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 6:20 PM. Which entry is the same time on the 24-hour clock? Click it.
6:20 PM
118:20
206:20
319:20
417:20
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion starts at 19:55 and finishes at 02:45 the next morning (24-hour clock). How many minutes t did it run?
19:5502:45
t = min
3.Dosage calculationsMedium
A vial contains 1 g of powder. The label says: add 4.2 mL of water for injection to give a total volume of 5 mL. The prescription is 120 mg. What volume V of the reconstituted solution do you give?
1 g+ 4.2 mL → 5 mL120 mg
V = mL
4.Dosage calculationsHard
An infusion contains 50000 units of a drug in 1000 mL. The prescription is 1250 units per hour. At what rate R do you set the pump, in mL/h?
50000 units/1000 mL1250 units/h
R = mL/h
5.IV infusion ratesMedium
500 mL was ordered over 10 hours. After 6 hours you find that 230 mL is still in the bag, and the order must still finish on time. To what rate R in mL/h must the pump be reset?
500 mL / 10 hafter 6 h: 230 mL
R = mL/h
6.IV infusion ratesHard
A drip runs at 50 gtt/min through a set of 20 gtt/mL. There are 400 mL left in the bag. How many hours t until it is empty? Round to one decimal place.
50 gtt/min20 gtt/mL400 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 patient weighs 48 kg. Find the average urine output U in mL/kg/h. Round to two decimal places.
Practice exercise (made-up values, not clinical guidance). A 1000 mL bag runs by pump at 120 mL/h. At 15:00, 150 mL have already been infused. How many hours t until the bag is empty? Round to one decimal place.
1000 mL150 mL infused120 mL/h
t = h
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 25 000 units of heparin in 250 mL. The order is 18 units/kg/h for a patient who weighs 97 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
25 000 units/250 mL18 units/kg/h97 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dopamine 400 mg in 250 mL. The order is 15 mcg/kg/min for a patient who weighs 73 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
400 mg/250 mL15 mcg/kg/min73 kg
R = mL/h
11.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains oxacillin 2000 mg as a powder. The practice label says to add 11.5 mL of sterile water; the powder adds 1 mL to the volume. What is the concentration C in mg/mL after reconstitution?
2000 mg11.5 mL+1 mL
C = mg/mL
12.Pharmacy calculationsHard
A vial holds 1000 mg of powder. You add 9.4 mL of diluent, and the powder adds 0.6 mL of volume. The prescription is 130 mg. Draw up the dose: what volume V do you give?
1000 mg9.4 mL + 0.6 mL130 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: 18:20
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
6 PM → 6 + 12 = 18
Answer
18:20
Answer
18:20
2.Nursing math & unit conversions
Answer: t = 410 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
19:55 → 24:00 = 245 min
After midnight
00:00 → 02:45 = 165 min
Total
t = 245 + 165 = 410 min
Answer
t = 410 min
3.Dosage calculations
Answer: V = 0.6 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
1000 mg/5 mL = 200 mg/mL
Volume
V = 120/200 = 0.6 mL
Answer
V = 0.6 mL
4.Dosage calculations
Answer: R = 25 mL/h
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
50000/1000 = 50 units/mL
Pump rate
R = 1250/50 = 25 mL/h
Answer
R = 25 mL/h
5.IV infusion rates
Answer: R = 57.5 mL/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.
Original rate
500/10 = 50 mL/h
New rate
R = 230/4 = 57.5 mL/h
Answer
R = 57.5 mL/h
Many hospitals allow such an adjustment up to 25% without a new order; check local policy.
6.IV infusion rates
Answer: t = 2.7 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 = 400/150 = 2.667 ≈ 2.7 h
Answer
t = 2.7 h
7.IV fluids & fluid balance
Answer: U = 1.56 mL/kg/h
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.
Total urine
225 + 375 = 600 mL
Per kilogram per hour
U = 600/(48·8) = 1.563 ≈ 1.56 mL/kg/h
Answer
U = 1.56 mL/kg/h
8.IV fluids & fluid balance
Answer: t = 7.1 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
1000 − 150 = 850 mL
Time
t = 850/120 = 7.083 ≈ 7.1 h
Answer
t = 7.1 h
That is about 7 h 05 min, so the bag runs out at about 22:05.
9.Pediatric & critical-care dosing
Answer: R = 17.5 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
18·97 = 1 746 units/h
Concentration
25 000/250 = 100 units/mL
Pump rate
R = 1746/100 = 17.46 ≈ 17.5 mL/h
Answer
R = 17.5 mL/h
10.Pediatric & critical-care dosing
Answer: R = 41.1 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
400 mg = 400 000 mcg
400 000/250 = 1600 mcg/mL
Dose per minute and per hour
15·73 = 1095 mcg/min
1095·60 = 65700 mcg/h
Pump rate
R = 65700/1600 = 41.06 ≈ 41.1 mL/h
Answer
R = 41.1 mL/h
11.Pharmacy calculations
Answer: C = 160 mg/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
11.5 + 1 = 12.5 mL
Concentration
C = 2000/12.5 = 160 mg/mL
Answer
C = 160 mg/mL
12.Pharmacy calculations
Answer: V = 1.3 mL
Strength to volume: turn the strength into mg per mL first. A w/v percentage is grams per 100 mL, so x% = 10x mg/mL. A ratio strength 1:n is 1 g in n mL. After reconstitution the concentration is the powder's dose over the final volume (diluent + powder volume). Then volume = dose/concentration.