Med Math Practice Quiz

19 Questions 11 min

This Med Math Practice Quiz checks EMS medication calculations using the Master Formula and dimensional analysis. You will practice weight-based dosing (mg/kg, mcg/kg/min), concentration and dilution math, and infusion conversions to mL/hr and gtt/min. Paramedics, EMTs, AEMTs, and ED nurses use these setups to prevent unit-driven dose errors.

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Part 1 — Questions

Answer each question on paper. Do not turn the page until you are ready to check your work.

A protocol orders a medication in mg/kg. Your patient weighs 110 lb. What weight should you use in kilograms (rounded to the nearest whole kg)?

55 kg
45 kg
50 kg
60 kg

1 mg equals 1,000 mcg.

True
False

You grab a microdrip set for a gravity infusion. What drop factor should you assume?

15 gtt/mL
10 gtt/mL
20 gtt/mL
60 gtt/mL

Order: morphine 4 mg IV. Vial: 2 mg/mL. How many mL will you draw up?

2 mL
1 mL
4 mL
3 mL

You need to document a dose in mg. How many mg are in 0.5 g?

5,000 mg
50 mg
500 mg
5 mg

If an order is written in mg/kg, it is acceptable to keep the patient weight in pounds as long as you label the unit.

True
False

Order: 0.25 mg. On hand: 1 mg in 2 mL. How many mL do you give?

1 mL
2 mL
0.25 mL
0.5 mL

Your pump needs mL/hr. You are told to infuse 30 mL over 15 minutes. What rate should you program?

90 mL/hr
180 mL/hr
120 mL/hr
60 mL/hr

Order: 0.1 mg/kg. Patient weight: 60 kg. What total dose is ordered?

0.6 mg
600 mg
60 mg
6 mg

10.

Order: ketamine 0.3 mg/kg IV. Patient: 176 lb. Vial: 50 mg/mL. How many mL will you administer (round to the nearest hundredth)?

0.48 mL
1.20 mL
0.96 mL
0.24 mL

11.

Order: norepinephrine 0.08 mcg/kg/min. Patient: 70 kg. Bag: 4 mg in 250 mL. What pump rate in mL/hr do you program (round to the nearest whole mL/hr)?

14 mL/hr
21 mL/hr
7 mL/hr
42 mL/hr

12.

A pump is running at 125 mL/hr, but the pump fails and you must switch to gravity with 15 gtt/mL tubing. Approximately what rate in gtt/min will match 125 mL/hr (round to the nearest whole drop)?

125 gtt/min
47 gtt/min
31 gtt/min
21 gtt/min

13.

If the tubing drop factor (gtt/mL) is unknown, you cannot safely calculate a gravity drip rate in gtt/min.

True
False

14.

Order: dopamine 5 mcg/kg/min. Patient: 80 kg. Bag: 400 mg in 250 mL. What pump rate in mL/hr do you program (round to the nearest whole mL/hr)?

15 mL/hr
150 mL/hr
30 mL/hr
6 mL/hr

15.

Order: fentanyl 1 mcg/kg IV. Patient: 72 kg. Vial: 50 mcg/mL. How many mL will you administer (round to the nearest hundredth)?

1.44 mL
14.40 mL
2.88 mL
0.72 mL

16.

You are running 1,000 mL of NS over 8 hours using 10 gtt/mL tubing. What drip rate in gtt/min is closest (round to the nearest whole drop)?

31 gtt/min
17 gtt/min
26 gtt/min
21 gtt/min

17.

Order: lidocaine 1.5 mg/kg IV. Patient: 198 lb. Vial: 100 mg in 5 mL. How many mL will you administer (round to the nearest hundredth)?

7.50 mL
6.75 mL
4.50 mL
9.00 mL

18.

Order: amiodarone 1 mg/min infusion. Bag: 150 mg in 100 mL. What pump rate in mL/hr will deliver 1 mg/min?

60 mL/hr
40 mL/hr
90 mL/hr
25 mL/hr

19.

You must run 250 mL over 20 minutes by gravity using microdrip tubing (60 gtt/mL). What drip rate in gtt/min should you set (round to the nearest whole drop)?

375 gtt/min
125 gtt/min
750 gtt/min
900 gtt/min

20.

For a vasoactive infusion ordered in mcg/kg/min, rounding the patient weight to the nearest 10 kg before calculating the rate is best practice.

True
False

21.

Order: epinephrine infusion 0.1 mcg/kg/min. Patient: 18 kg. Mix: 1 mg in 250 mL. What pump rate in mL/hr do you program (round to the nearest whole mL/hr)?

54 mL/hr
7 mL/hr
27 mL/hr
108 mL/hr

22.

Order: atropine 0.15 mg IV. Vial: 0.4 mg/mL. How many mL will you administer (round to the nearest hundredth)?

0.38 mL
1.50 mL
0.40 mL
0.15 mL

Part 2 — Answer key

Compare your answers after you have finished Part 1.

A protocol orders a medication in mg/kg. Your patient weighs 110 lb. What weight should you use in kilograms (rounded to the nearest whole kg)?
50 kg
1 mg equals 1,000 mcg.
True
You grab a microdrip set for a gravity infusion. What drop factor should you assume?
60 gtt/mL
Order: morphine 4 mg IV. Vial: 2 mg/mL. How many mL will you draw up?
2 mL
You need to document a dose in mg. How many mg are in 0.5 g?
500 mg
If an order is written in mg/kg, it is acceptable to keep the patient weight in pounds as long as you label the unit.
False
Order: 0.25 mg. On hand: 1 mg in 2 mL. How many mL do you give?
0.5 mL
Your pump needs mL/hr. You are told to infuse 30 mL over 15 minutes. What rate should you program?
120 mL/hr
Order: 0.1 mg/kg. Patient weight: 60 kg. What total dose is ordered?
6 mg
Order: ketamine 0.3 mg/kg IV. Patient: 176 lb. Vial: 50 mg/mL. How many mL will you administer (round to the nearest hundredth)?
0.48 mL
Order: norepinephrine 0.08 mcg/kg/min. Patient: 70 kg. Bag: 4 mg in 250 mL. What pump rate in mL/hr do you program (round to the nearest whole mL/hr)?
21 mL/hr
A pump is running at 125 mL/hr, but the pump fails and you must switch to gravity with 15 gtt/mL tubing. Approximately what rate in gtt/min will match 125 mL/hr (round to the nearest whole drop)?
31 gtt/min
If the tubing drop factor (gtt/mL) is unknown, you cannot safely calculate a gravity drip rate in gtt/min.
True
Order: dopamine 5 mcg/kg/min. Patient: 80 kg. Bag: 400 mg in 250 mL. What pump rate in mL/hr do you program (round to the nearest whole mL/hr)?
15 mL/hr
Order: fentanyl 1 mcg/kg IV. Patient: 72 kg. Vial: 50 mcg/mL. How many mL will you administer (round to the nearest hundredth)?
1.44 mL
You are running 1,000 mL of NS over 8 hours using 10 gtt/mL tubing. What drip rate in gtt/min is closest (round to the nearest whole drop)?
21 gtt/min
Order: lidocaine 1.5 mg/kg IV. Patient: 198 lb. Vial: 100 mg in 5 mL. How many mL will you administer (round to the nearest hundredth)?
6.75 mL
Order: amiodarone 1 mg/min infusion. Bag: 150 mg in 100 mL. What pump rate in mL/hr will deliver 1 mg/min?
40 mL/hr
You must run 250 mL over 20 minutes by gravity using microdrip tubing (60 gtt/mL). What drip rate in gtt/min should you set (round to the nearest whole drop)?
750 gtt/min
For a vasoactive infusion ordered in mcg/kg/min, rounding the patient weight to the nearest 10 kg before calculating the rate is best practice.
False
Order: epinephrine infusion 0.1 mcg/kg/min. Patient: 18 kg. Mix: 1 mg in 250 mL. What pump rate in mL/hr do you program (round to the nearest whole mL/hr)?
27 mL/hr
Order: atropine 0.15 mg IV. Vial: 0.4 mg/mL. How many mL will you administer (round to the nearest hundredth)?
0.38 mL

1A protocol orders a medication in mg/kg. Your patient weighs 110 lb. What weight should you use in kilograms (rounded to the nearest whole kg)?

21 mg equals 1,000 mcg.

True / False

3You grab a microdrip set for a gravity infusion. What drop factor should you assume?

4Order: morphine 4 mg IV. Vial: 2 mg/mL. How many mL will you draw up?

5You need to document a dose in mg. How many mg are in 0.5 g?

6If an order is written in mg/kg, it is acceptable to keep the patient weight in pounds as long as you label the unit.

True / False

7Order: 0.25 mg. On hand: 1 mg in 2 mL. How many mL do you give?

8Your pump needs mL/hr. You are told to infuse 30 mL over 15 minutes. What rate should you program?

9Order: 0.1 mg/kg. Patient weight: 60 kg. What total dose is ordered?

10Order: ketamine 0.3 mg/kg IV. Patient: 176 lb. Vial: 50 mg/mL. How many mL will you administer (round to the nearest hundredth)?

11Order: norepinephrine 0.08 mcg/kg/min. Patient: 70 kg. Bag: 4 mg in 250 mL. What pump rate in mL/hr do you program (round to the nearest whole mL/hr)?

12A pump is running at 125 mL/hr, but the pump fails and you must switch to gravity with 15 gtt/mL tubing. Approximately what rate in gtt/min will match 125 mL/hr (round to the nearest whole drop)?

13If the tubing drop factor (gtt/mL) is unknown, you cannot safely calculate a gravity drip rate in gtt/min.

True / False

14Order: dopamine 5 mcg/kg/min. Patient: 80 kg. Bag: 400 mg in 250 mL. What pump rate in mL/hr do you program (round to the nearest whole mL/hr)?

15Order: fentanyl 1 mcg/kg IV. Patient: 72 kg. Vial: 50 mcg/mL. How many mL will you administer (round to the nearest hundredth)?

16You are running 1,000 mL of NS over 8 hours using 10 gtt/mL tubing. What drip rate in gtt/min is closest (round to the nearest whole drop)?

17Order: lidocaine 1.5 mg/kg IV. Patient: 198 lb. Vial: 100 mg in 5 mL. How many mL will you administer (round to the nearest hundredth)?

18Order: amiodarone 1 mg/min infusion. Bag: 150 mg in 100 mL. What pump rate in mL/hr will deliver 1 mg/min?

19You must run 250 mL over 20 minutes by gravity using microdrip tubing (60 gtt/mL). What drip rate in gtt/min should you set (round to the nearest whole drop)?

20For a vasoactive infusion ordered in mcg/kg/min, rounding the patient weight to the nearest 10 kg before calculating the rate is best practice.

True / False

21Order: epinephrine infusion 0.1 mcg/kg/min. Patient: 18 kg. Mix: 1 mg in 250 mL. What pump rate in mL/hr do you program (round to the nearest whole mL/hr)?

22Order: atropine 0.15 mg IV. Vial: 0.4 mg/mL. How many mL will you administer (round to the nearest hundredth)?

Med Math Setup Traps: Units, Time, and Concentration Mix-ups

1) Mixing patient weight units (lb vs kg)

Most EMS protocols order mg/kg or mcg/kg/min. If weight is in pounds, convert first and then stop writing lb anywhere in the setup. Use kg = lb ÷ 2.2. A quick self-check is that adult weights in kg often fall between 40 and 120.

2) Blurring “dose ordered” with “dose on hand”

“Give 4 mg” is not the same as “4 mg/mL.” Keep two labeled lines: Desired dose (order) and Dose on hand (vial or syringe). Then apply the Master Formula with the actual label concentration and volume.

3) Prefix errors (mg vs mcg) and missing the 1,000 factor

Infusions often use mcg/kg/min while bags are mixed in mg. Write the prefix on every number and every intermediate result. Convert deliberately using 1 mg = 1,000 mcg. If your final rate changes by a factor of 1,000 after a “late” conversion, the setup was not controlled.

4) Dropping time units during infusions

Pumps require mL/hr, but many orders are per minute. Keep min and hr visible until the last step. Convert mcg/min to mcg/hr by multiplying by 60 before solving for mL/hr.

5) Using gtt/min without a drop factor

Gravity drip math is not solvable without tubing drop factor. Microdrip is 60 gtt/mL. Macrodrip is commonly 10, 15, or 20 gtt/mL. If it is not specified, flag the question as missing data.

6) Rounding too early

Carry at least two decimals through conversions and concentration steps. Round once at the end based on what you can measure or program (syringe markings, pump increment, whole drops for gtt/min).

EMS Med Math Master Formula + Infusion Conversion Quick Sheet (Printable)

Print/save as PDF: Use this as a one-page reference while practicing calculations.

Core workflow (use for every question)

Write the goal unit first (mL, mg, mcg/min, mL/hr, gtt/min).
Convert early (lb to kg, g to mg, mg to mcg, min to hr).
Label every number with units and cross-cancel units line by line.
Round once at the end, based on measurable or programmable increments.
Run a reasonableness check: does the dose, volume, and rate fit clinical reality and the concentration provided?

High-use conversions

kg = lb ÷ 2.2
1 g = 1,000 mg
1 mg = 1,000 mcg
1 hr = 60 min

Master Formula (volume to administer)

(Desired dose ÷ Dose on hand) × Volume on hand = Volume to give

Desired dose: order or protocol dose (mg, mcg).
Dose on hand: amount in vial, syringe, or vial strength (mg, mcg).
Volume on hand: mL that contains the dose on hand.

Weight-based bolus dosing

Total dose (mg or mcg) = ordered dose per kg × patient kg
Then convert dose to mL using Master Formula or a given concentration (mg/mL, mcg/mL).

Concentration, dilution, and reconstitution

Concentration = total drug amount ÷ final total volume
Volume needed (mL) = ordered dose ÷ concentration
For reconstitution, use the final volume (drug plus diluent), not the diluent alone.

Infusions

Pump rate (mL/hr) = volume (mL) ÷ time (hr)
Gravity drip (gtt/min) = (mL/hr × gtt/mL) ÷ 60

mcg/kg/min to mL/hr (common EMS pattern)

Convert lb to kg.
Compute mcg/min = (mcg/kg/min) × kg.
Convert mcg/hr = mcg/min × 60.
Compute bag concentration in mcg/mL.
Solve mL/hr = mcg/hr ÷ (mcg/mL).

Step-by-Step Paramedic Med Math: mcg/kg/min to mL/hr and Bolus mL

Example 1: Infusion conversion (mcg/kg/min to mL/hr)

Order: 0.1 mcg/kg/min. Patient: 176 lb. Bag: 4 mg in 250 mL. Goal: mL/hr.

Convert weight: 176 lb ÷ 2.2 = 80 kg.
Compute mcg/min: 0.1 mcg/kg/min × 80 kg = 8 mcg/min.
Convert to mcg/hr: 8 mcg/min × 60 = 480 mcg/hr.
Find concentration: 4 mg = 4,000 mcg. 4,000 mcg ÷ 250 mL = 16 mcg/mL.
Solve rate: 480 mcg/hr ÷ 16 mcg/mL = 30 mL/hr.

Reasonableness check: 30 mL/hr is a plausible pump rate and the units cancel cleanly to mL/hr.

Example 2: Master Formula for a bolus (mg to mL)

Order: 2 mg IV. Supply: 4 mg in 1 mL. Goal: mL to draw up.

Desired dose = 2 mg.
Dose on hand = 4 mg.
Volume on hand = 1 mL.
(2 mg ÷ 4 mg) × 1 mL = 0.5 mL.

Check: Half the mg equals half the volume because the concentration is linear.

Med Math Practice FAQ: Master Formula, Dimensional Analysis, and Pump Rates

Should I use the Master Formula or dimensional analysis for EMS med math?

Use either, but commit to one clean setup per question. The Master Formula is fast for “dose ordered” to “mL to give.” Dimensional analysis is safer for multi-step infusions because it forces units (mcg, kg, min, hr, mL) to cancel in a controlled way.

How do I prevent mg vs mcg infusion errors in mcg/kg/min problems?

Write the prefix on every line and convert the bag to a single concentration unit before solving. A reliable pattern is to convert the bag to mcg/mL first, then compute ordered mcg/hr, then divide to get mL/hr. If you see a factor-of-1,000 swing late in the work, restart and convert earlier.

What rounding is acceptable for paramedic pump rates and drip rates?

Round based on what you can deliver. For pump rates, follow the question’s pump increment if given, otherwise round to a practical decimal (often tenths). For gravity drips, you generally need a whole number of gtt/min, so round at the end after calculating with full precision.

What information must be present to calculate gtt/min?

You need the intended flow rate (usually mL/hr or total volume and time) and the tubing drop factor in gtt/mL. Microdrip is 60 gtt/mL. Macrodrip sets vary (often 10, 15, or 20 gtt/mL). If the drop factor is missing, the problem is incomplete.

I keep missing basic conversions. What else should I practice?

Practice conversions as short, timed drills: lb to kg, mg to mcg, and min to hr. If you want extra dosage calculation practice in a nursing testing format, use Nursing Entrance Exam Practice Test Questions for more unit-handling reps.

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