As a fitness professional, you are expected to know a certain amount of exercise science, and part of science is math! I know many of you hear the word “math” and want to turn and run in the opposite direction, but my goal is to convince you that you’re fully capable of being an effective exercise mathematician!
First, let me start by saying that the rules regarding a calculator have recently been modified—you will now be supplied with a calculator function on your exam. To see what this is going to look like and get some practice, check out our test administrator, Castle Worldwide, and Take a Sample Test. In the menu at the top, there is a calculator option. The asterisk (*) is the multiplication symbol and the forward slash (/) is the division symbol (see photo below). This is a great way to get familiar with the format of the test and become more comfortable navigating the exam.
There are only a few questions that deal with equations (namely BMI, % Body Fat, and Predicted 1-RM). Other questions might require you to calculate how many calories are in a pound of fat, and then how many calories to create a caloric deficit or surplus each day. I am going to walk you through the math you could potentially see on an ACE Personal Training Certification Exam (those taking the Group Fitness Instructor or Health Coach exam may not see the Predicted 1-RM equation).
Okay let’s get started!
Desired Percent Body Fat
For this example, we’re going to use a theoretical female client who weighs 195 pounds and has 37% body fat. Her goal is lose 10% body fat (27%) to reduce her risk of type 2 diabetes.
Step 1: Determine Fat Mass vs. Lean Mass in Pounds. There are two ways to get this number, and they’re pretty much the same thing so just select the method that makes the most sense to you.
- Variation 1: (100% BF) to give you % Lean Body Mass (LBM) and then multiply their weight by that number
- (100 - 37) = 63 % Lean Body Mass
- 195 lbs. x 0.63 = 122.85 lbs.
- This person has ~123 lbs. of LBM
- Variation 2: Multiply weight by % Fat Mass (FM) and then subtract that from their weight
- 195 x 0.37 = 72.15 lbs. of FM
- 195 - 72.15 = 122.85 of LBM
- This person has ~123 lbs. of LBM
Step 2: Determine Goal Weight Mass Distribution. Essentially, you’re asking, “At her current weight, her lean body mass makes up 63% of her total mass. But if she decreased her FM to 27% then her LBM would now make up what %?”
- Process: Subtract desired % BF from 100
Step 3: Calculate it all out.
- Divide Current LBM in pounds by desired % LBM
- 123/0.73 = 168.49315
- 168.5 pounds to reach desired body composition goal
Body Mass Index and Waist-to-Hip Ratio
Next, let’s look at some of the other anthropometric measurements you might use: Body Mass Index (BMI) and Waist-to-Hip Ratio. While BMI is a quick and easy way to classify someone according to their height and weight, it does NOT take into account someone’s body composition. So, someone who has a shorter, more muscular body type might read a little high, but have a normal % Body Fat (BF). Conversely, a person could appear very petite, but still have a high % BF, so use this information wisely. (The advantages and disadvantages of BMI can be found on pages 185-186 of the ACE Personal Training Manual.)
Here is how we calculate BMI:
Your Client is 5 feet 3 inches and weighs 135 pounds.
Version 1: Using Weight in Kilograms and Height in Meters Squared
- Step 1: Convert pounds into kilograms by dividing weight in pounds by 2.2
- 135/2.2 = 61.363636 or ~61.4 kg
- Step 2: Convert inches to meters by multiplying inches by 0.0254
- 63 x 0.0254 = 1.6002 or ~ 1.6 m
- Step 3: Square (multiply by itself) their height in meters
- 1.6 x 1.6 = 2.56 meters-squared
- Step 4: Divide weight in kilograms by height in meters-squared where BMI = kg/(m x m)
- 61.4 kg / 2.56 = 23.984375 or ~ 24
- This persons BMI would be 24 which would place them in the “Normal Weight” Category
Version 2: Using Weight in Pounds and Height in Inches where BMI = pounds x [703/(inches x inches)]
- Step 1: Square height in inches
- Step 2: Divide 703 by height in inches-squared
- 703/3969 = 0.1771227 or ~ 0.18
- Step 3: Multiply weight in pound by product from step 2
- 135 x 0.18 = 24.3
- This person’s BMI is 24.3 which would place them in the “Normal Weight” Category
NOTE: There is a slight difference between the two answers due to rounding differences.
Waist-to-hip ratio looks at the distribution of fat, which can provide information about a person’s health risk. For example, some have more fat around the midsection, known as Android body shape (like an apple), while others carry more fat in the hips, buttocks and thighs, which is known as Gynoid body shape (like a pear). There are two types of fat: subcutaneous fat and visceral fat. Subcutaneous fat sits on top of the muscle (this is what we pinch with the skinfold calipers). Visceral fat sits in your mid-section underneath the muscle and surrounds all of our organs and is associated with insulin resistance (for more detailed explanation see page 188 of the ACE Personal Training Manual). The criteria for obesity in reference to waist circumference is 35 inches for females and 40 inches for males.
Let’s calculate the WHR for another theoretical client:
A male has a waist circumference of 35 inches and a hip circumference of 39.
- Divide Waist Circumference by Hip Circumference
- 35/39 = 0.8974358 or ~0.90 which would place this man in the “Average” category
- Hint: If you forget which number goes on top, just remember the Waist is above the Hips - W/H
Predicted 1-RM Equation
For assessments pertaining to muscular strength, the Predicted 1-RM equation is very helpful, particularly when you are unable to determine a client’s actual 1 Rep Max (RM). You are expected to know the % 1 RM Values for the different number of repetitions listed on Table 8-27 of the ACE Personal Training Manual pictured here (page 224). Hint: For 2, 4, 6, 8 and 10, the values decrease in 5% increments.
Determining 1 RM: What would the 1-RM be for a client who is able to lift 150 pounds 6 times?
- Step 1: Determine % 1 RM based on number of repetitions lifted: 85%
- Step 2: Divide weight lifted (150 pounds) by the percentage determined
- 150/0.85 = 176.47058 or ~176.5 lbs.
Karvonen Formula – Heart Rate Reserve (HRR)
Let’s switch gears to the Karvonen Formula, also known as Heart Rate Reserve (HRR). For clients who enjoy tracking their heart rate, but aren’t comfortable with assessments, you can use the Karvonen Formula to create appropriate heart-rate ranges for them to work in for each of the three zones. While this formula is MOST accurate when you have a measured maximum heart rate (MHR), you can still create a good estimation of where they should be. You will need to measure their resting heart rate (RHR) for this equation.
For this example, your 45-year-old male client has a resting heart rate of 75 and wants to work at 70% of his HRR.
- Step 1: Determine Maximum Heart Rate (MHR): 220 - Age
- Step 2: Calculate Heart Rate Reserve (HRR) by subtracting Resting Heart Rate (HRR) from MHR
- Step 3: Multiply HRR by desired intensity (70%)
- Step 4: Add back RHR to get heart rate for desired training intensity
- 70% HRR + RHR = 70 + 75 = 145
- For this person to work at 70% of their HRR, they will want their heart rate at 145.
HINT: If you calculate their heart-rate range for Zone 2: 60-84% (see page 392 of the ACE Personal Training Manual), then you will know that anything below is going to be in Zone 1, and anything above it will be in Zone 3. You get all three zones with only one calculation!
I hope you’re feeling a little bit more comfortable with why and how we use these calculations. If not, please feel free to contact one of our Study Coaches by calling our Resource Center at 800-825-3636, Ext. 796, Monday-Friday 7 a.m. – 6 p.m. We are always happy to assist you with your studies.