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 dose is charted at 04:30 (24-hour clock). Which entry is the same time on the 12-hour clock? Click it.
04:30
13:30 AM
26:30 AM
34:30 AM
44:30 PM
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion starts at 17:50 and finishes at 02:45 the next morning (24-hour clock). How many minutes t did it run?
17:5002:45
t = min
3.Dosage calculationsMedium
A vial contains 500 mg of powder. The label says: add 1.8 mL of water for injection to give a total volume of 2 mL. The prescription is 100 mg. What volume V of the reconstituted solution do you give?
500 mg+ 1.8 mL → 2 mL100 mg
V = mL
4.Dosage calculationsHard
The prescription is 6800 units of a drug that comes as 10000 units/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
6800 units10000 units/mL
V = mL
5.IV infusion ratesMedium
Infuse 500 mL over 4 hours with a giving set of 10 gtt/mL. Find the drip rate R in drops per minute. Round to the nearest whole number.
500 mL4 h10 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A drip runs at 50 gtt/min through a set of 20 gtt/mL. There are 300 mL left in the bag. How many hours t until it is empty?
50 gtt/min20 gtt/mL300 mL
t = 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. Count ice chips as half their volume.
water: 240 mLmilk: 100 mLice chips: 100 mLIV infusion: 75 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 bag runs by pump at 150 mL/h. At 13:00, 300 mL have already been infused. How many hours t until the bag is empty? Round to one decimal place.
500 mL300 mL infused150 mL/h
t = h
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion contains 50 units of regular insulin in 50 mL. The order is 0.05 units/kg/h for a patient who weighs 52 kg. Find the pump rate R in mL/h. Round to one decimal place.
50 units/50 mL0.05 units/kg/h52 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 85 kg has an order for nitroglycerin at 15 mcg/min. The bag contains 50 mg in 250 mL. Find the pump rate R in mL/h. Round to one decimal place.
50 mg/250 mL15 mcg/min85 kg
R = mL/h
11.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains cefuroxime 750 mg as a powder. The practice label says to add 7.2 mL of sterile water; the powder adds 0.3 mL to the volume. The prescribed dose is 375 mg. What volume V do you draw up? Round to one decimal place.
750 mg7.2 mL+0.3 mL375 mg
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 900 mL of 6% hydrogen peroxide from a 30% stock and purified water. How many mL V of water do you need? Round to the nearest whole mL.
30%0%6%900 mL
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: 4:30 AM
24-hour clock: from 1 PM onwards add 12 to the hour (3:45 PM = 15:45). Midnight to 12:59 AM is 00:00–00:59, and 12:00–12:59 PM stays 12:00–12:59. Going back, subtract 12 from hours 13–23 and add PM; hours 00 become 12 AM. Count time across midnight in two parts: up to 24:00 (00:00), then from 00:00 on.
Convert the hour
04 → 4 AM
Answer
4:30 AM
Answer
4:30 AM
2.Nursing math & unit conversions
Answer: t = 535 min
24-hour clock: from 1 PM onwards add 12 to the hour (3:45 PM = 15:45). Midnight to 12:59 AM is 00:00–00:59, and 12:00–12:59 PM stays 12:00–12:59. Going back, subtract 12 from hours 13–23 and add PM; hours 00 become 12 AM. Count time across midnight in two parts: up to 24:00 (00:00), then from 00:00 on.
Before midnight
17:50 → 24:00 = 370 min
After midnight
00:00 → 02:45 = 165 min
Total
t = 370 + 165 = 535 min
Answer
t = 535 min
3.Dosage calculations
Answer: V = 0.4 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.
Concentration after mixing
500 mg/2 mL = 250 mg/mL
Volume
V = 100/250 = 0.4 mL
Answer
V = 0.4 mL
4.Dosage calculations
Answer: V = 0.68 mL
Drawing up a dose: volume = (prescribed dose/stock strength) × stock volume. Convert to the same units first, then check that the volume fits the syringe and lands on one of its graduations.
Volume
V = 6800/10000 = 0.68 mL
On the syringe
On this 1 mL syringe every small line is 0.01 mL.
Answer
V = 0.68 mL
5.IV infusion rates
Answer: R = 21 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
4·60 = 240 min
Drip rate
R = 500·10/240 = 20.83 ≈ 21 gtt/min
Answer
R = 21 gtt/min
At the bedside you round to the nearest whole drop: 21 gtt/min.
6.IV infusion rates
Answer: t = 2 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.
Rate in mL/h
50·60/20 = 150 mL/h
Time left
t = 300/150 = 2 h
Answer
t = 2 h
7.IV fluids & fluid balance
Answer: I = 1190 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: 240 + 100 = 340 mL
ice chips: 100/2 = 50 mL
IV infusion: 75·8 = 600 mL
IV antibiotic: 2·100 = 200 mL
I = 1190 mL
Answer
I = 1190 mL
8.IV fluids & fluid balance
Answer: t = 1.3 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.
Volume left
500 − 300 = 200 mL
Time
t = 200/150 = 1.333 ≈ 1.3 h
Answer
t = 1.3 h
That is about 1 h 20 min, so the bag runs out at about 14:20.
9.Pediatric & critical-care dosing
Answer: R = 2.6 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
0.05·52 = 2.6 units/h
Concentration
50/50 = 1 units/mL
Pump rate
R = 2.6/1 = 2.6 mL/h
Answer
R = 2.6 mL/h
10.Pediatric & critical-care dosing
Answer: R = 4.5 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
50 000/250 = 200 mcg/mL
Dose per hour
The order is per minute for the whole patient, so the weight is not needed.
15·60 = 900 mcg/h
Pump rate
R = 900/200 = 4.5 mL/h
Answer
R = 4.5 mL/h
11.Pharmacy calculations
Answer: V = 3.8 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
7.2 + 0.3 = 7.5 mL
Concentration
750/7.5 = 100 mg/mL
Volume to give
V = 375/100 = 3.75 ≈ 3.8 mL
Answer
V = 3.8 mL
12.Pharmacy calculations
Answer: V = 720 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
30%: 6 − 0 = 6 parts
0%: 30 − 6 = 24 parts
total: 30 parts
Water
V = 900·24/30 = 720 mL
Answer
V = 720 mL
Check: 180 mL of 30% contains 54 g of drug, which is 6% of 900 mL.