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 calculation for a small injection gives 0.27164 mL. The rule in this exercise is that volumes below 1 mL are rounded to the nearest hundredth of a mL. What value x do you record?
0.27164 mL
x = mL
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion starts at 22:00 and finishes at 04:30 the next morning (24-hour clock). How many minutes t did it run?
22:0004:30
t = min
3.Dosage calculationsMedium
A patient weighs 25 kg. The prescribed dose is 2 mg/kg per day, given in 2 equal doses. How many milligrams D are given per dose?
25 kg2 mg/kg/day2× per day
D = mg
4.Dosage calculationsHard
An infusion contains 40000 units of a drug in 500 mL. The prescription is 800 units per hour. At what rate R do you set the pump, in mL/h?
40000 units/500 mL800 units/h
R = mL/h
5.IV infusion ratesMedium
A drip runs at 30 gtt/min through a set of 60 gtt/mL. How many millilitres V does the patient receive in 8 hours?
30 gtt/min60 gtt/mL8 h
V = mL
6.IV infusion ratesHard
A drip runs at 25 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?
25 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 12-hour shift. The patient weighs 76 kg. Find the average urine output U in mL/kg/h. Round to two decimal places.
76 kg12 hurine: 450 mLurine: 450 mLwound drain: 130 mL
U = mL/kg/h
8.IV fluids & fluid balanceHard
Practice exercise (made-up values, not clinical guidance). A 1000 mL infusion starts at 12:00 at 100 mL/h. After 2 hours the rate is changed to 80 mL/h and is not changed again. How many hours t after the start will the bag be empty? Round to one decimal place.
1000 mL100 mL/h · 2 h80 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 10 mL/h. How many units per hour D does the patient receive?
250 units/250 mL10 mL/h
D = units/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 86 kg has an order for norepinephrine at 10 mcg/min. The bag contains 4 mg in 250 mL. Find the pump rate R in mL/h. Round to one decimal place.
4 mg/250 mL10 mcg/min86 kg
R = mL/h
11.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains cefazolin 1000 mg as a powder. The practice label says to add 4.5 mL of sterile water; the powder adds 0.5 mL to the volume. What is the concentration C in mg/mL after reconstitution?
1000 mg4.5 mL+0.5 mL
C = mg/mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 400 mL of 20% dextrose by mixing 50% and 10% dextrose. How many mL V of the 50% solution do you need? Round to the nearest whole mL.
50%10%20%400 mL
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: x = 0.27 mL
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 hundredths place
0.27164 → 7
Only the next digit decides
0.27164 → 1
1 is 4 or less, so 7 stays.
The digits after it (64) are ignored: round once, never step by step.
Round
x = 0.27 mL
Answer
x = 0.27 mL
2.Nursing math & unit conversions
Answer: t = 390 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
22:00 → 24:00 = 120 min
After midnight
00:00 → 04:30 = 270 min
Total
t = 120 + 270 = 390 min
Answer
t = 390 min
3.Dosage calculations
Answer: D = 25 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
2·25 = 50 mg
Per dose
D = 50/2 = 25 mg
Answer
D = 25 mg
4.Dosage calculations
Answer: R = 10 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
40000/500 = 80 units/mL
Pump rate
R = 800/80 = 10 mL/h
Answer
R = 10 mL/h
5.IV infusion rates
Answer: V = 240 mL
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
30·60/60 = 30 mL/h
Volume
V = 30·8 = 240 mL
Answer
V = 240 mL
6.IV infusion rates
Answer: t = 4.5 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
25·60/15 = 100 mL/h
Time left
t = 450/100 = 4.5 h
Answer
t = 4.5 h
7.IV fluids & fluid balance
Answer: U = 0.99 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
450 + 450 = 900 mL
Per kilogram per hour
U = 900/(76·12) = 0.9868 ≈ 0.99 mL/kg/h
Answer
U = 0.99 mL/kg/h
8.IV fluids & fluid balance
Answer: t = 12 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.
First part
100·2 = 200 mL
1000 − 200 = 800 mL left
Second part
800/80 = 10 h
Total time
t = 2 + 10 = 12 h
Answer
t = 12 h
That is about 12 h 00 min, so the bag runs out at about 00:00.
9.Pediatric & critical-care dosing
Answer: D = 10 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 = 10·1 = 10 units/h
Answer
D = 10 units/h
10.Pediatric & critical-care dosing
Answer: R = 37.5 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
4 000/250 = 16 mcg/mL
Dose per hour
The order is per minute for the whole patient, so the weight is not needed.
10·60 = 600 mcg/h
Pump rate
R = 600/16 = 37.5 mL/h
Answer
R = 37.5 mL/h
11.Pharmacy calculations
Answer: C = 200 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
4.5 + 0.5 = 5 mL
Concentration
C = 1000/5 = 200 mg/mL
Answer
C = 200 mg/mL
12.Pharmacy calculations
Answer: V = 100 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.