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 drip-rate calculation gives 47.238 gtt/min. The rule in this exercise is that drip rates are rounded to the nearest whole drop. What value x do you record?
47.238 gtt/min
x = gtt/min
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). A serum creatinine result is 2.9 mg/dL. Using 1 mg/dL = 88.4 µmol/L for creatinine, find c in µmol/L to the nearest whole number.
2.9 mg/dL1 mg/dL = 88.4 µmol/L
c = µmol/L
3.Dosage calculationsMedium
How many milligrams of drug m are in 2 mL of a 5% (w/v) solution?
5% w/v2 mL
m = mg
4.Dosage calculationsHard
You must prepare 500 mL of a 0.5% (w/v) solution from a 25% (w/v) stock solution. How much water W must be added to the stock?
C₁ = 25%C₂ = 0.5%V₂ = 500 mL
W = mL
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 2 hours?
30 gtt/min60 gtt/mL2 h
V = mL
6.IV infusion ratesHard
A drip runs at 30 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? Round to one decimal place.
30 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 55 kg. Find the average urine output U in mL/kg/h. Round to two decimal places.
55 kg12 hurine: 325 mLurine: 275 mLurine: 175 mL
U = mL/kg/h
8.IV fluids & fluid balanceHard
Practice exercise (made-up values, not clinical guidance). A 1000 mL bag was started at 12:30 and runs by pump at 60 mL/h. How many mL V are left in the bag at 19:30?
1000 mL60 mL/h12:30 → 19:30
V = mL
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A practice protocol calls for a heparin bolus of 60 units/kg for a patient who weighs 94 kg. The vial contains 1 000 units/mL. What volume V do you draw up? Round to one decimal place.
60 units/kg94 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 5 mcg/kg/min for a patient who weighs 72 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
500 mg/250 mL5 mcg/kg/min72 kg
R = mL/h
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.8 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.8 mg
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You have 60 g of 5% coal tar ointment. How many grams m of 1% coal tar ointment must you add to make a 2% ointment? Round to the nearest whole gram.
60 g · 5%1%2%
m = g
3Solutions
1.Nursing math & unit conversions
Answer: x = 47 gtt/min
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 ones place
47.238 → 7
Only the next digit decides
47.238 → 2
2 is 4 or less, so 7 stays.
The digits after it (38) are ignored: round once, never step by step.
Round
x = 47 gtt/min
Answer
x = 47 gtt/min
2.Nursing math & unit conversions
Answer: c = 256 µmol/L
Dimensional analysis: write the given quantity, then multiply by conversion factors written as fractions (for example 60 min/1 h or 1 mg/1000 mcg) so that each unwanted unit appears once on top and once underneath and cancels. When only the wanted unit is left, calculate. Use the equivalents the question gives and round only the final answer.
Convert
c = 2.9·88.4 = 256.4 ≈ 256 µmol/L
Answer
c = 256 µmol/L
3.Dosage calculations
Answer: m = 100 mg
Solution strengths: a percentage strength is grams per 100 mL, so 1% = 1 g/100 mL = 10 mg/mL. A ratio strength 1:1000 means 1 g in 1000 mL = 1 mg/mL; 1:10 000 is 0.1 mg/mL. For a dilution the amount of drug stays the same: C₁·V₁ = C₂·V₂.
Concentration
5% = 5 g/100 mL = 50 mg/mL
Mass of drug
m = 50·2 = 100 mg
Answer
m = 100 mg
4.Dosage calculations
Answer: W = 490 mL
Solution strengths: a percentage strength is grams per 100 mL, so 1% = 1 g/100 mL = 10 mg/mL. A ratio strength 1:1000 means 1 g in 1000 mL = 1 mg/mL; 1:10 000 is 0.1 mg/mL. For a dilution the amount of drug stays the same: C₁·V₁ = C₂·V₂.
Volume of stock
V₁ = 0.5·500/25 = 10 mL
Water to add
W = 500 − 10 = 490 mL
Answer
W = 490 mL
5.IV infusion rates
Answer: V = 60 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 = 30·2 = 60 mL
Answer
V = 60 mL
6.IV infusion rates
Answer: t = 3.8 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
30·60/15 = 120 mL/h
Time left
t = 450/120 = 3.75 ≈ 3.8 h
Answer
t = 3.8 h
7.IV fluids & fluid balance
Answer: U = 1.17 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
325 + 275 + 175 = 775 mL
Per kilogram per hour
U = 775/(55·12) = 1.174 ≈ 1.17 mL/kg/h
Answer
U = 1.17 mL/kg/h
8.IV fluids & fluid balance
Answer: V = 580 mL
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.
Elapsed time
12:30 → 19:30 = 7 h
Volume infused
60·7 = 420 mL
Volume left
V = 1000 − 420 = 580 mL
Answer
V = 580 mL
9.Pediatric & critical-care dosing
Answer: V = 5.6 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
60·94 = 5 640 units
Volume
V = 5640/1000 = 5.64 ≈ 5.6 mL
Answer
V = 5.6 mL
10.Pediatric & critical-care dosing
Answer: R = 10.8 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
5·72 = 360 mcg/min
360·60 = 21600 mcg/h
Pump rate
R = 21600/2000 = 10.8 mL/h
Answer
R = 10.8 mL/h
11.Pharmacy calculations
Answer: V = 8 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 = 0.8/0.1 = 8 mL
Answer
V = 8 mL
12.Pharmacy calculations
Answer: m = 180 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.