Nurse Arcade
Nursing reference guide
Dosage
Calculations
One method from medication conversions to programmed IV infusions.
Dimensional analysis – weight based – IV rates – pump programming
Learning aid. Verify the patient, current order, original label, drug information, dose limits, calculation, device configuration, monitoring, policy, and required independent checks every time.
Learning path
One method, harder problems
Dimensional analysis scales because the units show you what must cancel.
1 – Convert
Metric and common clinical equivalents. Build the conversion factor.
2 – Simple dose
Tablets, capsules, and liquids. Convert dose to amount given.
3 – Prepare
Injections and reconstitution. Read concentration after mixing.
4 – Personalize
Weight-based dose and safe range. Convert weight and time.
5 – Infuse
mL/hr, gtt/min, and medication rates. Carry every unit to the pump.
Conversion toolkit
Medication conversions come first
Use exact metric relationships. Treat household equivalents as approximate and follow the course or facility standard.
| Type | Equivalence | Second relationship | Use it safely |
|---|---|---|---|
| Mass | 1 g = 1,000 mg | 1 mg = 1,000 mcg | Move by factors of 1,000; keep the unit attached. |
| Volume | 1 L = 1,000 mL | 1 mL = 1 cm3 | Use mL for medication volumes; avoid ambiguous cc. |
| Weight | 1 kg = 2.2 lb | lb / 2.2 = kg | Weight-based orders are usually calculated in kg. |
| Household | 1 tsp = 5 mL | 1 Tbsp = 15 mL; 1 fl oz = 30 mL | Approximate teaching conversions; use a metric device. |
| Time | 60 min = 1 hr | 24 hr = 1 day | Time must cancel into the requested rate. |
| Drops | Read the tubing package | 10, 15, 20, or 60 gtt/mL are common | Never assume a drop factor. |
Medication language
Before the math: read the order safely
A correct calculation cannot rescue an incomplete, ambiguous, or misread order.
Order
Pull out the medication, ordered dose, route, frequency or rate, and indication. Confirm whether the amount is per dose, per day, or continuous.
Available
Read both the concentration and the quantity that carries it: per tablet, per 5 mL, or per 1 mL.
Answer unit
Name the requested answer before setting up: tablets, mL/dose, mg/dose, units/hr, mL/hr, or gtt/min.
Safety
Use a leading zero for amounts below one and no trailing zero after a whole number. Write unit instead of U.
The method
Dimensional analysis: build a path for the units
Start with what you know. End with the unit you need. Let everything else cancel.
1 – Name the destination
Write the answer unit first: tablets, mL/dose, mL/hr, or gtt/min.
2 – Start with the order
Place the ordered dose or rate on the left with its unit.
3 – Add conversion factors
Flip each factor so the unwanted unit can cancel.
4 – Cancel before multiplying
Each unwanted unit must appear once on top and once on the bottom.
ordered unit1available amountavailable unit= answer unitConversion demonstrations
Watch the units do the work
The arithmetic is simple after the direction of each conversion is correct.
Example 1: micrograms to milligrams
Given: 1,500 mcg. Need: mg. Use 1 mg = 1,000 mcg and place mcg on the bottom so it cancels.
Example 2: pounds to kilograms
Given: 154 lb. Need: kg. Use 1 kg = 2.2 lb with lb on the bottom.
1,500 mcg11 mg1,000 mcg= 1.5 mg154 lb11 kg2.2 lb= 70 kgSimple doses
Tablets and liquids
The quantity on the label is part of the conversion factor.
Tablet example
Order: 750 mg PO. Available: 250 mg per tablet. Need: tablets.
Liquid example
Order: 375 mg PO. Available: 125 mg in 5 mL. Need: mL/dose.
750 mg11 tablet250 mg= 3 tablets375 mg15 mL125 mg= 15 mLParenteral doses
Injectable concentrations and units
Read the route, vial amount, concentration per mL, and whether the container is single-dose or multidose.
Injection example
Order: 0.4 mg IM. Available: 1 mg/mL. Need: mL.
Unit example
Order: 2,500 units subcutaneous. Available: 10,000 units/mL. Need: mL.
0.4 mg11 mL1 mg= 0.4 mL2,500 units11 mL10,000 units= 0.25 mLPowdered medications
Reconstitution changes the concentration
Use the concentration after reconstitution, not the dry amount printed on the vial front.
1 – Read the instructions
Identify the approved diluent, volume to add, storage, stability, and route.
2 – Find the final concentration
Use the resulting mg/mL after mixing. Do not assume final volume equals diluent volume.
3 – Calculate the volume
Example: order 750 mg; final concentration 250 mg/mL.
4 – Label and verify
Record date/time, concentration, preparer, beyond-use information, and required checks.
750 mg11 mL250 mg= 3 mLPersonalized doses
Weight-based dosing: convert, calculate, divide
Keep kg, day, dose, and concentration visible so none disappear accidentally.
Worked example
Find mL per dose. Order: 20 mg/kg/day every 8 hours. Weight: 33 lb. Available: 125 mg/5 mL.
33 lb1 kg2.2 lb= 15 kg20 mgkg · day15 kg1 day3 doses= 100 mg/dose100 mgdose5 mL125 mg= 4 mL/doseDose verification
Safe-dose range: compare like with like
Calculate the ordered amount and recommended range in the same time frame before comparing.
| Step | Calculation | Result |
|---|---|---|
| 1. Convert weight | 18 kg is already in the required unit. | 18 kg |
| 2. Recommended daily range | 40-60 mg/kg/day x 18 kg | 720-1,080 mg/day |
| 3. Ordered daily amount | 250 mg every 6 hr = 4 doses/day | 1,000 mg/day |
| 4. Compare | 1,000 mg/day falls inside 720-1,080 mg/day | Within stated practice range |
| 5. Continue the check | Confirm maximum single dose, indication, organ function, allergies, and current reference. | Range alone is not authorization |
Infusion fundamentals
Basic IV rates: volume divided by time
The pump rate is usually mL/hr. Convert minutes to hours when needed.
Volume over hours
Given: 1,000 mL total and 8 hours. Need: mL/hr.
Volume over minutes
Given: 100 mL over 30 minutes. Convert 30 minutes to 0.5 hour.
1,000 mL8 hr= 125 mL/hr100 mL30 min60 min1 hr= 200 mL/hrManual infusion
Gravity flow: convert to drops per minute
The tubing package supplies the drop factor in gtt/mL.
Worked example
Volume: 100 mL. Time: 30 min. Drop factor: 15 gtt/mL. Destination: gtt/min.
100 mL30 min15 gtt1 mL= 50 gtt/min1 – Read the tubing
Never assume the drop factor.
2 – Cancel mL
Only gtt/min should remain.
3 – Round whole drops
A partial drop cannot be counted.
Advanced dimensional analysis
Medication infusions: carry every unit to mL/hr
This is the same method with more conversion factors.
Practice infusion
Order: 5 mcg/kg/min. Weight: 176 lb. Concentration: 800 mg/500 mL. Destination: mL/hr.
176 lb1 kg2.2 lb= 80 kg5 mcgkg · min80 kg60 minhr1 mg1,000 mcg500 mL800 mg= 15 mL/hrIV medication workflow
From calculation to pump programming
The calculation and device entry are two separate verification steps.
1 – Order
Read dose or rate, route, concentration, titration direction, maximum, and monitoring.
2 – Calculate
Calculate with every unit visible and round only at the approved final step.
3 – Match
Match order, pharmacy label, concentration, tubing, patient, and smart-pump library entry.
4 – Enter
Select the correct channel and profile. Enter dose or rate, concentration when prompted, and VTBI.
5 – Verify
Complete the required independent check. Read and resolve every alert.
6 – Start + watch
Trace the line, open the clamp, start the correct channel, and reassess the patient and IV site.
Show the units
Practice set
Write every setup before calculating. Answers are in the next section.
1
Convert 0.75 g to mg.
2
Convert 2,500 mcg to mg.
3
Order 600 mg. Available 300 mg/tablet. Tablets?
4
Order 225 mg. Available 150 mg/5 mL. mL?
5
Order 1,200 units. Available 5,000 units/mL. mL?
6
Order 900 mg. Reconstituted concentration 300 mg/mL. mL?
7
Infuse 750 mL over 6 hr. mL/hr?
8
Infuse 250 mL over 2.5 hr. mL/hr?
9
100 mL over 45 min with 15 gtt/mL. gtt/min?
10
10 mcg/kg/min for 60 kg; 400 mg/250 mL. mL/hr?
Answer key
Practice answers + reasoning checks
A number without the correct unit is not a complete answer.
1 – 750 mg
0.75 g x 1,000 mg/1 g
2 – 2.5 mg
2,500 mcg x 1 mg/1,000 mcg
3 – 2 tablets
600 mg x 1 tablet/300 mg
4 – 7.5 mL
225 mg x 5 mL/150 mg
5 – 0.24 mL
1,200 units x 1 mL/5,000 units
6 – 3 mL
900 mg x 1 mL/300 mg
7 – 125 mL/hr
750 mL/6 hr
8 – 100 mL/hr
250 mL/2.5 hr
9 – 33 gtt/min
100 mL/45 min x 15 gtt/mL = 33.3; whole drops
10 – 22.5 mL/hr
10 mcg/kg/min x 60 kg x 60 min/hr x 1 mg/1,000 mcg x 250 mL/400 mg
Reference notes
Sources + boundaries
Reviewed against authoritative and educational sources in July 2026.
NIST SI and unit-conversion guidance
Metric relationships, unit symbols, and conversion method.
Institute for Safe Medication Practices
Leading/trailing zero and error-prone abbreviation safeguards.
OpenStax Pharmacology for Nurses
Dosage-calculation concepts, dimensional analysis, labels, and weight-based examples.
OpenStax Clinical Nursing Skills
Factor-label method, conversions, dosing, and administration context.
BD Alaris System User Manual
Device-specific programming context and configuration boundaries.
Practice packet reviewed
A self-created, AI-assisted study packet used for practice informed topic progression only.