# Math Calculations in Pharmacology: Formulas & Conversions

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• 0:00 Background on Conversions
• 0:54 What Are Conversions?
• 3:09 Formulas
• 6:01 Lesson Summary
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Lesson Transcript
Instructor: Artem Cheprasov

Artem has a doctor of veterinary medicine degree.

This lessons offers you an introductory look at the important conversions and calculations people in the medical field perform with respect to pharmaceutical preparations.

## Background on Conversions

If you've ever cooked from a recipe, you would've noticed that you were told to get x ounces of one thing and y grams of another. And if you didn't have the right measuring cups, utensils, and the like, you would've been at a loss as to how much you actually needed to measure out. Unless, of course, you knew how to convert various units between one another. Even if you guesstimated, the worst that would've happened was a ruined meal.

In medicine, we can't take chances. There's no room for guesstimation when someone's life is at stake. As a result, you need to know how to convert important units and how to perform many different calculations. This lesson will give you an idea of the many conversions and formulas you should be aware of when performing calculations involving various pharmaceuticals.

## What Are Conversions?

If you've ever looked at the International System of Units brochure, then you'll know that one of the things you need to be very familiar with in medicine is a decimal system that's based on the power of 10. We call this the metric system. Important basic units in this system include the following ones you're probably familiar with:

• Grams, usually abbreviated as g, for weight.
• Liter, often seen as L, for volume.
• Meter, primarily written as m, for length.

You must know how to convert between these basic units and their various larger and smaller units. For example, 1000 g is equal to 1 kg (kilogram), where kilo means one thousand. In other words, in the metric system there are 1000 units in a kilo. A kilometer has 1,000 m and a kiloliter has 1,000 L. On the opposite end of things is the concept of a milli. Milli means one thousandth. That is to say, 1 mg is one thousandth of 1 g. 1 mL is one thousandth of 1 L. Check out the rest of the table below for some important prefixes, symbols, and powers of ten used in the metric system:

Prefix Symbol Power of Ten Example
kilo k 10 3 1 kilometer (km) is equal to 1000 m
hecto h 10 2 1 hectogram is equal to 100 g
deca da 10 1 1 decaliter is equal to 10 L
(none) (none) 10 0 This is just your basic unit, like 1 g or 1 L
deci d 10 -1 10 deciliters (dL) are in 1 L
centi c 10 -2 100 centimeters (cm) are in 1 m
milli m 10 -3 1,000 millimeters (mm) are in 1 m
micro mc 10 -6 1,000,000 micrograms (mcg) are in 1 g
nano n 10 -9 1,000,000,000 nanograms (ng) are in 1 g

The most important conversions that you should be aware of in a practical sense in medicine are the following:

• 1 g = 1000 mg
• 1 mg = 1000 mcg
• 1 L = 1000 mL

## Formulas

These conversions are the most basic ones you must be aware of, but plenty of other ones, like conversions between the metric system and the imperial system, as well as between the metric system and household equivalents, aren't covered in this lesson. For now, we need to move on to the basic understanding of important formulas in pharmacology.

One such important formula for calculating drug dosages is known appropriately as the basic formula. The basic formula is:

That is all pretty ethereal, so let's solidify this formula with an example. Let's say that the order is for a drug called Panacea at 120 mg, by mouth, to be given immediately. So what do we know?

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