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 37.5 °C. Convert it to degrees Fahrenheit T with °F = °C × 9/5 + 32. Round to one decimal place.
37.5 °C
T = °F
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion starts at 17:40 and finishes at 01:00 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.
17:4001:00
t = h
3.Dosage calculationsMedium
A child weighing 8 kg is prescribed 15 mg/kg of a drug. The stock solution contains 40 mg/mL. Draw up the dose: what volume V do you give?
8 kg15 mg/kg40 mg/mL
V = mL
4.Dosage calculationsHard
An infusion contains 20000 units of a drug in 1000 mL. The prescription is 1200 units per hour. At what rate R do you set the pump, in mL/h?
20000 units/1000 mL1200 units/h
R = mL/h
5.IV infusion ratesMedium
1000 mL was ordered over 6 hours. After 3 hours you find that 590 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?
1000 mL / 6 hafter 3 h: 590 mL
R = mL/h
6.IV infusion ratesHard
500 mL was ordered over 6 hours. After 4 hours you find that 200 mL is still in the bag, and the order must still finish on time. By what percentage Δ must the original pump rate be increased?
500 mL / 6 hafter 4 h: 200 mL
Δ = %
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 67 kg. Find the average urine output U in mL/kg/h. Round to two decimal places.
67 kg8 hurine: 425 mLurine: 500 mL
U = mL/kg/h
8.IV fluids & fluid balanceHard
Practice exercise (made-up values, not clinical guidance). A 500 mL infusion starts at 10:00 at 125 mL/h. After 2 hours the rate is changed to 60 mL/h and is not changed again. How many hours t after the start will the bag be empty? Round to one decimal place.
500 mL125 mL/h · 2 h60 mL/h
t = h
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A practice protocol calls for a heparin bolus of 80 units/kg for a patient who weighs 54 kg. The vial contains 1 000 units/mL. What volume V do you draw up? Round to one decimal place.
80 units/kg54 kg1 000 units/mL
V = mL
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dobutamine 500 mg in 250 mL. The order is 7.5 mcg/kg/min for a patient who weighs 50 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
500 mg/250 mL7.5 mcg/kg/min50 kg
R = mL/h
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.26 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.26 mg
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 1000 mL of 4% 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%4%1000 mL
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: T = 99.5 °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
37.5·9/5 = 67.5
Add 32
T = 67.5 + 32 = 99.5 °F
Answer
T = 99.5 °F
2.Nursing math & unit conversions
Answer: t = 7.33 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
17:40 → 24:00 = 380 min
After midnight
00:00 → 01:00 = 60 min
Total
380 + 60 = 440 min
t = 440/60 = 7.333 ≈ 7.33 h
Answer
t = 7.33 h
3.Dosage calculations
Answer: V = 3 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 = 15·8 = 120 mg
Volume
V = 120/40 = 3 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 3 mL
4.Dosage calculations
Answer: R = 60 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
20000/1000 = 20 units/mL
Pump rate
R = 1200/20 = 60 mL/h
Answer
R = 60 mL/h
5.IV infusion rates
Answer: R = 196.7 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
1000/6 = 166.7 mL/h
New rate
R = 590/3 = 196.7 mL/h
Answer
R = 196.7 mL/h
Many hospitals allow such an adjustment up to 25% without a new order; check local policy.
6.IV infusion rates
Answer: Δ = 20 %
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
500/6 = 83.33 mL/h
New rate
R = 200/2 = 100 mL/h
Percentage change
Δ = (100 − 83.33)/83.33·100% = 20%
Answer
Δ = 20%
Many hospitals allow such an adjustment up to 25% without a new order; check local policy.
7.IV fluids & fluid balance
Answer: U = 1.73 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
425 + 500 = 925 mL
Per kilogram per hour
U = 925/(67·8) = 1.726 ≈ 1.73 mL/kg/h
Answer
U = 1.73 mL/kg/h
8.IV fluids & fluid balance
Answer: t = 6.2 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.
First part
125·2 = 250 mL
500 − 250 = 250 mL left
Second part
250/60 = 4.167 h
Total time
t = 2 + 4.167 = 6.167 ≈ 6.2 h
Answer
t = 6.2 h
That is about 6 h 10 min, so the bag runs out at about 16:10.
9.Pediatric & critical-care dosing
Answer: V = 4.3 mL
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 needed
80·54 = 4 320 units
Volume
V = 4320/1000 = 4.32 ≈ 4.3 mL
Answer
V = 4.3 mL
10.Pediatric & critical-care dosing
Answer: R = 11.3 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
500 mg = 500 000 mcg
500 000/250 = 2000 mcg/mL
Dose per minute and per hour
7.5·50 = 375 mcg/min
375·60 = 22500 mcg/h
Pump rate
R = 22500/2000 = 11.25 ≈ 11.3 mL/h
Answer
R = 11.3 mL/h
11.Pharmacy calculations
Answer: V = 2.6 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 = 0.26/0.1 = 2.6 mL
Answer
V = 2.6 mL
12.Pharmacy calculations
Answer: V = 800 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%: 4 − 0 = 4 parts
0%: 20 − 4 = 16 parts
total: 20 parts
Water
V = 1000·16/20 = 800 mL
Answer
V = 800 mL
Check: 200 mL of 20% contains 40 g of drug, which is 4% of 1000 mL.