# Drug Dose Calculation Formula

Two basic formula for drug dose calculation is mentioned below -

Formula 1

D/H × Q = X, [Where, X is the amount to administer]

or

Dose amount to administer = (Desired or Ordered Dose amount/Amount on Hand) x Quantity.

Formula 2

H : Q = D : X

[ Where, D = Desired dose or dose ordered by the primary care provider; H = dose on hand or dose on the label; Q = Quantity; X = amount to administer]

Dose have on hand / Quantity = Desired Amount / X

#### Dosage Calculation Examples

A provider requests lorazepam 4 Mg IV Push for a patient in severe alcohol withdrawal. The clinician has 2 mg/mL vials on hand. How many milliliters should he or she draw up in a syringe to deliver the desired dose?

Option 1:

[Ordered Dose (4 mg) / Have (2 mg)] x Quantity (1 mL) = Amount wanted to give (2 mL)

Option 2:

Have on hand (2 mg) / Quantity you have (1 ml) = Desired Amount (4 mg)/ X

2 mg/1 mL = 4 mg/x

2x/2 = 4/2

x = 2 mL

#### Dosage Calculation Practice (Problem with Answer)

Calculation 1

The doctor orders 90 milligrams of liquid cough syrup. The liquid cough syrup has a label that reads 120 milligrams (mg for short) in 5 milliliters (or mL for short). How much cough syrup should the nurse give to the patient?

Here, D = 90 mg, H = 120 mg & Q = 5 mL

So,

X = D/H × Q

X = 90/120 × 5

X = 3.75 mL

Calculation 2

Ampicillin 500 mg capsules are supplied. MD orders 1.5 g. How many capsules should be given to the patient?

Here, D = 1.5 g = 1500 mg, H = 500 mg & Q = 1 capsule

So,

X = D/H × Q

X = 1500 mg/ 500 mg × 1

X = 3 Capsules

Calculation 3

The doctor orders “ibuprofen 600 mg PO BID”. You have 300 mg tablets of ibuprofen on hand. How many tablets should be given to the patient at one time?

Here, D = 600 mg, H = 300 mg & Q = 1 tablet

X = D/H × Q

X = 600 mg/ 300 mg × 1

X = 2 tablets

Calculation 4

The doctor orders “Valporic acid 0.5 g PO TID.” The bottle of Valporic acid on hand says 50 mg per 1 mL. How many milliliters should be given?

Here, D = 0.5 g = 500 mg, H = 50 mg & Q = 1 mL

X = D/H × Q

X = 500 mg/ 50 mg × 1 mL

X = 10 ml

#### Dosage Calculations for Nursing Students

Q1. How much dextrose is in 4L of 20% solution?

Answer: 4L = 4000 ml × 20% = 800 ml

Q2. A patient needs 0.075g of a medicine that comes in 30 mg tablets. How many tablets will the patient take?

Answer: 0.075 g = 75 mg; 75 mg/30 mg = 2.5 tablets.

Q3. A child weighs 15.5 kg is prescribed 300 µg/ kg of a medication. How much of the medication should be given?

Answer: 15.5 × 300 = 4650 µg = 4.65 mg

#### Dosage Calculation Conversions Factors

• 1 kg = 2.2 lb
• 1 lb = 16 oz
• 8 oz = 240 mL = 1 glass
• 1 tsp = 5 mL
• 1 gallon = 4 quart
• 1 L = 1,000 mL
• 1 kg = 1,000 g
• 1 oz = 30 mL = 2 tbsp
• 1 g = 1,000 mg
• 1 inch = 2.54 cm
• 1 mg = 1,000 mcg
• 1 cm = 10 mm
• 1 cup = 8 fl oz
• 1 tbsp = 15 mL
• 1 pint = 2 cups
• 12 inches = 1 foot
• 1 L = 1.057 qt
• 1 tbsp = 3 tsp
• 60 minute = 1 hour
• 1 cc = 1 mL
• 2 pints = 1 qt
• 1 pt = 500 mL = 16 oz
• 1 tsp = 60 gtt
• 1 oz = 30 mL
• 4 oz = 120 mL (Casey, 2018)

#### Abbreviation Term

• po: by mouth (or orally)
• susp: suspension
• pm: as needed
• tab: tablet
• cap: capsule
• q: every
• bid: twice a day
• tid: three times a day
• qid: four times a day