Fun Pyramid Set Math

Push Up PyramidsIf you’re doing work out sets with a pyramid, i.e. 1, 2, 3, 4, 3, 2, 1 , there is some really cool math to figure out your totals, or work backwards from a total to get your max count in the pyramid.

Pyramids are a great way to increase your max rep in a given set, for example in pushups, pullups, and situps. For example, with a maximum number of reps at 5, you can knock out a total count of 25.

Now, for the fun math.

To find out how many total you’re doing (Let’s call this variable c), simply square your max rep count (let’s call this n). For example, if you’re doing a pyramid from 1 through 8, your total would be 8 x 8 or 64.

Why? There’s a great way to visualize why this works. If you line up the rep count for the entire set, i.e. 1, 2, 3, 4, 5, 6, 7, 8, 7, 6, 5, 4, 3, 2, 1, you can link groups of numbers. Sum the first 1 and the second 7 (8), then the first 2 and the second 6 (8) and so on (7 times) until you end up at the top by itself (8). Notice how they’re all the same sum? (1+7) + (2+6) + (3+5) + (4+4) + (5+3) + (6+2) + (7+1) + 8 = 64. This works out to (n)(n-1) + n or more simplified…

c = n2

Now, what if you want to hit the higher numbers faster and not get bored to tears with endless sets?

Try going in twos or threes, for example 2, 4, 6, 8, 10, 8, 6, 4, 2 or 3, 6, 9, 12, 9, 6, 3.

How does the math work for these? Simple. Divide the square of the max count by two, divide the cube of the max by three, etc… If the total count is defined as c, the step is defined as s and the max is defined as n, then to find your total, use:

c = n2/s

To get your pyramid top (n) from the max count (c) for a given step (s), simply reverse it with:

n = (c × s)1/2

Lastly, if you want to know how many sets (t) you’re doing, use this:

t = 2(n/s) – 1

May these fun formulas run through your head as they do mine while doing reps! 🙂

2 thoughts on “Fun Pyramid Set Math”

  1. On a mildly related note, one generally does pullups in 1 pullup increments, pushups in 2 pushup increments and situps in 3 situp increments. Adjust to taste. 🙂

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