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 54.2653 kg. The rule in this exercise is that weights are rounded to the nearest tenth of a kilogram. What value x do you record?
54.2653 kg
x = kg
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion starts at 18:50 and finishes at 04:25 the next morning (24-hour clock). How many minutes t did it run?
18:5004:25
t = min
3.Dosage calculationsMedium
A child weighing 40 kg is prescribed 2 mg/kg of a drug. The stock solution contains 25 mg/mL. Draw up the dose: what volume V do you give?
40 kg2 mg/kg25 mg/mL
V = mL
4.Dosage calculationsHard
A patient weighs 101.2 lb. The prescription is 5 mg/kg as a single dose, and the stock contains 125 mg in 5 mL. Using 1 kg = 2.2 lb, what volume V do you give?
101.2 lb5 mg/kg125 mg/5 mL1 kg = 2.2 lb
V = mL
5.IV infusion ratesMedium
Infuse 1000 mL over 10 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 mL10 h20 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A bag contains 200 mg of a drug in 250 mL and runs at 8 mL/h. How many milligrams per hour D does the patient receive?
200 mg/250 mL8 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 fluid balance B = intake − output in mL (a negative answer means a net loss).
Practice exercise (made-up values, not clinical guidance). A 500 mL bag runs by pump at 50 mL/h. At 11:30, 50 mL have already been infused. How many hours t until the bag is empty? Round to one decimal place.
500 mL50 mL infused50 mL/h
t = h
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 12 500 units of heparin in 250 mL. The order is 14 units/kg/h for a patient who weighs 106 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
12 500 units/250 mL14 units/kg/h106 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 74 kg has an order for nitroglycerin at 30 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 mL30 mcg/min74 kg
R = mL/h
11.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial of penicillin G contains 5 000 000 units. Its practice label gives three strengths (see the table). You add 8.2 mL of diluent. The prescribed dose is 1 500 000 units. What volume V do you draw up? Round to one decimal place.
8.2 mL → 500 000 units/mL1 500 000 units
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You have 120 g of 20% zinc oxide ointment. How many grams m of plain ointment base (0%) must you add to make a 15% ointment? Round to the nearest whole gram.
120 g · 20%0%15%
m = g
3Solutions
1.Nursing math & unit conversions
Answer: x = 54.3 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
54.2653 → 2
Only the next digit decides
54.2653 → 6
6 is 5 or more, so round 2 up.
The digits after it (53) are ignored: round once, never step by step.
Round
x = 54.3 kg
Answer
x = 54.3 kg
2.Nursing math & unit conversions
Answer: t = 575 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
18:50 → 24:00 = 310 min
After midnight
00:00 → 04:25 = 265 min
Total
t = 310 + 265 = 575 min
Answer
t = 575 min
3.Dosage calculations
Answer: V = 3.2 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.
Dose from body weight
D = 2·40 = 80 mg
Volume
V = 80/25 = 3.2 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 3.2 mL
4.Dosage calculations
Answer: V = 9.2 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.
Weight in kg
101.2/2.2 = 46 kg
Dose
5·46 = 230 mg
Volume
V = (230/125)·5 = 9.2 mL
Answer
V = 9.2 mL
5.IV infusion rates
Answer: R = 33 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
10·60 = 600 min
Drip rate
R = 1000·20/600 = 33.33 ≈ 33 gtt/min
Answer
R = 33 gtt/min
At the bedside you round to the nearest whole drop: 33 gtt/min.
6.IV infusion rates
Answer: D = 6.4 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 = 0.8·8 = 6.4 mg/h
Answer
D = 6.4 mg/h
7.IV fluids & fluid balance
Answer: B = 445 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.
Total intake
oral: 150 + 120 + 100 = 370 mL
IV infusion: 125·8 = 1000 mL
IV antibiotic: 1·100 = 100 mL
total intake = 1470 mL
Total output
475 + 450 + 100 = 1025 mL
Balance
B = 1470 − 1025 = 445 mL
Answer
B = 445 mL
Positive: more fluid went in than came out.
8.IV fluids & fluid balance
Answer: t = 9 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 − 50 = 450 mL
Time
t = 450/50 = 9 h
Answer
t = 9 h
That is about 9 h 00 min, so the bag runs out at about 20:30.
9.Pediatric & critical-care dosing
Answer: R = 29.7 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
14·106 = 1 484 units/h
Concentration
12 500/250 = 50 units/mL
Pump rate
R = 1484/50 = 29.68 ≈ 29.7 mL/h
Answer
R = 29.7 mL/h
10.Pediatric & critical-care dosing
Answer: R = 9 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.
30·60 = 1800 mcg/h
Pump rate
R = 1800/200 = 9 mL/h
Answer
R = 9 mL/h
11.Pharmacy calculations
Answer: V = 3 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.
Concentration from the label
8.2 mL → 500 000 units/mL
Volume to give
V = 1 500 000/500 000 = 3 mL
Answer
V = 3 mL
12.Pharmacy calculations
Answer: m = 40 g
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.