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 35 °C. Convert it to degrees Fahrenheit T with °F = °C × 9/5 + 32. Round to one decimal place.
35 °C
T = °F
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion starts at 22:40 and finishes at 04:55 the next morning (24-hour clock). How many minutes t did it run?
22:4004:55
t = min
3.Dosage calculationsMedium
A patient weighs 45 kg and is prescribed 15 mg/kg as a single dose. Find the dose D in mg.
45 kg15 mg/kg
D = mg
4.Dosage calculationsHard
An infusion contains 50000 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?
50000 units/500 mL800 units/h
R = mL/h
5.IV infusion ratesMedium
Infuse 1000 mL over 10 hours with a giving set of 60 gtt/mL. Find the drip rate R in drops per minute.
1000 mL10 h60 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A bag contains 400 mg of a drug in 50 mL and runs at 25 mL/h. How many milligrams per hour D does the patient receive?
400 mg/50 mL25 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 IV infusion ran at the rate shown for the whole shift. Find the total intake I in mL. Count ice chips as half their volume.
soup: 150 mLjuice: 100 mLice chips: 100 mLIV infusion: 75 mL/h × 12 hIV antibiotic: 1 × 100 mL
I = mL
8.IV fluids & fluid balanceHard
Practice exercise (made-up values, not clinical guidance). A 1000 mL bag runs by pump at 120 mL/h. At 10:00, 200 mL have already been infused. How many hours t until the bag is empty? Round to one decimal place.
1000 mL200 mL infused120 mL/h
t = h
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 20 000 units of heparin in 500 mL. The order is 20 units/kg/h for a patient who weighs 59 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
20 000 units/500 mL20 units/kg/h59 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 85 kg has an order for norepinephrine at 12 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 mL12 mcg/min85 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 18.2 mL of diluent. The prescribed dose is 2 400 000 units. What volume V do you draw up? Round to one decimal place.
18.2 mL → 250 000 units/mL2 400 000 units
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You have 30 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.
30 g · 20%0%15%
m = g
3Solutions
1.Nursing math & unit conversions
Answer: T = 95 °F
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.
Multiply by 9/5
35·9/5 = 63
Add 32
T = 63 + 32 = 95 °F
Answer
T = 95 °F
2.Nursing math & unit conversions
Answer: t = 375 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
22:40 → 24:00 = 80 min
After midnight
00:00 → 04:55 = 295 min
Total
t = 80 + 295 = 375 min
Answer
t = 375 min
3.Dosage calculations
Answer: D = 675 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.
Dose
15·45 = 675 mg
Answer
D = 675 mg
4.Dosage calculations
Answer: R = 8 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
50000/500 = 100 units/mL
Pump rate
R = 800/100 = 8 mL/h
Answer
R = 8 mL/h
5.IV infusion rates
Answer: R = 100 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 = 1000·60/600 = 100 gtt/min
Answer
R = 100 gtt/min
6.IV infusion rates
Answer: D = 200 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
400/50 = 8 mg/mL
Dose rate
D = 8·25 = 200 mg/h
Answer
D = 200 mg/h
7.IV fluids & fluid balance
Answer: I = 1300 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.
Add the intake
oral: 150 + 100 = 250 mL
ice chips: 100/2 = 50 mL
IV infusion: 75·12 = 900 mL
IV antibiotic: 1·100 = 100 mL
I = 1300 mL
Answer
I = 1300 mL
8.IV fluids & fluid balance
Answer: t = 6.7 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 − 200 = 800 mL
Time
t = 800/120 = 6.667 ≈ 6.7 h
Answer
t = 6.7 h
That is about 6 h 40 min, so the bag runs out at about 16:40.
9.Pediatric & critical-care dosing
Answer: R = 29.5 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
20·59 = 1 180 units/h
Concentration
20 000/500 = 40 units/mL
Pump rate
R = 1180/40 = 29.5 mL/h
Answer
R = 29.5 mL/h
10.Pediatric & critical-care dosing
Answer: R = 45 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.
12·60 = 720 mcg/h
Pump rate
R = 720/16 = 45 mL/h
Answer
R = 45 mL/h
11.Pharmacy calculations
Answer: V = 9.6 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
18.2 mL → 250 000 units/mL
Volume to give
V = 2 400 000/250 000 = 9.6 mL
Answer
V = 9.6 mL
12.Pharmacy calculations
Answer: m = 10 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.