How to Use the Rectangular Box & Square Pyramid Calculator
Enter length, width, and height to calculate the volume and surface area of a rectangular box, or enter a base side and height to calculate those values for a square pyramid. These are two of the first solid shapes taught in school, and they show up constantly in real life — from packaging boxes to architectural models.
A box's volume equals length x width x height, and its surface area adds up the three distinct pairs of faces (length x width, length x height, width x height), each counted twice: 2 x (lw + lh + wh). A square pyramid's volume uses the standard formula (1/3) x base area x height, and its surface area is the square base plus the four triangular side faces.
To find the side faces' area, you first need the slant height, found using the Pythagorean theorem: it's the hypotenuse of a right triangle formed by the pyramid's height and half the base side. Once you have the slant height, multiply it by the base and divide by 2 to get one triangle's area, then multiply by 4 for all four sides. Useful for packaging design, architectural modeling, and geometry homework.
Frequently Asked Questions
The surface area equals the base area (s squared) plus the combined area of the four triangular side faces. Each side face's area uses the base times the slant height divided by 2, and the slant height is found using the Pythagorean theorem.
A cube is just a special case of a rectangular box where length, width, and height are all equal, so the same formulas apply: volume = length x width x height, and surface area = 2 x (lw + lh + wh).