Shingles for a Pyramid Hip Roof

The Shingles for a Pyramid Roof calculator computes the number of bundles of shingles and ridge shingles needed for a pyramid hip roof. It also computes the number of roofing nails for both normal and high wind conditions. It also computes the cost of roofing shingles (not ridge) base on a costs per bundle.

INSTRUCTIONS: Choose units and enter the following:

• (S) Length of Base Sides
• (P) Pitch
• (SBC) Shingle Bundle Coverage 
• (BC) Shingle Bundle Cost

Pyramid Roof Shingle (PRS): The calculator returns:

• (TSA) Total Surface Area in square feet. 
• (nB) Number of Bundles of Shingles
• (TC) Total Cost of Roof Shingles (not including ridge shingles)
• (nR) Number of 25' bundles of Ridge Shingles
• (nN) Number of Roofing Nails

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

The Math / Science

Based on the input parameters, the calculator computes the surface area of the four faces of the pyramid shaped roof and computes the number of bundles of shingles based on the bundle size (33.3 ft² for 3-tab or 32.8 ft² for architectural).  It also uses the total area to compute the number of roofing nails.  The calculator then uses the Hip Ridge Length (HRL) to compute the number of bundles of ridge shingles based on 25' per bundle.

Pyramid Hip Roof

A Pyramid Hip Roof is a special case of a hip roof where the hips come to a single point and do not form a ridge line.  All four faces create triangular ends (faces) to the roof which are all exposed to rain and snow from above and require roofing material.

The specifications of a Pyramid Hip Roof can be defined by a span, pitch and overhang (see diagram). These calculators compute the area, hip ridge lengths and materials required for a pyramid hip roof.

Roofing Materials

The roofing materials to cover a pyramid roof include:

• 4x8 sheathing
• purlins
• underlayment
• shingles (3 tab, architectural and ridge)
• metal panels and trim

Pyramid Hip Roof Geometries

A pyramid hip roof is geometrically a square based pyramid.  The surface area and four hip ridge lengths can be computed using simple trigonometry using the span, including overhang and the pitch. 

The photograph shows two sheds located in Colonial Williamsburg, Virginia that have pyramid hip roofs.

Pyramid Hip Roof Calculators

• Shingles for a Pyramid Roof: Number of shingles (normal and ridge), roofing nails and cost estimate.
• 4x8 Sheathing for a Pyramid Roof: Number of 4x8 sheathing needed to cover roof.
• Underlayment for a Pyramid Roof: Square feet of underlayment and estimated cost.
• Metal Panels for a Pyramid Roof: Metal panels, hip ridge trims, and angle.
• Purlins for a Pyramid Roof: Number of rows of purlins and the length of each row.
• Pyramid Roof Geometries: Surface area, volume, lengths of hips, face length, base area of a pyramid.

Single Price Survey Data

The Roofing Shingles Cost Survey list the observed price of a bundle of shingles. A bundle is equal to roughly 33 1/3 ft²  or one third of a roofing square (100 ft²) for standard 3-tab shingles.  Architectural shingles cover slightly less at 32.8 ft². The survey includes a date, the name of the store, and the five price points for shingles: economy, low, median, high and premium.

One  should use the pricing for roofing materials that can be bought locally.  However, the following prices are for different quality grades of shingles in the United States:

• Shingle Price Survey Online Source : Lowes
• Shingle Price Survey Date: 12/22/22
  • Cost of Premium Shingles: $90.0 USD.
  • Cost of High Grade Shingles: $52.34 USD.
  • Cost of Medium Grade Shingles: $43.32 USD.
  • Cost of Low Grade Shingles: $37.98 USD.
  • Cost of Economy Grade Shingles: $36.0 USD.

All prices are U.S. dollars for one bundle of shingles. 

Roofing Nails

The number of roofing nails is based on the two factors, one for normal wind conditions and one for high wind conditions.  For normal wind, the algorithm uses 348 nails per 100 ft2 based on the nailing patter shown below. For high wind conditions, the algorithm uses 522 nails per 100 ft2 based on the nailing pattern below.