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Medical Dosage Calculations For DummiesFrom Medical Dosage Calculations For Dummies by Richard Snyder, Barry Schoenborn

No matter what initials you have after your name (RN, CNA, PA, and so on), you can bet you’ll see math on a daily basis if you’re going into (or are already in) a career in the medical field. Grasping some medical math basics — such as how to break down medical dosage problems into steps and use conversion factors — can simplify everyday situations all healthcare professionals face. In addition to just knowing math, you’re going to need to know how to read and interpret doctors’ orders and spot when there’s potential trouble.

Figuring IV Flow Rate, Infusion Time, and Total VolumeWhenever you’re administering intravenous (IV) infusions, you need to know the flow rate, infusion time, and total volume. Fortunately, calculating any one of these three variables is easy to do when you know the other two variables. Use the following equations:

• flow rate (mL/hr) = total volume (mL) ÷ infusion time (hr)

• infusion time (hr) = total volume (mL) ÷ flow rate (mL/hr)

• total volume (mL) = flow rate (mL/hr) × infusion time (hr)

For example, if you must administer 1 L (1,000 mL) of fluid over 4 hours, use the first formula to calculate the flow rate, like so:

flow rate (mL/hr) = total volume (mL) ÷ infusion time (hr)

flow rate (mL/hr) = 1,000 ÷ 4

flow rate (mL/hr) = 250

The flow rate is 250 mL/hr.

Common Conversion Factors in Medical Dosage CalculationsAs a healthcare professional, you have to convert patient weights, fluid volumes, medication weights,

and more. Conversion math isn’t hard to do as long as you know the basic conversion factors. Here are the most useful ones:

• Converting lb to kg and kg to lb

lb = kg × 2.2

kg = lb ÷ 2.2

• Converting mL to L and L to mL

mL = L × 1,000

L = mL ÷ 1,000

• Converting mg to g, g to mg, mg to mcg, and mcg to mg

mg = g × 1,000

g = mg ÷ 1,000

mcg = mg × 1,000

mg = mcg ÷ 1,000

Unacceptable Abbreviations in PrescriptionsMaking sure that you correctly calculate a dose doesn’t matter much if the medication itself is incorrect or the dosing instructions are unclear. Some abbreviations in prescriptions are unacceptable because they cause ambiguity and confusion (the enemies of patient safety and quality healthcare!). For this reason, you don’t want to see these abbreviations on any medical orders you work with.

Abbreviation Mistaken Meanings Better Choice

DC or D/CDoes it mean “discontinue” or “discharge”?

Write discontinue or discharge.

HSDoes it mean “half-strength” or “at bedtime”?

Write at bedtime or a designated time.Also write out the specific dosing strength and/or quantity

QDDoes it mean “every day” or “right eye”? QD looks like OD, which means “right eye.” (OS means “left eye.”)

Write every day.

QODDoes it mean “every other day” or “daily”?

Write every other day or daily, according to patient’s needs.

MSO4Does it mean “magnesium sulfate” or “morphine sulfate”?

Write magnesium sulfate or morphine sulfate.

U or IUDoes it mean “unit” or “zero”? Could it be mistaken for “0” or “10”?

Write units.

IVDoes it mean “intravenous,” “international units,” or “4”?

IV is an acceptable abbreviation for “intravenous,” but the doc could write international units or intravenous to be clearer.Or “4”

SQ or SC Does it mean “subcutaneous” or could it Write Subq, subcut, subcutaneous, or 5

be mistaken for “5Q” (“5 every”)? every.

TIWDoes it mean “twice a week” or “three times a week” (the real meaning)?

Write twice a week or three times a week.

ccDoes it mean “cubic centimeter” or “milliliter”? Could it be mistaken for “00”?

Write milliliter or mL.

Ug or gDoes it mean “microgram” or “Ugh”? Could it be mistaken for mg?

Write microgram or mcg.

OD Does it mean “once daily” or “right eye”? Write once daily or right eye.Source: The National Coordinating Council for Medication Error Reporting and Prevention (NCC MERP). http://www.nccmerp.org/

ML per minute method

Determine ml/ hr.

Divide Total ml infused divided by the hours to be infused. Total ml/ total hrs = ml/hr

Determine ml/minute.

Divide ml per hour by 60 minutes (or number of minutes of infusion).

ml/hr / 60 minutes = ml/minute.

Determine drops per minute

Multiply ml/min times gtts/ ml = gtts/min

ml/minute X gtts/ml = gtts/min

‘What you want, over what you’ve got, times what it’s in’

Type A calculations

When the dose you want is not a whole ampoule.

For example:

• Prescription states 200mg (milligrams) • You have an ampoule of 500mg (milligrams) in 4ml (millilitres).

What volume contains the dose you need?

If you have an ampoule of 500mg in 4ml, and you need 200mg, it can appear to be a daunting calculation. The first step is to find out what volume contains 1mg (4/500) and then multiply it by how many mg you want (200).

The easy way to remember this is the famous nursing equation:

‘What you want, over what you’ve got, times what it’s in’

In this instance:

200mg x 4ml / 500mg = 1.6ml

The common error here is to get it upside down, and divide what you’ve got by what you want. This fortunately gives you a stupid answer, which is obviously wrong, in this case 10ml. You already know that you need a fraction of an ampoule and not two and a bit ampoules, which highlights the error.

To help make sure you get it the right way up, remember “WIG”:

• What you want x what it’s in / what you’ve got

Converting units

All weights, volumes and times in any equation must be in the same units. With weights the unit changes every thousand. For example, you need 1000 micrograms (mcg) to make 1 milligram (mg) and 1000 milligrams to make one gram (g) (Box 2).

Type B calculationsThese are infusion rate calculations.

For example:

• Prescription states 30 mg/hour• You have a bag containing 250mg in 50ml

At what rate (ml/hr) do you set the pump?

These are the same as type A calculations, only once you have worked out the volume that contains the amount of drug you need, you set the pump to give that amount per hour.

In this instance, work out how many ml contain ONE mg of drug

Using the WIG equation:

30 x 50 / 250 = 6ml

Therefore the calculation shows that, to give 30mg per hour, the infusion pump rate would need to be set at 6ml per hour.

This calculation is straightforward when the rate you want (30mg/hour) and the amount of the drug in

the bag (250mg) are both in the same units (mg).

However, if the infusion required that 600 micrograms were to be infused each hour instead, this would first need to be converted into mg before the infusion rate was calculated, that is, 600 micrograms = 0.6mg.

The equation for infusion rate calculation is dose stated in prescription (milligrams per hour) times volume in syringe (in millilitres) divided by the amount in the syringe (in milligrams) equals the infusion rate (millilitres per hour), or:

Dose (mg/hr) x volume in syringe (ml) / Amount in syringe (mg) = Infusion rate

Type C calculationsInfusion rate is required, but dose is ‘mg per kg’.

For example:

• Prescription states 0.5mg/kg/hour• You have a bag of 250mg in 50ml• Your patient weighs 70kg

At what rate (ml/hr) do you set the pump?

To do this calculation you still use the WIG equation as above, but with one extra step to work out the ‘what you want’.

First you need to convert the mg per kg into total mg by multiplying it by the patient’s weight.

So for a person who weighs 70kg, 0.5mg per kg is the same as 35mg. Once you have calculated this, the infusion rate can be worked out as in the Type B calculations.

In this instance:

0.5mg/kg/hr x 70kg x 50ml / 250mg = 7ml/hr

Type D calculationsInfusion rate required, but dose is in mg/kg/min.

For example:

• Prescription states 0.5mg/kg/min• You have a syringe of 250mg in 50ml• Your patient weighs 70kg

At what rate (ml/hr) do you set the pump?

As before, you will need to calculate what you want by multiplying the amount per kg by the patient’s weight. In this case:

0.5mg x 70kg = 35mg

This time, however, the prescription states the rate per minute. The pump demands that the rate be set in ml per hour, therefore the rate per minute will need to be converted before the equation can be completed, by multiplying 35 by 60; that is, 35mg/min (35 milligrams per minute) is converted to

2100mg/hr (2100 milligrams per hour).

From here, once again we use the type B calculation to find the infusion rate, which as shown will be 420ml/hr.

2100 x 50 / 250mg = 420ml/hr

Type E calculationsInfusion rate is required, but the dose is in mcg/kg/min.

For example:

• Prescription states 3 micrograms (mcg)/kg/min• You have a syringe of 100mg in 50ml• Your patient weighs 70kg

At what rate do you set the pump (ml/hr)?

As before, what you want is calculated by multiplying the amount per kg by the patient’s weight, that is:

3mcg/kg for a 70kg person is 210mcg

Next the prescription rate needs to be converted into rate per hour, that is,

210mcg/min = 12 600mcg/hr

The prescription is in micrograms, but in your syringe you have milligrams. Both need to be in the same units, so you must convert one to the other, in this case mcg to mg. 12 600mcg/hr is the same as 12.6mg/hr.

The calculation is then as follows:

12.6 x 50 / 100 = 6.3ml/hr

AbbreviationsAbbreviations rule the medical world. It is important to know the recognized abbreviations in clinical setting so you will not be lost when preparing medications for your patient. Here are the most commonly used abbreviations when preparing drugs:

cc- cubic centimeter

DD- Desired Dose

IM- Intramuscular

IO- Intraosseous

SL – Sublingual

IV- Intravenous

IVP- Intravenous Push

Kg- Kilogram

gm- gram

mg- milligram

mcg- microgram

mEq- milliequivalent

L- Liter

mL- milliliter

µg- microgram

gtt – drop

µgtt – micro drop

tbsp – tablespoon

tsp – teaspoon

ConversionsBefore mastering drug dosage formula, you should first learn how to convert the commonly used units of measurements in drug preparation. It is essential so you will not get lost between drug calculations as physicians commonly order a medication available in a different preparation.

The most common conversion factors you will use for drug dosage calculations are the following:

Solid Conversions

gr 1 = 60 mg

gr 15 = 1 g

2.54 cm = 1 in

2.2 lb = 1 kg

Liquid Conversions

30 mL = 1 oz

1 tsp = 5 mL

1 standard measuring cup = 240 mL

Mass:

mcg ← mg ← g ← kg ( x by 1,000 )

mcg → mg → g → kg ( ÷ by 1,000 )

lb ← kg ( x by 2.2 )

lb → kg ( ÷ by 2.2 )

Volume:

mcL ← mL ← L ← kL ( x by 1,000 )

mcL → mL → L → kL ( ÷ by 1,000 )

Time:

min ← hr ( x by 60 )

min → hr ( ÷ by 60 )

Example:

Convert 0.008 kg to mg

mcg ← mg ← g ← kg ( x by 1,000 )

0.008 L x 1,000 = 8 mg

8 mg x 1,000 = 8,000 mg

Convert 1,000 mcL to mL

mcL → mL → L → kL ( ÷ by 1,000 )

1,000 L ÷ 1,000 = 1 mL

Convert 480 minutes to hour

min → hr ( ÷ by 60 )

480 ÷ 60 = 8 hr

Drug Calculation Formulas

Below are the four most important calculation formulas that you should know in preparing medications and drips.

Calculating Tablet Dosages

In calculating tablet dosages, the following formula is useful:

Desired dosage ÷ stock strength = number of tablets

The desired dosage is the ordered dosage of the physician while the stock strength is the amount of drug present in each tablet. Stock strength is also known as stock dose.

Example:

• The physician orders 1,500 mg of calcium carbonate for the patient. The drug is available in 250 mg tablets. How many tablets should be given to the patient?

Desired dosage ÷ stock strength = number of tablets

1,500 mg ÷ 250 mg = 6 tablets

• The patient is ordered to have 2 g of potassium chloride. The drug is available in 500 mg tablets. How many tablets should be given?

Convert 2 g to mg = 2 x 1,000 = 2,000 mg

Desired dosage ÷ stock strength = number of tablets

2,000 mg ÷ 500 mg = 4 tablets

Calculating Mixtures and SolutionsThe following formula is useful in calculating mixtures and solutions:

Desired dosage ÷ stock strength x stock volume = amount of solution to be given

The desired dosage is the ordered dosage of the physician. The stock strength is the amount of drug present in the preparation while the stock volume is the amount of the solution where the drug is diluted.

Example:

• The physician orders 375 mg of cefuroxime for the patient. The drug is available in 750 mg vial. You plan to dilute it in 10 mL of sterile water. How much should you give to your patient?

[Desired dosage ÷ stock strength] x stock volume = amount of solution to be given

[375 mg ÷ 750 mg] x 10 mL = amount of solution to be given

0.5 mg x 10 mL = 5 mL

• A pediatric patient recovering from accidental fall is about to be given with 130 mg paracetamol syrup. The drug is available in 250 mg per 5 mL preparation. How much should you give to your patient?

[Desired dosage ÷ stock strength] x stock volume = amount of solution to be given

[130 mg ÷ 250 mg] x 5 mL = amount of solution to be given

0.52 x 5 mL = 2.6 mL

Calculate IV Rate – mL per hour and minute

It is easy to calculate the running rate of IV fluids in terms of mL per hour or mL per minute:

Total IV volume ÷ time (hour or minute) = mL per hour or minute

The total IV volume is the amount of fluid to be infused while the time is the number of running hours or minutes.

Example:

• Start venoclysis with D5 0.9 NaCl 1 L to be infused for 16 hours. How many mL of the IV fluid should you infuse per hour?

Total IV volume ÷ time (hour or minute) = mL per hour

1 L ÷ 16 hours = mL per hour

[1 L x 1,000] ÷ 16 hours = mL per hour

1,000 mL ÷ 16 hours = 62.5 mL per hour

You are going to start IV infusion with Plain Lactated Ringer’s Solution 1 L. By regulating it for 11 hours, how much fluid are you going to infuse per minute?

Total IV volume ÷ time (hour or minute) = mL per minute

1 L ÷ 11 hours = mL per minute

[1 L x 1,000] ÷ [11 hours x 60] = mL per minute

1,000 mL÷ [11 hours x 60] = mL per minute

1,000 mL ÷ 660 = 1.5 mL per minute

Calculate IV Rate – drops per minute

Calculating for drops per minute is simple with the following formula:

[Total IV volume ÷ time (minute)] x drop factor = drops per minute

The total IV volume is the amount of IV fluid to be infused while time is the duration of how long the IV fluid should be infused in terms of minutes.

The drop factor is the “drops per milliliter” delivered to the patient and it depends on the macrodrip used for the infusion. The common drop factors used in different hospitals are 10, 15 and 20.

Example:

• The physician orders to start venoclysis with D5 0.3 NaCl 1 L solution. The IV fluid will be infused for 14 hours and the drop factor of the macrodrip used is 20. It should be regulated to how many drops per minute?

[Total IV volume ÷ time (minute) ] x drop factor = drops per minute

[1 L ÷ 14 hours] x 20 = drops per minute

[{1 L x 1,000} ÷ {14 hours x 60} ] x 20 = drops per minute

[1,000 mL ÷ 840 minutes] x 20 = drops per minute

1.19 x 20 = 23 to 24 drops per minute

• You are going to regulate D5 0.9 NaCl 500 mL solution for 7 hours. The macrodrip used has 15 drop factor. You should regulate the IV fluid for how many drops per minute?

[Total IV volume ÷ time (minute) ] x drop factor = drops per minute

[500 mL ÷ 7 hours] x 15 = drops per minute

[500 mL ÷ {7 hours x 60}] x 15 = drops per minute

[500 ÷ 420] x 15 = drops per minute

1.19 x 15 = 17 to 18 drops per minute

Calculate IV Rate – Remaining Time of Infusion

Calculating for the remaining time of infusion for a certain IV fluid is possible with the following formula:

[Volume remaining (in mL) ÷ drops per minute] x drop factor = minutes remaining

The volume remaining is the amount of IV fluid remaining for the infusion while the drops per minute is the regulation of the IV infusion. The drop factor can be determined in the macrodrip used in the hospital.

Example:

• You see that your patient has D5 0.9 NaCl IV infusion at 400 mL level. It is regulated to run for 22 drops per minute using a macrodrip set with drop factor 20. How many minutes are remaining before you are due to change the IV fluid?

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[Volume remaining (in mL) ÷ drops per minute] x drop factor = minutes remaining

[400 mL ÷ 22] x 20 = minutes remaining

18.18 x 20 = 363 minutes or 6 hours

• A patient has 350 mL of Plain 0.9 NaCl solution as IV infusion regulated at 20 drops per minute. Drop factor 10 was used for the patient’s macrodrip set. Considering the IV fluid level of the patient, for how many minutes will it run?

[Volume remaining (in mL) ÷ drops per minute] x drop factor = minutes remaining

[350 mL ÷ 20] x 10 = minutes remaining

17.5 x 10 = 175 minutes or 3 hours