Enter the base length, base width, and height of the pyramid into the calculator to determine the unitless ratio R = (L + W) ÷ H (base semi-perimeter divided by height). If desired, you can compare R to the golden ratio constant φ ≈ 1.618.

Pyramid (L + W) ÷ H Ratio Calculator

Enter any 3 values to calculate the missing variable

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Pyramid (L + W) ÷ H Ratio Formula

The following formula is used to calculate the unitless ratio R = (L + W) ÷ H, which is the base semi-perimeter divided by the height. (This is not the golden ratio constant by definition, but you can compare the result to φ = (1 + √5) / 2 ≈ 1.618 if desired.)

R = (L + W) / H

Variables:

  • R is the unitless ratio (base semi-perimeter ÷ height)
  • L is the base length of the pyramid
  • W is the base width of the pyramid
  • H is the height of the pyramid

To calculate R, add the base length and base width of the pyramid (in the same units), then divide the result by the height of the pyramid.

What is the Pyramid (L + W) ÷ H Ratio?

The value R = (L + W) ÷ H is a simple, unitless way to describe how “wide” a pyramid’s base is compared to its height (using the base’s semi-perimeter L + W). It is not the golden ratio by definition. The golden ratio is a fixed mathematical constant φ = (1 + √5) / 2 ≈ 1.6180339887. A pyramid’s dimensions can be chosen so that R (or some other pyramid-related proportion) is numerically close to φ, but that does not make R itself “the” golden ratio.

How to Calculate Pyramid (L + W) ÷ H Ratio?

The following steps outline how to calculate the ratio R = (L + W) ÷ H.

  1. First, determine the base length (L) of the pyramid.
  2. Next, determine the base width (W) of the pyramid.
  3. Next, determine the height (H) of the pyramid.
  4. Finally, calculate the ratio using the formula R = (L + W) / H.
  5. After inserting the values and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Base Length (L) = 10 m

Base Width (W) = 8 m

Height (H) = 11.1246 m (so that R ≈ 18 / 11.1246 ≈ 1.6180, which is close to φ)