Reference formulas
Five calculations cover most NCLEX drug math questions. Learn the logic behind each one — dimensional analysis works for all of them if a formula slips your mind mid-exam.
Basic dosage (oral or parenteral)
Desired ÷ Have × Quantity = Amount to give
Order: amoxicillin 500 mg PO. On hand: 250 mg tablets.
500 ÷ 250 × 1 tab = 2 tablets
IV flow rate — mL/hr (infusion pump)
Volume (mL) ÷ Time (hr) = mL/hr
Order: 1000 mL NS over 8 hours.
1000 ÷ 8 = 125 mL/hr
IV drip rate — gtt/min (gravity infusion)
Volume (mL) × Drop factor (gtt/mL) ÷ Time (min) = gtt/min
Order: 1000 mL over 8 hours, tubing drop factor 15 gtt/mL. 8 hr = 480 min.
1000 × 15 ÷ 480 = 31.25 → 31 gtt/min
Weight-based dosage
Dose (mg/kg/day) × Weight (kg) ÷ Doses per day = Amount per dose
Order: amoxicillin 40 mg/kg/day divided q8h. Child weighs 15 kg (3 doses/day).
40 × 15 = 600 mg/day → 600 ÷ 3 = 200 mg/dose
Critical care drip — mcg/kg/min
(Dose mcg/kg/min × Weight kg × 60) ÷ Concentration (mcg/mL) = mL/hr
Order: dopamine 5 mcg/kg/min. Patient 70 kg. Bag: 400 mg in 250 mL → 1,600 mcg/mL.
(5 × 70 × 60) ÷ 1,600 = 21,000 ÷ 1,600 = 13.1 mL/hr
Safe dose range — check before you calculate
Low end (mg/kg/day) × Weight = Minimum safe daily dose
High end (mg/kg/day) × Weight = Maximum safe daily dose
High end (mg/kg/day) × Weight = Maximum safe daily dose
Vancomycin safe range is 40–60 mg/kg/day. Patient weighs 20 kg.
40 × 20 = 800 mg/day (low) · 60 × 20 = 1,200 mg/day (high)
An order for 1,500 mg/day falls outside this range — hold the dose and call the prescriber before giving it, regardless of whether the arithmetic on the order is otherwise correct.
Insulin dosing
Units ordered ÷ Concentration (units/mL) = mL to give
Insulin is dosed in units, never mg. U-100 means 100 units per mL — the concentration used in the U.S.
Order: regular insulin 8 units subcut, no insulin syringe on hand, so it's drawn up in a 1 mL syringe marked in mL.
8 ÷ 100 = 0.08 mL
Always use an insulin syringe when one is available — it's marked directly in units and removes this conversion. Never abbreviate "units" as "U"; it's a classic look-alike for "0" or "4" on a written order.
Maximum daily dose (MDD) can override the math
A weight-based calculation can produce a number higher than the drug's absolute ceiling. When that happens, the ceiling wins. Acetaminophen is capped near 4,000 mg/day for an adult no matter what a per-kg calculation suggests; epinephrine for anaphylaxis is capped at 0.3 mg IM regardless of a heavier patient's weight-based result. Always check the drug's listed maximum after you calculate, not just the per-kg formula.
Rounding rules the exam expects
- mL/hr on a pump: round to the nearest tenth.
- gtt/min (gravity): round to the nearest whole drop — you can't give a fraction of a drop.
- Tablets: round to the nearest half or quarter, only if the tablet is scored.
- Always double-check the order is safe for the patient's weight and age before calculating — the math being correct doesn't make the order correct.
Heparin drip — weight-based initiation and nomogram titration
Protocol dose (units/kg/hr) × Weight (kg) ÷ Concentration (units/mL) = Initial rate (mL/hr)
Protocol: 18 units/kg/hr. Patient weighs 70 kg. Bag is mixed 25,000 units in 250 mL (100 units/mL).
(18 × 70) ÷ 100 = 12.6 mL/hr
Once running, the aPTT result tells you how to adjust it — the nomogram gives a units/hr change, which you convert back into mL/hr:
Current rate 12.6 mL/hr. Nomogram step: increase by 200 units/hr.
200 ÷ 100 = 2 mL/hr increase → new rate = 14.6 mL/hr Every institution's nomogram is different — this shows the arithmetic pattern, not a specific protocol to follow. Always use the facility's own heparin chart.
200 ÷ 100 = 2 mL/hr increase → new rate = 14.6 mL/hr Every institution's nomogram is different — this shows the arithmetic pattern, not a specific protocol to follow. Always use the facility's own heparin chart.
Body surface area (BSA) dosing
$$\text{BSA (m}^2\text{)} = \sqrt{\frac{\text{Height (cm)} \times \text{Weight (kg)}}{3600}}$$
Cyclophosphamide ordered at 750 mg/m². Patient is 165 cm tall and weighs 65 kg.
BSA = √((165 × 65) ÷ 3600) = √2.98 = 1.73 m²
1.73 × 750 = 1,297.5 mg Used for chemotherapy and some pediatric dosing, where a per-kg dose would be too imprecise across a wide size range.
1.73 × 750 = 1,297.5 mg Used for chemotherapy and some pediatric dosing, where a per-kg dose would be too imprecise across a wide size range.
Renal function — creatinine clearance (Cockcroft-Gault)
$$\text{CrCl (mL/min)} = \frac{(140 - \text{Age}) \times \text{Weight (kg)} \times (0.85 \text{ if female})}{72 \times \text{Serum creatinine (mg/dL)}}$$
68-year-old male, 80 kg, serum creatinine 1.1 mg/dL.
((140 - 68) × 80 × 1) ÷ (72 × 1.1) = 5,760 ÷ 79.2 = 72.7 mL/min
This is an estimate of kidney function, not a dose. Once you have it, the actual dose adjustment is always drug-specific — check the facility's renal dosing chart or the drug's product literature next.
This site's practice tests cover both NCLEX and NAPLEX — the ten calculations below show up on both, since they're clinical math rather than pure dosage arithmetic.
Mean arterial pressure (MAP)
[(2 × Diastolic) + Systolic] ÷ 3 = MAP
Blood pressure is 120/80 mmHg.
[(2 × 80) + 120] ÷ 3 = 280 ÷ 3 = 93.3 mmHg
Temperature conversion (°F ↔ °C)
(°F − 32) ÷ 1.8 = °C (°C × 1.8) + 32 = °F
Patient's temperature is 101.3°F.
(101.3 − 32) ÷ 1.8 = 69.3 ÷ 1.8 = 38.5°C
BUN:creatinine ratio — dehydration screen
BUN ÷ Serum creatinine = BUN:SCr ratio (greater than 20:1 suggests dehydration)
BUN 42 mg/dL, serum creatinine 1.0 mg/dL.
42 ÷ 1.0 = 42:1 → well above 20:1, consistent with dehydration (prerenal)
Anion gap
Na − Cl − HCO₃ = Anion gap (normal range roughly 8–12 mEq/L)
Na 140, Cl 100, HCO₃ 24 mEq/L.
140 − 100 − 24 = 16 mEq/L → above normal range
Absolute neutrophil count (ANC)
WBC × [(% segs + % bands) ÷ 100] = ANC
WBC 4,000 cells/mm³, 40% segs, 5% bands.
4,000 × (45 ÷ 100) = 1,800 cells/mm³
Neutropenic precautions are typically considered below 1,500 cells/mm³ — check facility policy for the exact threshold.
Pack-year smoking history
Packs per day × Years smoked = Pack-years
Patient has smoked 1.5 packs/day for 20 years.
1.5 × 20 = 30 pack-years
Corrected calcium for low albumin
Measured calcium + [(4.0 − Albumin) × 0.8] = Corrected calcium
Measured calcium 7.8 mg/dL, albumin 2.5 g/dL.
7.8 + [(4.0 − 2.5) × 0.8] = 7.8 + 1.2 = 9.0 mg/dL
Not needed if an ionized calcium level is already available.
Ideal and adjusted body weight — which weight to dose from
IBW (male) = 50 kg + 2.3 kg × inches over 5 feet
IBW (female) = 45.5 kg + 2.3 kg × inches over 5 feet
Adjusted BW = IBW + 0.4 × (Total body weight − IBW)
IBW (female) = 45.5 kg + 2.3 kg × inches over 5 feet
Adjusted BW = IBW + 0.4 × (Total body weight − IBW)
Male, 5'8" tall (8 inches over 5 feet), total body weight 100 kg.
IBW = 50 + (2.3 × 8) = 68.4 kg
Adjusted BW = 68.4 + 0.4 × (100 − 68.4) = 68.4 + 12.6 = 81.0 kg Most drugs are dosed on total body weight at normal or obese weight. Known exceptions dose on IBW instead (acyclovir, aminophylline, levothyroxine, theophylline), and aminoglycosides in obese patients use the adjusted weight above.
Adjusted BW = 68.4 + 0.4 × (100 − 68.4) = 68.4 + 12.6 = 81.0 kg Most drugs are dosed on total body weight at normal or obese weight. Known exceptions dose on IBW instead (acyclovir, aminophylline, levothyroxine, theophylline), and aminoglycosides in obese patients use the adjusted weight above.
Insulin — carbohydrate ratio, correction factor, and correction dose
500 ÷ Total daily dose (TDD) = grams of carb covered by 1 unit of rapid-acting insulin
1,800 ÷ TDD = mg/dL drop from 1 unit of rapid-acting insulin
(Blood glucose now − Target) ÷ Correction factor = Correction dose
1,800 ÷ TDD = mg/dL drop from 1 unit of rapid-acting insulin
(Blood glucose now − Target) ÷ Correction factor = Correction dose
Patient's total daily insulin dose is 50 units. Blood glucose is 250 mg/dL, target is 120 mg/dL.
Carb ratio: 500 ÷ 50 = 1 unit covers 10 g carbohydrate
Correction factor: 1,800 ÷ 50 = 1 unit drops glucose by 36 mg/dL
Correction dose: (250 − 120) ÷ 36 = 3.6 units Regular insulin uses the 450 and 1,500 rules instead of 500 and 1,800 — same structure, different constants.
Correction factor: 1,800 ÷ 50 = 1 unit drops glucose by 36 mg/dL
Correction dose: (250 − 120) ÷ 36 = 3.6 units Regular insulin uses the 450 and 1,500 rules instead of 500 and 1,800 — same structure, different constants.
Daily fluid maintenance (Holliday-Segar, over 20 kg)
1,500 mL + [20 mL × (Weight in kg − 20)] = Daily fluid requirement
Patient weighs 45 kg.
1,500 + [20 × (45 − 20)] = 1,500 + 500 = 2,000 mL/day
A quick estimate of 30–40 mL/kg/day is also commonly used for adults.
| From | To | Factor |
|---|---|---|
| 1 kg | lb | 2.2 lb |
| 1 lb | kg | 0.454 kg |
| 1 tsp | mL | 5 mL |
| 1 tbsp | mL | 15 mL |
| 1 oz | mL | 30 mL |
| 1 g | mg | 1,000 mg |
| 1 mg | mcg | 1,000 mcg |
| 1 L | mL | 1,000 mL |
Calculations
Eleven worked problems covering unit conversions, dimensional analysis, and the rounding conventions that trip people up most — whole number, nearest tenth, and nearest 10 mg all look similar but aren't interchangeable.
1. Household conversion — tsp to mL over multiple days
A prescription reads: "take 2 tsp PO Q6H x 7 days." How many milliliters must be dispensed to complete 7 days of therapy?
$$2 \text{ tsp} \times \frac{5 \text{ mL}}{1 \text{ tsp}} = 10 \text{ mL per dose}$$
$$\frac{10 \text{ mL}}{\text{dose}} \times \frac{4 \text{ doses}}{\text{day}} \times 7 \text{ days} = 280 \text{ mL}$$
2. Household conversion — ounces to mL, volume remaining
If 1 ounce = 30 mL, how many milliliters of sterile water will remain after 50 mL are used from a 16 ounce bottle?
$$16 \text{ oz} \times \frac{30 \text{ mL}}{1 \text{ oz}} = 480 \text{ mL bottle of sterile water}$$
480 mL - 50 mL = 430 mL of sterile water will remain
3. Pediatric daily volume — rounding to the nearest whole number
A pediatric patient is receiving 5.25 mL of drug every 4 hours. How many milliliters will be required for the entire day? Round to the nearest whole number.
5.25 mL (per dose) × 6 times/day = 31.5 mL
Round to the nearest whole number = 32 mL
Round to the nearest whole number = 32 mL
4. BID dose splitting — nearest whole number vs. nearest tenth
A patient requires 410.9 mg of a drug daily. The daily dose will be divided for BID administration. How many milligrams will the patient receive BID? Round to the nearest whole number.
410.9 mg daily ÷ 2 times per day = 205.45 mg BID
Round to the nearest whole number = 205 mg BID What if the problem said "round to the nearest tenth?" The correct answer would then be 205.5 mg. Rounding to the nearest tenth is the same as rounding to one decimal place.
Round to the nearest whole number = 205 mg BID What if the problem said "round to the nearest tenth?" The correct answer would then be 205.5 mg. Rounding to the nearest tenth is the same as rounding to one decimal place.
5. Enoxaparin — rounding to the nearest 10 mg
Enoxaparin 56.5 mg was ordered for a patient. The hospital rounds enoxaparin doses to the nearest 10 mg. What dose should be dispensed?
Correct answer: 60 mg
Rounding to the nearest 10 mg is different than rounding to the nearest tenth.
6. Height conversion — feet and inches to centimeters
A patient is 5'2" tall. What is her height in centimeters? Round to the nearest whole number.
$$5 \text{ feet} \times \frac{12 \text{ inches}}{1 \text{ foot}} = 60 \text{ inches} + 2 \text{ inches} = 62 \text{ inches}$$
$$62 \text{ inches} \times \frac{2.54 \text{ cm}}{1 \text{ inch}} = 157.48 \text{ cm}$$
Round to the nearest whole number = 157 cm
Watch for products that cannot be split
You cannot dispense part of an insulin vial or part of a Byetta pen to a patient, so rounding to the nearest whole vial or pen is required, even if the math itself comes out to a decimal.
Example: A patient takes Novolog 16 units TID before meals. How many vials of Novolog should be dispensed for a 30-day supply?
Answer: The patient takes 48 units per day, or 1,440 units per month. Since each vial of Novolog contains 1,000 units, the patient requires two vials for a 30-day supply.
7. Weight conversion — pounds to kilograms (proportion vs. dimensional analysis)
A patient weighs 176 pounds. What is the patient's weight in kilograms?
Method 1: Proportion. Solve for X by multiplying diagonally and then dividing. Set up in either of the two ways shown.
$$\frac{176 \text{ lbs}}{X \text{ kg}} = \frac{2.2 \text{ lbs}}{1 \text{ kg}} \quad X = 80 \text{ kg}$$
or
$$\frac{176 \text{ lbs}}{2.2 \text{ lbs}} = \frac{X \text{ kg}}{1 \text{ kg}} \quad X = 80 \text{ kg}$$
Method 2: Dimensional analysis. Cancel out the same units diagonally, leaving the desired units.
$$176 \text{ lbs} \times \frac{1 \text{ kg}}{2.2 \text{ lbs}} = 80 \text{ kg}$$
Notice that there is an equal sign (=) between the fractions in a proportion, and a multiplication symbol (×) between the fractions in dimensional analysis.
8. How many milliliters are in 5 liters?
Method 1: Proportion
$$\frac{5 \text{ L}}{X \text{ mL}} = \frac{1 \text{ L}}{1,000 \text{ mL}} \quad X = 5,000 \text{ mL}$$
or
Method 2: Dimensional analysis
$$5 \text{ L} \times \frac{1,000 \text{ mL}}{1 \text{ L}} = 5,000 \text{ mL}$$
9. Convert 5,000 mL to liters
$$5,000 \text{ mL} \times \frac{1 \text{ L}}{1,000 \text{ mL}} = 5 \text{ L}$$
10. Multi-step metric conversion — kilograms to nanograms
How many nanograms are equal to 5 kg? This example requires four separate proportions, or one dimensional-analysis chain (shown).
$$5 \text{ kg} \times \frac{1,000 \text{ g}}{1 \text{ kg}} \times \frac{1,000 \text{ mg}}{1 \text{ g}} \times \frac{1,000 \text{ mcg}}{1 \text{ mg}} \times \frac{1,000 \text{ ng}}{1 \text{ mcg}} = 5 \text{ trillion ng } (5 \times 10^{12} \text{ ng})$$
11. Multi-step metric conversion — nanograms to grams
How many grams are equal to 50,000,000 nanograms?
$$50,000,000 \text{ ng} \times \frac{1 \text{ mcg}}{1,000 \text{ ng}} \times \frac{1 \text{ mg}}{1,000 \text{ mcg}} \times \frac{1 \text{ g}}{1,000 \text{ mg}} = 0.05 \text{ g}$$
From this point forward, worked dimensional-analysis chains will be shown as the final cancellation only — the step-by-step cancel marks are omitted for readability, not because the intermediate steps don't matter.
Want the full set, worked out by category?
These 11 cover the core patterns — but every calculation type has its own dedicated article with more problems and full step-by-step answers. See all worked answers with explanations →
Practice calculator
Enter your own numbers and see the worked steps — good for checking homework problems or testing a formula until it's automatic.
Quiz
Randomly generated problems across all seven calculation types. Type your answer and check it — repetition here is what makes the math fast on test day.
Loading a problem…