Math In Medicine: Know Your 'Rithmetic
Last reviewed on January 26, 2011
By Robert H. Shmerling, M.D.
Perhaps you were not convinced. I know I had my doubts. But when my parents told me that the math I was learning in high school would be useful in my everyday adult life, my response was predictable: When will I need to calculate the area of a triangle? OK, so I was right about that one. Still, when it comes to medical matters, math can come in handy. More specifically, it can help you take an active role in your own care and help you to understand what your doctor is saying. Here are some of the ways your math teacher was right.
Recently, my daughter complained that she lost credit on a math test because she didn't include the proper units with her answer. As aggravating as that may be and she was aggravated using the wrong units or ignoring them altogether can be dangerous when dealing with medical issues. A common example is weight; most medication doses for children are based on the child's weight, and that's true for some medicines for adults as well. Usually, the dose is expressed as mg per kg that is, for each kilogram (kg) a person weighs he or she should get a certain number of milligrams (mg) of the medicine. If pounds are used instead of kilograms, the dosage will be more than twice the intended amount. There are simple formulas to convert pounds to kilograms and to make similar conversions between units (see below).
Some medications are available in micrograms (mcg), some in milligrams, and others in grams (gm). To make matters even more confusing, a medication dosage may use different units depending on the dose. For example, once the dose is more than 1000 mg (which is the same as one gram), a prescription could read 1000 mg twice each day or 1 gm twice each day.
The importance of units comes up all the time in medical care, not just with medications. I have patients who typically report their temperature in degrees Celsius (C) because that's how they were raised. I'm used to Fahrenheit (F), so I have to do the math to convert it to a number I know. For example, a fever of 101 degrees F is 38.3 degrees C. Our hospital computer has an automatic conversion tool, because the formula is a bit cumbersome: If you know the temperature in Fahrenheit, subtract 32 and divide the total by 1.8 to get the temperature in Celsius; if you know the temperature in Celsius, multiply it by 1.8 and add 32 to the total. Right about now, your math teachers are saying I told you so .
When I see patients in the office, I constantly find myself multiplying numbers. One of the most common reasons is figuring out how long a prescription will last. For example, if a medicine is taken three times each day, an average month's supply will be 90 doses; but many patients prefer (and insurance companies will cover) a two- or three-month supply. So, I'm getting lots of practice at calculating the common totals for prescriptions, as listed below:
Another way that multiplication can be important is for those medicines that have weight-based doses. For example, if the recommended dosage of a medication is 2 mg/kg, a 132-pound (or 60-kg) woman should be taking 120 mg each day less than that may not be effective; more than that may cause side effects.
Converting pounds to kg requires division: A person's weight in pounds divided by 2.2 gives the weight in kilograms. Similarly, splitting pills one way to reduce the price of your medicines, by the way also requires division. If you have a 10-mg pill that is made to split (with a score on the surface an indentation that makes it easy to break the pill evenly in half), each half will be 5 mg; a supply of 10-mg pills that you split will last twice as long as the same number of 5-mg tablets.
Dosages based on weight are particularly common and important when treating children because size is so variable during development; however, a number of adult medications are adjusted for size as well. Finally, multiplication skills are needed when the total daily dose, not the dose for each pill, is the important measure. For example, generic methotrexate pills come in one dose: 2.5 mg. However, the usual starting dosage for rheumatoid arthritis is three pills once each week; so when your doctors ask you how much you are taking, the most accurate response is 7.5 mg per week (or 12.5 mg per week if you are taking five pills per week, and so on).
As in the examples above, many medications come in fractions of doses such as 2.5 mg or even 1.25 mg. To avoid confusion, it's important to keep these straight. Decimals also show up in the results of blood or urine tests. If your blood creatinine, a measure of kidney function, is 0.8, that's good, but more than 1.3 or so could indicate some degree of kidney disease. These numbers actually refer to a concentration of the creatinine, that is, so many mg in a deciliter of blood measured to one decimal place. And certain test results are reported in decimals but require additional multiplication. For example, the white blood cell count is typically reported as a number between 4 and 10 with one decimal place. A normal result might be 6.3, but that really means that in each drop of blood (or more specifically, in each microliter) there are 6,300 white blood cells. And you thought high-school math quizzes were hard!
One of the most recent and frequent applications of basic math to health matters is in many of the current fitness recommendations. Many aerobic exercise programs encourage measurement of the heart rate (by counting your pulse for 10 seconds and multiplying by 6) and aiming for a target heart rate at 60% of your maximum heart rate. Again, this calls for subtracting and multiplying: the maximum heart rate can be calculated by subtracting your age from 220 and then multiplying the result by 0.6 to get the range of your target heart rate.
The body mass index (BMI) has become the standard for assessing ideal weight (though it may be inaccurate for some people, such as athletes and body builders). Again, calculators programmed with the equation can provide your BMI even faster than a math teacher, but the formula is as follows:
For most people, an ideal BMI is between 19 and 25. A person is considered overweight if the BMI is 25 to 29.9, and obesity is defined as having a BMI of 30 or greater. All over America, fitness enthusiasts are counting their pulses and multiplying, dividing and calculating their heights and weights like crazy to assess their aerobic condition and size. Some probably wish they'd paid more attention in school.
The next time your kids complain about how their math studies will never be something they need or use, remind them about your last visit to the doctor. And when your doctor suggests exercise to achieve 60% of your target heart rate and hands you a prescription for 270 pills, you'll know where the numbers came from. Just don't forget to thank your teachers.
Body mass index (BMI)
Robert H. Shmerling, is associate physician at Beth Israel Deaconess Medical Center and associate professor at Harvard Medical School. He has been a practicing rheumatologist for over 20 years at Beth Israel Deaconess Medical Center. He is an active teacher in the Internal Medicine Residency Program, serving as the Robinson Firm Chief. He is also a teacher in the Rheumatology Fellowship Program.