A “flat roof” is actually a “low sloping roof” and the finish material will determine how low you can go. Low slope roofs have a pitch of 2:12 (2 inches of drop over 12 inches horizontal) or less. Low slope roofs use membranes and metals as apposed to shingles to provide water protection. Most shingle roofs require 4:12 pitches or steeper.
Think of a membrane roof like a giant pool liner for your roof, draining water to the edges or on larger roofs, toward center drains. The most popular type of roofing membrane now days is Thermoplastic Polyolefin or TPO. TPO is a single layer of synthetic material which comes in rolls between 10 and 20 feet in width. The membrane is seamed together on-site and offers 30+ years of protection depending on the thickness and manufacturer. Most TPO systems offer 1/4:12 slope and are considered the industry choice for most applications. Other membrane roofs include Ethylene Propylene Diene Terpolymer (EPDM) which is a synthetic rubber and PVC which is similar to TPO but is more flexible yet more susceptible to tearing.
Some metal roof finishes offer low sloping capabilities. Standing seam metal roofs, depending on the manufacturer and height of the ribs, can allow 1/4:12 slope as well.
So why not shingles?
Shingle roofs are not a sealed system. They rely on the watershed and are not designed to hold water. Some manufacturers will allow 2:12 slope with shingles depending on the underlayment used. Instead of the typically felt paper, 2:12 shingle roofs require ice/water shield membrane underlayments to prevent water from getting in.
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