The question is always the same: how many tablets, or how many mL, deliver the ordered dose? Three methods give the same answer. Learn one well and use a second to check.
Formula method (D/H × Q)
Amount to give = (D ÷ H) × Q
- D (desired) = the dose ordered
- H (have) = the dose contained in one unit of the product
- Q (quantity) = the amount that contains H (1 tablet, 5 mL, 2 mL)
- D and H must be in the same unit before you divide.
Ratio-proportion method
H : Q = D : X, then cross-multiply: H × X = D × Q, so X = (D × Q) ÷ H. Written as fractions: H/Q = D/X.
Dimensional analysis
Start with the ordered dose and multiply by factors so every unit cancels except the answer unit:
X = D (ordered unit) × (conversion factor if needed) × Q/H
Dimensional analysis handles unit conversions in the same line, which is why many schools prefer it for multi-step problems.
Rounding conventions (follow facility policy)
| Situation | Rule |
|---|
| Tablets | Give whole tablets; half tablets only if the tablet is scored and splitting is allowed. Never split extended-release, enteric-coated, or unscored tablets or open capsules unless the label allows |
| Oral liquids | Measure with an oral syringe; round to the syringe markings (commonly tenths of a mL) |
| Injection volume of 1 mL or more | Round to tenths (3 mL syringe marked in 0.1 mL) |
| Injection volume under 1 mL | Round to hundredths (1 mL syringe marked in 0.01 mL) |
| Insulin | Measure in units with an insulin syringe or pen; do not convert to mL |
| General | Round only the final answer; a leading zero is always written (0.75 mL) |
Oral forms: tablets, capsules, oral solutions and suspensions. Parenteral forms: ampules, single-dose and multiple-dose vials, prefilled syringes, powders that must be reconstituted, and unit-based drugs (insulin, heparin).
Worked examples
Example 1 — tablets, three methods. Order: amoxicillin 500 mg PO. Available: 250 mg capsules.
- Formula: (500 mg ÷ 250 mg) × 1 capsule = 2 capsules
- Ratio-proportion: 250 mg : 1 capsule = 500 mg : X → 250X = 500 → X = 2
- Dimensional analysis: 500 mg × 1 capsule/250 mg = 2 capsules (mg cancels)
- Answer: 2 capsules. Check: 2 × 250 = 500 mg. Safety: ask about penicillin allergy before the first dose.
Example 2 — tablets with a unit conversion. Order: digoxin 0.125 mg PO daily. Available: 250 mcg scored tablets.
- Convert: 0.125 mg × 1,000 mcg/mg = 125 mcg
- Formula: (125 mcg ÷ 250 mcg) × 1 tablet = 0.5 tablet
- Dimensional analysis: 0.125 mg × 1,000 mcg/1 mg × 1 tablet/250 mcg = 0.5 tablet
- Answer: one-half tablet (scored, so splitting is acceptable; use a tablet cutter). Safety: count the apical pulse for 1 full minute first; hold and notify per parameters (commonly under 60/min in adults) or with signs of toxicity (nausea, visual changes, new dysrhythmia).
Example 3 — oral suspension. Order: cephalexin 375 mg PO. Available: 250 mg/5 mL.
- Formula: (375 ÷ 250) × 5 mL = 1.5 × 5 = 7.5 mL
- Answer: 7.5 mL in an oral syringe. The classic error is stopping at 1.5 and giving 1.5 mL (Q not multiplied).
- Check: 7.5 mL × 250 mg/5 mL = 7.5 × 50 = 375 mg.
Example 4 — injection under 1 mL. Order: morphine 3 mg IV. Available: 4 mg/mL.
- Formula: (3 ÷ 4) × 1 mL = 0.75 mL
- Rounding: under 1 mL → hundredths in a 1 mL syringe → 0.75 mL
- Check: 0.75 × 4 = 3 mg. Safety: assess sedation and respiratory rate before and after; keep naloxone available (boxed warning: respiratory depression — risk rises with benzodiazepines or other CNS depressants); morphine is a controlled substance — waste the unused 0.25 mL with a witness.
Example 5 — reconstituted powder. Order: ceftriaxone 500 mg IM. Available: 1 g vial; label for IM use: add 2.1 mL diluent to give 350 mg/mL.
- Step 1 — concentration after reconstitution comes from the label: 350 mg/mL (the powder adds volume, so 1 g is in about 2.86 mL, not 2.1 mL)
- Step 2 — formula: (500 ÷ 350) × 1 mL = 1.428… mL
- Rounding: over 1 mL → tenths → 1.4 mL
- Check: 1.4 × 350 = 490 mg (the rounding difference is acceptable; 1.43 × 350 = 500.5). If policy and the syringe allow hundredths, 1.43 mL may be measured.
- Label the vial with date, time, concentration, and your initials if any remains, and store per label. Safety: severe hypersensitivity (ask about cephalosporin and penicillin allergy); ceftriaxone is contraindicated in hyperbilirubinemic neonates, and in neonates it must not be given with IV calcium-containing solutions.
Example 6 — units. Order: heparin 5,000 units subcutaneously every 12 hours. Available: 10,000 units/mL vial.
- Formula: (5,000 ÷ 10,000) × 1 mL = 0.5 mL
- Dimensional analysis: 5,000 units × 1 mL/10,000 units = 0.5 mL
- Safety: heparin comes in many strengths (1,000, 5,000, 10,000 units/mL and more) that look alike — confirm the strength with an independent double check; monitor platelets (heparin-induced thrombocytopenia) and signs of bleeding; antidote protamine sulfate.
Two more patterns
- Insulin: order regular insulin 24 units subcutaneously. Draw up to the 24-unit mark on a U-100 insulin syringe (24 units = 0.24 mL, but never measure insulin in a standard mL syringe). U-500 insulin is given only with a U-500 pen or a dedicated U-500 syringe.
- Milliequivalents: order potassium chloride 40 mEq PO. Available: oral solution 20 mEq/15 mL. (40 ÷ 20) × 15 mL = 30 mL, diluted in water or juice to reduce GI irritation. Never give concentrated potassium by IV push.
Harm from calculation errors in this topic usually comes from:
- Forgetting Q for liquids (answer given as a ratio, not mL)
- Mismatched units (mg vs mcg; the order in g and the label in mg)
- Wrong concentration chosen from look-alike vials (heparin, insulin, morphine, potassium)
- Reconstitution confusion — using the diluent volume instead of the label's final concentration, or choosing the IM concentration for an IV dose
- Wrong syringe — measuring 0.75 mL in a 3 mL syringe, or insulin in a tuberculin syringe
- Unsafe IM volume — adults: deltoid up to 1 mL; ventrogluteal and vastus lateralis up to about 3 mL. A larger calculated volume means rechecking the order and the concentration, and possibly dividing the dose between sites per policy.
- Do not crush or split extended-release (ER, XR, XL, SR), enteric-coated, or sublingual forms, or capsules with beads, unless the label allows; ask the pharmacist for an alternative form.
- A single dose that needs more than 2–3 tablets or an unusually large volume is a signal to recheck the order and the product.
- Multiple-strength vials: read the concentration on each vial; a "2 mL" answer from the wrong strength can be a tenfold error.
- Reconstitution: use the diluent type and volume on the label (sterile water, sodium chloride, or lidocaine for some IM products only when the label permits — lidocaine-containing solutions are never given IV). When a label offers more than one concentration, choose the one for the ordered route.
- High-alert drugs (insulin, heparin, opioids, potassium) require an independent double check per facility policy.
Listed in priority order.
- Right client, right drug, right dose, right route, right time, right documentation — check two identifiers and allergies before preparing.
- Assess before giving — apical pulse for digoxin, sedation and respiratory rate for opioids, blood glucose before insulin, potassium level and urine output before potassium, bleeding and platelet count for heparin.
- Estimate, calculate, and recheck by a second method. For high-alert drugs, have a second nurse check independently (not by looking at your answer first).
- Choose the device that matches the answer: oral syringe for liquids, 1 mL syringe for volumes under 1 mL, insulin syringe for insulin.
- Prepare reconstituted drugs exactly as labeled; label multi-dose vials with date, time, concentration, and initials; discard per label.
- Give and observe for the expected effect and adverse effects; document dose, route, site, and response.
- Take the number of tablets on the label; do not split, crush, or chew extended-release or enteric-coated products.
- Use the oral syringe or dosing cup supplied with liquids; shake suspensions well before measuring.
- Keep insulin syringes matched to the insulin concentration (U-100 syringes for U-100 insulin).
- If a new refill looks different (color, size, number of tablets), check with the pharmacist before taking it — the strength may have changed.
| Error | Result | Response |
|---|
| Liquid dose given as ratio (1.5 mL instead of 7.5 mL) | Underdose | Recalculate; notify prescriber; follow policy |
| Digoxin mg/mcg slip | Toxicity: nausea, vomiting, visual changes, bradycardia, dysrhythmias | Hold, check level and potassium, notify; digoxin immune Fab for severe toxicity |
| Opioid tenfold error | Sedation, respiratory depression | Stimulate, support airway and breathing, naloxone diluted and titrated to breathing; watch for recurrent sedation |
| Heparin wrong vial strength | Bleeding | Stop heparin, notify, check aPTT or anti-Xa; protamine sulfate as ordered |
| Insulin measured in a mL syringe | Severe hypoglycemia | Check glucose; oral glucose if awake, IV dextrose or glucagon if not |
| IV potassium push or too fast | Cardiac arrest | Never push; pump only, per protocol |
Any error that reaches the client is assessed first, then reported to the prescriber and through the incident system.
- D/H × Q: dose ordered ÷ dose on hand × quantity; D and H in the same unit
- Ratio-proportion and dimensional analysis give the same answer — use one to check the other
- Liquids: always multiply by Q (375 mg from 250 mg/5 mL = 7.5 mL, not 1.5 mL)
- Injections: 1 mL or more → tenths; under 1 mL → hundredths in a 1 mL syringe
- Insulin is measured in units with a matching insulin syringe or pen
- Reconstitution: use the final concentration on the label, not the diluent volume
- Split only scored tablets; never crush extended-release or enteric-coated forms
- IM volume limits in adults: deltoid 1 mL; ventrogluteal or vastus lateralis about 3 mL
- An answer of many tablets or a very large volume → recheck before giving
- Assess before giving (apical pulse, respirations and sedation, glucose, potassium) and double-check high-alert drugs
Country Notes
United States
- Many hospitals use unit-dose dispensing, barcode scanning, and automated dispensing cabinets, so nurses more often verify prepared doses than calculate from stock bottles — but calculation questions and independent double checks for high-alert drugs remain standard.
- The same generic drug may appear in several vial strengths (for example, heparin); USP labeling standards require the strength per total volume and per mL on many injectable labels.
Philippines
- The generic name must appear on prescriptions and labels (Generics Act, RA 6675), and several brands of the same generic may carry different strengths — calculate from the strength printed on the product in hand.
- Nurses in many facilities prepare doses from multi-dose vials and reconstitute antibiotics on the ward, so reconstitution and labeling steps are practiced skills.