Write the given quantity with its unit and the unit you want.
Pick the equivalent: 1000 between kg, g, mg and mcg or L and mL; 1 kg = 2.2 lb; 1 tsp = 5 mL, 1 tbsp = 15 mL, 1 fl oz = 30 mL, 1 cup = 240 mL.
Write it as a fraction so that the unwanted unit cancels; for a rate, use one fraction per unit that changes.
Check the direction: a smaller unit gives a bigger number.
Round only the final answer, to the precision the question names.
Dosage calculations
Dose from strength
volume = dose / strength
Weight-based dose
dose = mg/kg × body weight
Tablets
number = dose / tablet strength
Units
1 g = 1000 mg, 1 mg = 1000 mcg
Method
Convert the ordered dose and the stock strength to the same unit.
Use desired over have times quantity: (D/H) × Q.
For weight-based doses, multiply by the weight in kg first, then divide the daily dose by the number of doses.
Estimate first and check that the answer is reasonable.
IV infusion rates
Pump rate
mL/h = volume (mL)/time (h)
Drip rate
drops/min = volume (mL) × drop factor / time (min)
Infusion time
time (h) = volume (mL)/rate (mL/h)
Method
Pump rate in mL/h: volume divided by time in hours.
Drip rate in drops/min: volume × drop factor divided by time in minutes.
For time remaining: volume left divided by the rate.
Round as the question or the equipment requires.
IV fluids & fluid balance
Holliday–Segar per hour
4 mL/kg (first 10 kg) + 2 mL/kg (next 10 kg) + 1 mL/kg (each kg above 20)
Holliday–Segar per day
100 / 50 / 20 mL/kg for the same bands
Fluid balance
intake − output
Ice chips
count as half their volume
Urine output
mL/kg/h = mL / (kg × h)
Infusion time
time (h) = volume left (mL) / rate (mL/h)
Volume infused
mL = rate × time
Pediatric & critical-care dosing
Daily dose
mg/day = mg/kg/day × weight (kg)
Doses per day
number = 24 h / dosing interval (h)
Pounds to kilograms
kg = lb / 2.2
Infusion concentration
units/mL = units in bag / bag volume
Pump rate
mL/h = dose per hour / concentration
Titrated drip
mL/h = mcg/kg/min × kg × 60 / (mcg/mL)
Dose from pump rate
mcg/kg/min = mL/h × (mcg/mL) / (60 × kg)
Units
1 mg = 1000 mcg
Pharmacy calculations
Percentage strength
% w/v = g per 100 mL
Amount in a solution
g = % × mL / 100
Ratio strength
1:X = 1 g in X mL; % = 100 / X
Reconstitution
final volume = diluent + powder volume
Concentration
mg/mL = drug in vial / final volume
Alligation
parts of H = T − L, parts of L = H − T
Water or base
0%
2Practice problems
1.Nursing math & unit conversionsMedium
Practice exercise (made-up values, not clinical guidance). A weight conversion gives 63.9316 kg. The rule in this exercise is that weights are rounded to the nearest tenth of a kilogram. What value x do you record?
63.9316 kg
x = kg
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion delivers 2 mg/h. Express this dose rate D in mcg/min. Round to one decimal place.
2 mg/h1 mg = 1000 mcg1 h = 60 min
D = mcg/min
3.Dosage calculationsMedium
A patient weighs 25 kg. The prescribed dose is 7.5 mg/kg per day, given in 3 equal doses. How many milligrams D are given per dose?
25 kg7.5 mg/kg/day3× per day
D = mg
4.Dosage calculationsHard
A patient weighs 189.2 lb. The prescription is 2 mg/kg as a single dose, and the stock contains 200 mg in 5 mL. Using 1 kg = 2.2 lb, what volume V do you give?
189.2 lb2 mg/kg200 mg/5 mL1 kg = 2.2 lb
V = mL
5.IV infusion ratesMedium
Infuse 1000 mL over 3 hours with a giving set of 15 gtt/mL. Find the drip rate R in drops per minute. Round to the nearest whole number.
1000 mL3 h15 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A bag contains 200 mg of a drug in 250 mL and runs at 25 mL/h. How many milligrams per hour D does the patient receive?
200 mg/250 mL25 mL/h
D = mg/h
7.IV fluids & fluid balanceMedium
Practice exercise (made-up values, not clinical guidance). The record shows a patient's intake and output for one 8-hour shift. The IV infusion ran at the rate shown for the whole shift. Find the total intake I in mL.
water: 250 mLjuice: 100 mLmilk: 240 mLIV infusion: 125 mL/h × 8 hIV antibiotic: 2 × 100 mL
I = mL
8.IV fluids & fluid balanceHard
Practice exercise (made-up values, not clinical guidance). A 500 mL infusion starts at 14:30 at 100 mL/h. After 3 hours the rate is changed to 60 mL/h and is not changed again. How many hours t after the start will the bag be empty? Round to one decimal place.
500 mL100 mL/h · 3 h60 mL/h
t = h
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 10 000 units of heparin in 250 mL. The order is 18 units/kg/h for a patient who weighs 93 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
10 000 units/250 mL18 units/kg/h93 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dopamine 800 mg in 500 mL. The order is 10 mcg/kg/min for a patient who weighs 65 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
800 mg/500 mL10 mcg/kg/min65 kg
R = mL/h
11.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains ceftriaxone 1000 mg as a powder. The practice label says to add 9.6 mL of sterile water; the powder adds 0.4 mL to the volume. The prescribed dose is 400 mg. What volume V do you draw up? Round to one decimal place.
1000 mg9.6 mL+0.4 mL400 mg
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 200 mL of 4% chlorhexidine from a 20% stock and purified water. How many mL V of water do you need? Round to the nearest whole mL.
20%0%4%200 mL
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: x = 63.9 kg
Rounding: look at the digit just after the place you round to: 5 or more rounds up, 4 or less leaves the digit as it is. Round only the final answer, never the steps. Typical exam rules: volumes of 1 mL or more to the nearest tenth, volumes below 1 mL to the nearest hundredth, drip rates to whole drops and weights to one decimal place; always follow the rule the question states.
Digit in the tenths place
63.9316 → 9
Only the next digit decides
63.9316 → 3
3 is 4 or less, so 9 stays.
The digits after it (16) are ignored: round once, never step by step.
Round
x = 63.9 kg
Answer
x = 63.9 kg
2.Nursing math & unit conversions
Answer: D = 33.3 mcg/min
Dimensional analysis: write the given quantity, then multiply by conversion factors written as fractions (for example 60 min/1 h or 1 mg/1000 mcg) so that each unwanted unit appears once on top and once underneath and cancels. When only the wanted unit is left, calculate. Use the equivalents the question gives and round only the final answer.
Set up the chain
D = 2 mg/h × (1000 mcg/1 mg) × (1 h/60 min)
Calculate
D = 2000/60 = 33.33 ≈ 33.3 mcg/min
Answer
D = 33.3 mcg/min
3.Dosage calculations
Answer: D = 62.5 mg
Dose calculation: the amount to give equals what is prescribed divided by what you have, times the quantity it comes in: amount = (desired dose/stock strength) × stock volume. Always keep the units the same (convert g to mg, mg to mcg first) and check that the answer is sensible.
Total per day
7.5·25 = 187.5 mg
Per dose
D = 187.5/3 = 62.5 mg
Answer
D = 62.5 mg
4.Dosage calculations
Answer: V = 4.3 mL
Dose calculation: the amount to give equals what is prescribed divided by what you have, times the quantity it comes in: amount = (desired dose/stock strength) × stock volume. Always keep the units the same (convert g to mg, mg to mcg first) and check that the answer is sensible.
Weight in kg
189.2/2.2 = 86 kg
Dose
2·86 = 172 mg
Volume
V = (172/200)·5 = 4.3 mL
Answer
V = 4.3 mL
5.IV infusion rates
Answer: R = 83 gtt/min
Infusion rates: a pump is set in mL/h = volume/time in hours. A gravity drip is counted in drops per minute: gtt/min = volume (mL) × drop factor (gtt/mL)/time (min). The drop factor is printed on the tubing package: macrodrip sets deliver 10, 15 or 20 gtt/mL (blood sets often 10 gtt/mL in the US, 15 in the UK) and microdrip sets 60 gtt/mL. Always use the drop factor the question or package gives.
Time in minutes
3·60 = 180 min
Drip rate
R = 1000·15/180 = 83.33 ≈ 83 gtt/min
Answer
R = 83 gtt/min
At the bedside you round to the nearest whole drop: 83 gtt/min.
6.IV infusion rates
Answer: D = 20 mg/h
Infusion rates: a pump is set in mL/h = volume/time in hours. A gravity drip is counted in drops per minute: gtt/min = volume (mL) × drop factor (gtt/mL)/time (min). The drop factor is printed on the tubing package: macrodrip sets deliver 10, 15 or 20 gtt/mL (blood sets often 10 gtt/mL in the US, 15 in the UK) and microdrip sets 60 gtt/mL. Always use the drop factor the question or package gives.
Concentration
200/250 = 0.8 mg/mL
Dose rate
D = 0.8·25 = 20 mg/h
Answer
D = 20 mg/h
7.IV fluids & fluid balance
Answer: I = 1790 mL
Intake and output: intake counts everything that goes in (oral fluids, IV infusions, IV medications and flushes, tube feeds); ice chips count as half their volume. Output counts urine, drains, vomit and other losses. Balance = total intake − total output; a negative balance is a net loss. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Add the intake
oral: 250 + 100 + 240 = 590 mL
IV infusion: 125·8 = 1000 mL
IV antibiotic: 2·100 = 200 mL
I = 1790 mL
Answer
I = 1790 mL
8.IV fluids & fluid balance
Answer: t = 6.3 h
Infusion time: time (h) = volume to infuse (mL)/rate (mL/h); use the volume still left in the bag, not the bag size. Volume infused = rate × time. Convert decimal hours to hours and minutes with the fraction × 60 (0.5 h = 30 min, not 50 min). The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
First part
100·3 = 300 mL
500 − 300 = 200 mL left
Second part
200/60 = 3.333 h
Total time
t = 3 + 3.333 = 6.333 ≈ 6.3 h
Answer
t = 6.3 h
That is about 6 h 20 min, so the bag runs out at about 20:50.
9.Pediatric & critical-care dosing
Answer: R = 41.9 mL/h
Heparin and insulin infusions: concentration = units in the bag/bag volume (units/mL). Pump rate (mL/h) = units per hour/concentration, and units per hour = mL/h × concentration. For a weight-based order, units/h = units/kg/h × weight first. A bolus volume = units needed/vial strength. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Units per hour
18·93 = 1 674 units/h
Concentration
10 000/250 = 40 units/mL
Pump rate
R = 1674/40 = 41.85 ≈ 41.9 mL/h
Answer
R = 41.9 mL/h
10.Pediatric & critical-care dosing
Answer: R = 24.4 mL/h
Titrated drips: first find the concentration in mcg/mL (mg × 1000/mL). For a weight-based order, mcg/min = mcg/kg/min × weight. Then mL/h = mcg/min × 60/concentration. Working backwards, mcg/kg/min = mL/h × concentration/(60 × weight). The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Concentration
800 mg = 800 000 mcg
800 000/500 = 1600 mcg/mL
Dose per minute and per hour
10·65 = 650 mcg/min
650·60 = 39000 mcg/h
Pump rate
R = 39000/1600 = 24.38 ≈ 24.4 mL/h
Answer
R = 24.4 mL/h
11.Pharmacy calculations
Answer: V = 4 mL
Reconstitution: the powder takes up space, so the final volume is the diluent plus the powder volume. Concentration = drug in the vial/final volume, and the volume to give = dose/concentration. On a multi-strength label, use the concentration that belongs to the amount of diluent you actually added. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Final volume
9.6 + 0.4 = 10 mL
Concentration
1000/10 = 100 mg/mL
Volume to give
V = 400/100 = 4 mL
Answer
V = 4 mL
12.Pharmacy calculations
Answer: V = 160 mL
Alligation: to mix a higher strength H and a lower strength L into a target strength T, take (T − L) parts of H and (H − T) parts of L. The parts are crossed: each stock gets the distance from the target to the other stock. Water or a plain base counts as 0%. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Alligation parts
20%: 4 − 0 = 4 parts
0%: 20 − 4 = 16 parts
total: 20 parts
Water
V = 200·16/20 = 160 mL
Answer
V = 160 mL
Check: 40 mL of 20% contains 8 g of drug, which is 4% of 200 mL.