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 5:20 AM. Which entry is the same time on the 24-hour clock? Click it.
5:20 AM
117:20
206:20
305:20
404:20
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion delivers 20 mcg/min. Express this dose rate D in mg/h.
20 mcg/min1 h = 60 min1 mg = 1000 mcg
D = mg/h
3.Dosage calculationsMedium
A patient weighs 30 kg. The prescribed dose is 7.5 mg/kg per day, given in 3 equal doses. How many milligrams D are given per dose?
30 kg7.5 mg/kg/day3× per day
D = mg
4.Dosage calculationsHard
A patient is 164 cm tall and weighs 40 kg. The prescription is 50 mg/m². Using the Mosteller formula BSA = √(height (cm) × weight (kg)/3600), find the dose D in mg.
164 cm40 kg50 mg/m²
D = mg
5.IV infusion ratesMedium
1500 mL was ordered over 8 hours. After 2 hours you find that 1350 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?
1500 mL / 8 hafter 2 h: 1350 mL
R = mL/h
6.IV infusion ratesHard
A drip runs at 30 gtt/min through a set of 15 gtt/mL. There are 450 mL left in the bag. How many hours t until it is empty? Round to one decimal place.
30 gtt/min15 gtt/mL450 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 89 kg. Find the average urine output U in mL/kg/h. Round to two decimal places.
89 kg8 hurine: 175 mLurine: 300 mL
U = mL/kg/h
8.IV fluids & fluid balanceHard
Practice exercise (made-up values, not clinical guidance). A 500 mL bag was started at 10:15 and runs by pump at 50 mL/h. How many mL V are left in the bag at 17:45?
500 mL50 mL/h10:15 → 17:45
V = mL
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion contains 50 units of regular insulin in 250 mL. The order is 0.1 units/kg/h for a patient who weighs 79 kg. Find the pump rate R in mL/h. Round to one decimal place.
50 units/250 mL0.1 units/kg/h79 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dobutamine 250 mg in 250 mL. The order is 10 mcg/kg/min for a patient who weighs 62 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
250 mg/250 mL10 mcg/kg/min62 kg
R = mL/h
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.38 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.38 mg
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 200 mL of 2% 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%2%200 mL
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: 05:20
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
5 AM → 05
Answer
05:20
Answer
05:20
2.Nursing math & unit conversions
Answer: D = 1.2 mg/h
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 = 20 mcg/min × (60 min/1 h) × (1 mg/1000 mcg)
Calculate
D = 20·60/1000 = 1.2 mg/h
Answer
D = 1.2 mg/h
3.Dosage calculations
Answer: D = 75 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
7.5·30 = 225 mg
Per dose
D = 225/3 = 75 mg
Answer
D = 75 mg
4.Dosage calculations
Answer: D = 67.49 mg
Body-surface-area dosing: many cytotoxic and some paediatric doses are prescribed per square metre of body surface area: dose (mg) = dose per m² × BSA (m²). The Mosteller formula estimates BSA = √(height (cm) × weight (kg)/3600).
Body surface area
BSA = √(164·40/3600) = √1.822 = 1.35 m²
Dose
D = 50·1.35 = 67.49 mg
Answer
D = 67.49 mg
5.IV infusion rates
Answer: R = 225 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
1500/8 = 187.5 mL/h
New rate
R = 1350/6 = 225 mL/h
Answer
R = 225 mL/h
Many hospitals allow such an adjustment up to 25% without a new order; check local policy.
6.IV infusion rates
Answer: t = 3.8 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
30·60/15 = 120 mL/h
Time left
t = 450/120 = 3.75 ≈ 3.8 h
Answer
t = 3.8 h
7.IV fluids & fluid balance
Answer: U = 0.67 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
175 + 300 = 475 mL
Per kilogram per hour
U = 475/(89·8) = 0.6671 ≈ 0.67 mL/kg/h
Answer
U = 0.67 mL/kg/h
8.IV fluids & fluid balance
Answer: V = 125 mL
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.
Elapsed time
10:15 → 17:45 = 7.5 h
Volume infused
50·7.5 = 375 mL
Volume left
V = 500 − 375 = 125 mL
Answer
V = 125 mL
9.Pediatric & critical-care dosing
Answer: R = 39.5 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
0.1·79 = 7.9 units/h
Concentration
50/250 = 0.2 units/mL
Pump rate
R = 7.9/0.2 = 39.5 mL/h
Answer
R = 39.5 mL/h
10.Pediatric & critical-care dosing
Answer: R = 37.2 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
250 mg = 250 000 mcg
250 000/250 = 1000 mcg/mL
Dose per minute and per hour
10·62 = 620 mcg/min
620·60 = 37200 mcg/h
Pump rate
R = 37200/1000 = 37.2 mL/h
Answer
R = 37.2 mL/h
11.Pharmacy calculations
Answer: V = 3.8 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.
Strength in mg/mL
1000 mg/10 000 mL = 0.1 mg/mL
Volume
V = 0.38/0.1 = 3.8 mL
Answer
V = 3.8 mL
12.Pharmacy calculations
Answer: V = 180 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%: 2 − 0 = 2 parts
0%: 20 − 2 = 18 parts
total: 20 parts
Water
V = 200·18/20 = 180 mL
Answer
V = 180 mL
Check: 20 mL of 20% contains 4 g of drug, which is 2% of 200 mL.