Pharmaco Medical Calculations

Q: What is the difference between dose, dosage regimen, drug strength/concentration, and frequency?

A dose is the amount given at one time,

a dosage regimen describes how the drug is given over time,

strength/concentration describes how much drug is in the available formulation,

and frequency describes how often each dose is given.

⭐ 3. Q: How do you convert pounds (lb) to kilograms (kg)?

1 kg is 2.2 lb.

⭐ Q: How do you convert grams (g) to milligrams (mg)?

1 g = 1000 mg

⭐ Q: How do you convert milligrams (mg) to micrograms (µg)?

1 mg = 1000 ug

⭐ Q: How do you convert micrograms (µg) to nanograms (ng)?

1 ug = 1000 ng

⭐ Q: How do you convert liters (L) to milliliters (mL)?

1 L = 1000 mL

Q: What is the relationship between milliliters (mL) and cubic centimeters (cc)?

1 mL = 1 cubic cm

Q: How do you convert a percent (%) solution to mg/mL?

1% = 1 g of drug per 100 mL

1000 mg / 100 mL = 10 mg/mL

So:

• 0.9% becomes 9 mg/mL

• 1% becomes 10 mg/mL

• 2% becomes 20 mg/mL

• 5% becomes 50 mg/mL

💡 Think: % × 10 gives mg/mL.

⭐ Q: How do you convert a required drug amount in mg to a liquid volume in mL?

To convert mg to mL, divide the required mg by the drug concentration in mg/mL.

Suppose the patient needs 30 mg, and the medication contains 10 mg/mL.

30 mg ÷ 10 mg/mL = 3 mL

Q: How do you convert a liquid volume in mL to the amount of drug in mg?

If a drug contains 50 mg and you need to administer 3 mL, how many mg is in the dose

3 mL x 50 mg/mL = 150 mg

Q: What does BID mean when calculating the total amount of medication to dispense?

2x per day

⭐ Q: How do you convert a fluid order in mL/kg/hr to a pump rate in mL/hr?

To convert mL/kg/hr to mL/hr, multiply the prescribed rate by the patient's body weight in kilograms.

20 kg dog x 4mL/kg/hr = 80 mL/hr

⭐ Q: How do you convert millimoles (mmol) to milliequivalents (mEq)?

To convert mmol to mEq, multiply the mmol by the absolute value of the ion's valence, or electrical charge.

🔎 What this means:

Valence means the size of an ion's electrical charge.

For ions with a charge of 1:

• Na⁺: 1 mmol corresponds to 1 mEq

• K⁺: 1 mmol corresponds to 1 mEq

For calcium, which has a charge of 2:

• Ca²⁺: 1 mmol corresponds to 2 mEq

mEq = mmol x |valence|

⭐ Q: How do you convert an ion's mass in mg to milliequivalents (mEq)?

To convert mg to mEq, multiply the mg by the absolute value of the ion's valence and divide by its molecular or atomic weight.

View pic attached

Q: iClicker — A 66 lb dog is prescribed 25 mg/kg BID for 7 days, using 250 mg tablets that cannot be split. How many tablets should be dispensed?

A. 18 tablets
B. 35 tablets
C. 42 tablets
D. 77 tablets

66 lb divided by 2.2kg = 30 kg

30 kg x 25 mg/kg = 750 mgs

750 mg / 250mg tablet size = 3 tablets

3 tablets x 2 times per day = 6 tablets per day

6 tablets per day x 7 days = 42 tablets total

Q: How do you calculate a volume when the available medication is given as a percent solution?

To calculate the volume of a percent solution, first convert the percentage to mg/mL, then calculate the patient's required mg dose, and finally use the concentration to determine the required mL.

Example:

a 20kg dog is prescribed 2mg/kg IV lidocaine and we have 2% lidocaine in stock

2% lidocaine converts to 1% x 10 = 20 mg/mL lidocaine

💡 Remember: % × 10 gives mg/mL

20 kg dog x 2 mg/kg dose lidocaine = 40 mgs lidocaine

40 mg lidocaine divided by 20 mg/ml = 2 mLs lidocaine

13. Q: iClicker — A medication is supplied as a 5% solution. What is its concentration in mg/mL?

A. 0.5 mg/mL
B. 5 mg/mL
C. 50 mg/mL
D. 500 mg/mL

5% solution

% x 10 = mg/ml
so 5 × 10 = 50 mg/ml

Answer = C

⭐ 14. Q: How do you calculate an IV fluid pump rate from an order written in mL/kg/hr?

Suppose a 44 lb dog is prescribed 4ml/kg/hr

44 lb divided by 2.2 kg = 20 kg

20 kg x 4 ml/kg/hr = 80 ml/hr

⭐ 15. Q: How do you calculate the total fluid volume a patient receives over a specified period?

Suppose a patient receives 80 ml/hr over 24 hours

80 ml/hr x 24 hrs = 1920 mls over 24 hours was received

or 1.92 Liters/day

⭐ 16. Q: How do you calculate the drug amount delivered by a continuous rate infusion (CRI) prescribed in µg/kg/min?

Say you have a 10 kg dog getting a CRI of 5 µg/kg/min

10 kg dog x 5 µg/kg/min = 50 µg/min

Then convert min to hours:

50 µg/min x 60 mins/hr = 3000 µg/hr

Then convert µg to mg:

3000 µg/hr divided by 1000 µg/mg = 3 mg/hr

17. Q: iClicker — A 25 kg dog is prescribed IV fluids at 3 mL/kg/hr. What rate should be entered into the fluid pump?

A. 8.3 mL/hr
B. 75 mL/hr
C. 150 mL/hr
D. 225 mL/hr

25 kg dog x 3 ml/kg/hr = 75 ml/hr

B. The fluid pump should be set to 75 mL/hr.

🟡 LOWER PRIORITY 18. Q: How can the same calculation principles be used to calculate toxicant exposure?

Toxicant exposure is calculated by first determining how much toxicant was actually consumed and then dividing that amount by the animal's body weight to express the exposure in mg/kg.

🔎 What this means:

Drug calculations usually ask:

“How much should I give?”

Toxicology often works in the opposite direction:

“The animal already ate something. How much toxicant did it receive?”

Calculate how much toxicant was ingested by this patient

20 kg dog ate 100g of bait that contains 0.01% toxicant
How much toxicant did it receive?

0.01% toxicant concentration = 0.01g / 100g

s0 0.01g of 100 grams of toxicant was ingested

0.01 g x 1000 mg = 10 mg

10 mg divided by 20 kg = 0.5 mg/kg

So the dog's exposure is 0.5 mg/kg.

You would then compare that calculated exposure with the appropriate toxicological information for that toxicant and species.

Q: What is a milliequivalent (mEq), and how is it different from a millimole (mmol)?

A milliequivalent (mEq) describes the amount of electrical charge carried by those ions.

A millimole (mmol) describes the amount of ions present

💡 Think:

mEq = amount of charge

mmol = amount of ions

For an ion with a charge of ±1:

• 1 mmol Na⁺ corresponds to 1 mEq

• 1 mmol K⁺ corresponds to 1 mEq

For an ion with a charge of ±2:

• 1 mmol Ca²⁺ corresponds to 2 mEq

20. Q: How do you convert an ion's mass in mg into milliequivalents (mEq)?

Calcium has an atomic weight of 40

Its valence is 2
the formula is given in the attached image

Suppose you have 20 mg of Ca²⁺, calculate the mEq

20 mg x |2| = 40

40 / 40 atomic weight = 1 mEq

20 mg Ca²⁺ corresponds to 1 mEq Ca²⁺

Q: iClicker — Which statement about mmol and mEq is correct?

A. 1 mmol Na⁺ corresponds to 2 mEq
B. 1 mmol Ca²⁺ corresponds to 1 mEq
C. 1 mmol Ca²⁺ corresponds to 2 mEq
D. 2 mmol K⁺ corresponds to 1 mEq

C. One mmol of Ca²⁺ corresponds to 2 mEq because calcium has a valence of 2.

Math is shown in the attached image