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 patient’s temperature is 102.4 °F. Convert it to degrees Celsius T with °C = (°F − 32) × 5/9. Round to one decimal place.
102.4 °F
T = °C
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion starts at 23:25 and finishes at 08:50 the next morning (24-hour clock). How many hours t did it run? Give the answer in hours as a decimal, rounded to two decimal places.
23:2508:50
t = h
3.Dosage calculationsMedium
A patient weighs 15 kg. The prescribed dose is 15 mg/kg per day, given in 3 equal doses. How many milligrams D are given per dose?
15 kg15 mg/kg/day3× per day
D = mg
4.Dosage calculationsHard
A child weighing 8 kg is prescribed 12.5 mg/kg per dose of an oral suspension that contains 250 mg in 5 mL. What volume V do you give?
8 kg12.5 mg/kg250 mg/5 mL
V = mL
5.IV infusion ratesMedium
Infuse 1000 mL over 5 hours with a giving set of 20 gtt/mL. Find the drip rate R in drops per minute. Round to the nearest whole number.
1000 mL5 h20 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A bag contains 400 mg of a drug in 100 mL and runs at 20 mL/h. How many milligrams per hour D does the patient receive?
400 mg/100 mL20 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 12-hour shift. The patient weighs 101 kg. Find the average urine output U in mL/kg/h. Round to two decimal places.
101 kg12 hurine: 225 mLurine: 250 mLwound drain: 150 mL
U = mL/kg/h
8.IV fluids & fluid balanceHard
Practice exercise (made-up values, not clinical guidance). A 500 mL bag runs by pump at 125 mL/h. At 10:00, 250 mL have already been infused. How many hours t until the bag is empty? Round to one decimal place.
500 mL250 mL infused125 mL/h
t = h
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion of 250 units of regular insulin in 250 mL runs at 2 mL/h. How many units per hour D does the patient receive?
250 units/250 mL2 mL/h
D = units/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dopamine infusion of 400 mg in 250 mL runs at 28 mL/h. The patient weighs 109 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
400 mg/250 mL28 mL/h109 kg
D = mcg/kg/min
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 800 mg. What volume V do you draw up? Round to one decimal place.
1000 mg9.6 mL+0.4 mL800 mg
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 250 mL of 40% dextrose by mixing 70% and 10% dextrose. How many mL V of the 10% solution do you need? Round to the nearest whole mL.
70%10%40%250 mL
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: T = 39.1 °C
Temperature: °C = (°F − 32) × 5/9 and °F = °C × 9/5 + 32. Subtract 32 before you multiply when going from °F, and add 32 after you multiply when going from °C. A quick check: 37 °C is 98.6 °F, and every 1 °C is 1.8 °F.
Subtract 32
102.4 − 32 = 70.4
Multiply by 5/9
T = 70.4·5/9 = 39.11 ≈ 39.1 °C
Answer
T = 39.1 °C
2.Nursing math & unit conversions
Answer: t = 9.42 h
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
23:25 → 24:00 = 35 min
After midnight
00:00 → 08:50 = 530 min
Total
35 + 530 = 565 min
t = 565/60 = 9.417 ≈ 9.42 h
Answer
t = 9.42 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
15·15 = 225 mg
Per dose
D = 225/3 = 75 mg
Answer
D = 75 mg
4.Dosage calculations
Answer: V = 2 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.
Dose from weight
12.5·8 = 100 mg
Volume
V = (100/250)·5 = 2 mL
Answer
V = 2 mL
5.IV infusion rates
Answer: R = 67 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
5·60 = 300 min
Drip rate
R = 1000·20/300 = 66.67 ≈ 67 gtt/min
Answer
R = 67 gtt/min
At the bedside you round to the nearest whole drop: 67 gtt/min.
6.IV infusion rates
Answer: D = 80 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
400/100 = 4 mg/mL
Dose rate
D = 4·20 = 80 mg/h
Answer
D = 80 mg/h
7.IV fluids & fluid balance
Answer: U = 0.39 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 + 250 = 475 mL
Per kilogram per hour
U = 475/(101·12) = 0.3919 ≈ 0.39 mL/kg/h
Answer
U = 0.39 mL/kg/h
8.IV fluids & fluid balance
Answer: t = 2 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 − 250 = 250 mL
Time
t = 250/125 = 2 h
Answer
t = 2 h
That is about 2 h 00 min, so the bag runs out at about 12:00.
9.Pediatric & critical-care dosing
Answer: D = 2 units/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.
Concentration
250/250 = 1 units/mL
Units per hour
D = 2·1 = 2 units/h
Answer
D = 2 units/h
10.Pediatric & critical-care dosing
Answer: D = 6.9 mcg/kg/min
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
400 000/250 = 1600 mcg/mL
Micrograms per minute
28·1600 = 44800 mcg/h
44800/60 = 746.7 mcg/min
Per kilogram
D = 746.7/109 = 6.85 ≈ 6.9 mcg/kg/min
Answer
D = 6.9 mcg/kg/min
11.Pharmacy calculations
Answer: V = 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
9.6 + 0.4 = 10 mL
Concentration
1000/10 = 100 mg/mL
Volume to give
V = 800/100 = 8 mL
Answer
V = 8 mL
12.Pharmacy calculations
Answer: V = 125 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.