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 0.88664 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?
0.88664 mL
x = mL
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion starts at 23:25 and finishes at 01:00 the next morning (24-hour clock). How many minutes t did it run?
23:2501:00
t = min
3.Dosage calculationsMedium
A dose of 12.5 mg is needed from a 0.5% (w/v) solution. What volume V contains this dose?
12.5 mg0.5% w/v
V = mL
4.Dosage calculationsHard
A child weighing 20 kg is prescribed 15 mg/kg per dose of an oral suspension that contains 120 mg in 5 mL. What volume V do you give?
20 kg15 mg/kg120 mg/5 mL
V = mL
5.IV infusion ratesMedium
An infusion is ordered at 90 mL/h, but no pump is available. It runs by gravity through a giving set of 10 gtt/mL. Find the drip rate R in drops per minute.
90 mL/h10 gtt/mL
R = gtt/min
6.IV infusion ratesHard
1500 mL was ordered over 10 hours. After 5 hours you find that 830 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?
1500 mL / 10 hafter 5 h: 830 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 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). Count ice chips as half their volume.
Practice exercise (made-up values, not clinical guidance). A 1000 mL bag runs by pump at 50 mL/h. At 13:30, 800 mL have already been infused. How many hours t until the bag is empty? Round to one decimal place.
1000 mL800 mL infused50 mL/h
t = h
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion contains 50 units of regular insulin in 50 mL. The order is 0.1 units/kg/h for a patient who weighs 93 kg. Find the pump rate R in mL/h. Round to one decimal place.
50 units/50 mL0.1 units/kg/h93 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dopamine 400 mg in 250 mL. The order is 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.
400 mg/250 mL5 mcg/kg/min50 kg
R = mL/h
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:1000. You need 0.57 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.57 mg
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You have 30 g of 5% coal tar ointment. How many grams m of 1% coal tar ointment must you add to make a 3% ointment? Round to the nearest whole gram.
30 g · 5%1%3%
m = g
3Solutions
1.Nursing math & unit conversions
Answer: x = 0.89 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
0.88664 → 8
Only the next digit decides
0.88664 → 6
6 is 5 or more, so round 8 up.
The digits after it (64) are ignored: round once, never step by step.
Round
x = 0.89 mL
Answer
x = 0.89 mL
2.Nursing math & unit conversions
Answer: t = 95 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
23:25 → 24:00 = 35 min
After midnight
00:00 → 01:00 = 60 min
Total
t = 35 + 60 = 95 min
Answer
t = 95 min
3.Dosage calculations
Answer: V = 2.5 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.
Concentration
0.5% = 5 mg/mL
Volume
V = 12.5/5 = 2.5 mL
Answer
V = 2.5 mL
4.Dosage calculations
Answer: V = 12.5 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.
Dose from weight
15·20 = 300 mg
Volume
V = (300/120)·5 = 12.5 mL
Answer
V = 12.5 mL
5.IV infusion rates
Answer: R = 15 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.
Millilitres per minute
90/60 = 1.5 mL/min
Drip rate
R = 1.5·10 = 15 gtt/min
Answer
R = 15 gtt/min
6.IV infusion rates
Answer: Δ = 10.67 %
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
1500/10 = 150 mL/h
New rate
R = 830/5 = 166 mL/h
Percentage change
Δ = (166 − 150)/150·100% = 10.67%
Answer
Δ = 10.67%
Many hospitals allow such an adjustment up to 25% without a new order; check local policy.
7.IV fluids & fluid balance
Answer: B = 865 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: 240 + 100 = 340 mL
ice chips: 100/2 = 50 mL
IV infusion: 125·8 = 1000 mL
IV antibiotic: 1·50 = 50 mL
total intake = 1440 mL
Total output
275 + 200 + 100 = 575 mL
Balance
B = 1440 − 575 = 865 mL
Answer
B = 865 mL
Positive: more fluid went in than came out.
8.IV fluids & fluid balance
Answer: t = 4 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 − 800 = 200 mL
Time
t = 200/50 = 4 h
Answer
t = 4 h
That is about 4 h 00 min, so the bag runs out at about 17:30.
9.Pediatric & critical-care dosing
Answer: R = 9.3 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
0.1·93 = 9.3 units/h
Concentration
50/50 = 1 units/mL
Pump rate
R = 9.3/1 = 9.3 mL/h
Answer
R = 9.3 mL/h
10.Pediatric & critical-care dosing
Answer: R = 9.4 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
400 mg = 400 000 mcg
400 000/250 = 1600 mcg/mL
Dose per minute and per hour
5·50 = 250 mcg/min
250·60 = 15000 mcg/h
Pump rate
R = 15000/1600 = 9.375 ≈ 9.4 mL/h
Answer
R = 9.4 mL/h
11.Pharmacy calculations
Answer: V = 0.57 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/1000 mL = 1 mg/mL
Volume
V = 0.57/1 = 0.57 mL
Answer
V = 0.57 mL
12.Pharmacy calculations
Answer: m = 30 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.