A few days ago, I received an email from my high school coach asking me about the "correct" way to calculate percentages of a given pace. This is a question that I am asked fairly frequently, and the answer has a few interesting angles, so I have decided to make a post about the details.
Many different training programs are predicated on doing workouts, easy runs, and interval sessions at various percentages of a particular pace, whether this is race pace or threshold pace or VO2 max pace. But if you ask a group of people how to calculate, say, 85% of 5:00 mile pace, you'll get two different answers. The first camp will say, "Simple, just multiply 5:00 per mile by 1.15, which gives you 5:45 per mile." The second will say, "No, you have to divide 5:00 by 0.85, which gives you 5:53." Who is correct?
In some sense, they are both correct. To break down what each of these particular strategies actually mean, mathematically speaking, it helps to compare and contrast the result for a variety of percentages. So, sticking with our example of 5:00 mile pace, let's do the math on a few various paces, both faster and slower than 5min-miles. To make things simple, let's call one variant—85% = 5 x 1.15— the "multiplication method" and the other—85% = 5 / 0.85— the "division method."