Each problem opens to its worked solution, the answer under a stated rounding rule and the sources it is built from.

What is the desired over have formula?

The desired over have formula, also called the formula method, gives the amount of a drug to give: the dose desired (D) divided by the dose on hand (H), times the quantity that holds the dose on hand (Q). Written out, D ÷ H × Q = x, with D and H in the same unit.

What does Q stand for in D/H × Q?

In the desired over have formula, Q is the quantity that holds the dose on hand: one tablet or capsule, or the volume the label's strength refers to, such as 1 mL or 5 mL. The answer comes out in Q's unit.

Do D and H have to be in the same unit?

Yes. The desired over have formula divides the dose desired by the dose on hand, so both must be in the same unit, for example both in milligrams. If the order is in milligrams and the label in micrograms, convert one of them first, with 1,000 mcg in 1 mg.

Can you use desired over have for IV rates?

Only when the order is a dose per hour: the hourly dose is D, and the drug in the bag and the bag's volume are H and Q, which gives mL/hr. A rate from a volume and a time is the volume divided by the hours, and drops per minute have their own formula.

1. [1]Toney-Butler TJ, Nicolas S, Wilcox L. Dose Calculation Desired Over Have Formula Method. StatPearls (2023)ncbi.nlm.nih.gov
2. [2]Bergen Community College Nursing, Pharmacological Math Computation Skills Self Learning Module (2023)bergen.edu
3. [3]Mercer County Community College Nursing, Medication Calculation Guidelines (updated September 2020)mccc.edu
4. [4]Open RN, Nursing Skills 2e, 5.5 Rounding (WisTech Open, 2023)wtcs.pressbooks.pub
5. [5]Open RN, Nursing Skills 2e, 5.17 Multi-Step Calculations (WisTech Open, 2023)wtcs.pressbooks.pub

No licensed clinician has reviewed this guide. How the guides are made. Exam practice, never for patient care. Follow your program's rules.

• The dosage calculation exam in nursing school: what is on it and how to prepare
• Dosage calculation exam rules by nursing program: passing scores, retakes and calculators
• Dosage calculation formulas for nursing: one table for the common problems
• Nursing dosage conversion chart: metric and household equivalents
• Rounding rules for dosage calculations
• Leading and trailing zeros in medication doses: the ISMP rules for nursing
• Ratio and proportion dosage calculations: how to set them up
• How to calculate mL/hr for an IV infusion
• How to calculate infusion time in hours and minutes
• Reconstitution dosage calculation: from a powder vial to milliliters
• Weight-based dosage calculation: mg/kg doses from a weight in pounds
• Six dosage calculation mistakes and the wrong answers they leave
• Dimensional analysis for nursing dosage calculations
• IV drip rate formula: how to work out drops per minute