Pyramid Geometries

The Pyramid Geometries calculator computes the metrics associated with of square based pyramid.

INSTRUCTIONS: Choose units and enter the following:

• (L) Length of Base Sides
• (θ) Pitch Angle 

Pyramid Geometric Specifications (PS): The calculator returns:

• (V) Volume in cubic meters. 
• (TSA) Total Surface Area in square meters. 
• (FA) Surface Area of one Face in square meters.
• (BA) Square Base Area in square meters.
• (BD) Square Base Diagonal in meters.
• (α) Angle of Face corners in degrees.
• (i) Face Slope Length in meters.
• (j) Hip Ridge Length in meters.
• (HRL) Total Hip Ridge Length in meters

Note: answers can be automatically converted to compatible units via the pull-down menu.

The Math / Science

Based on the input parameters and the assumption of a square base, this calculator makes the following calculations:

• y = L/2
• h = tan(Θ) * y
• z = sqrt(2*y²)
• j = sqrt(z² + h²)
• i = sqrt(y² + h²)
• α = asin(i/j)
• FA = y*i
• TSA = FA*4
• HRL = j*4
• BA = L*L
• BD = sqrt(L²+ L²)

Pyramid Calculators

• Pyramid Geometries
• Volume of a Pyramid
• Mass or Weight of a Pyramid 
• Volume of a Frustum of a Pyramid
• Mass of a Frustum of a Pyramid
• Volume of a Polygon Based Pyramid
• Mass of a Polygon Based Pyramid
• Volume of a Frustum of a Polygon Based Pyramid
• Mass of a Frustum of a Polygon Based Pyramid

A regular pyramid is a type of pyramid that has the following characteristics:

1. Base: The base of a regular pyramid is a regular polygon, meaning all sides of the polygon are equal in length, and all interior angles are equal. Examples of regular polygons include equilateral triangles, squares, and regular pentagons.
2. Apex: The apex is the point directly above the center of the base. In a regular pyramid, the apex is aligned such that the line segment (height) from the apex to the center of the base is perpendicular to the base.
3. Lateral Faces: The lateral faces of the pyramid are congruent isosceles triangles. Each triangle shares a side with the base of the pyramid and meets at the apex.
4. Height: The height of the pyramid is the perpendicular distance from the apex to the center of the base.

Because of these properties, a regular pyramid is symmetric around its vertical axis (the line connecting the apex to the center of the base).