Table of Contents
Introduction
This Roof Area Calculator helps you accurately determine the surface area of a roof, whether you’re a professional in the construction industry or a homeowner planning a roofing project.
You enter the width, length, and slope of each roof section, and the calculator computes the footprint area of the roof section, the roof pitch multiplier that applies for the given slope, and the actual surface area of the roof section.
You can get the dimensions of your roof sections by physically measuring the building (include roof overhangs in your measurements, not just the exterior wall dimensions), or you may be able to get usefully accurate measurements on Google Earth (this works much better for flat commercial roofs than for smaller pitched residential roofs). For help with this, see my article on how to measure a roof with Google Earth.
If you’re not sure what the slope of your roof is and you want to measure it, in either degrees or standard roof pitch (X:12), I recommend this slope finder on Amazon. It’s very inexpensive and very accurate. I also made an online roof pitch visualizer tool that you can use. You can see it here.
If your building is in the shape of a simple square or rectangle, you’ll only need to enter the width, length, and slope for the whole building, but the calculator also allows you to add the dimensions for multiple roof sections and then calculate their combined total area, which is useful for more complex building shapes.
This calculator works for gable roofs, hip roofs, basically any roof with a uniform pitch. Roof sections with different pitches should be calculated separately and then added together.
You can select feet or meters for your unit of measurement, and you can enter your roof slope in either standard roof pitch (X-in-12) or degrees.
Roof Surface Area Calculator
Roof Area & Intersecting Roof Sections
Question: Does an intersecting roof (roof section 2) increase roof surface area over the part of the building covered by the original roof (roof section 1) when both roofs have the same roof pitch?
Answer: No. When an intersecting roof, like the roof on an ell, has the same pitch as the main roof, the roof surface area over the footprint area covered by the main roof does not change from what it would be without the intersecting roof.
The area of the two new triangular planes created in the main roof to accommodate the intersection equals the area of the portion of the main roof that is removed for the intersection.
Math:
- The same roof pitch multiplier applies to all same-pitch roof planes.
- Surface area using slope in Degrees: For any roof pitch of angle θ, surface area equals horizontal plan (footprint) area multiplied by the roof pitch multiplier, which is sec θ.
Roof Surface Area = Footprint Area × sec θ
Note: “sec θ” means “the secant of the angle θ”.
Example: Footprint: 30 ft × 50 ft = 1,500 ft²; Pitch angle: θ = 30°; Pitch multiplier: sec 30° ≈ 1.1547; Roof surface area: 1,500 × 1.1547 ≈ 1,732 ft² - How to derive the pitch multiplier from standard pitch (“X in 12”): If the slope is X-in-12, the rise-run ratio is X/12. The multiplier can be found without using degrees since:
sec θ = √(1 + (X/12)²)
Example: An 8-in-12 pitch gives √(1 + (8/12)²) = √(1 + 64/144) ≈ √(1 + 0.44444) ≈ √1.44444 ≈ 1.2019 - Why roof intersections do not increase roof area over the original footprint (for roofs with the same pitch): Think in plan view first. The intersecting roof “cuts out” a region of the main roof’s plan area. Within that cut-out, the main roof plane is now subdivided into two triangular planes that meet the main roof plane at the two valleys and meet each other along the intersecting ridge. If those triangles have the same pitch as the original roof, they use the same roof pitch multiplier, sec θ. And their combined plan area equals the plan area that was removed from the main roof. So when that plan area is multiplied by the same roof pitch multiplier, you get the same roof surface area, whether the surface lies on the original main roof plane or on the two new roof planes formed by the intersecting roof.
- Logic: If you split a roof’s horizontal footprint into parts A, B, and C, the total surface area (S) at the same pitch is:
S = (A + B + C) × sec θ
Changing the shapes or their compass directions does not change the result, as long as the pitch angle is the same and the total footprint area stays the same. - When roof area can change: Different pitches. If the intersecting roof has a different pitch than the original roof, this will affect the surface area of the roof that covers the cut-out.
Gable Roofs and Hip Roofs Have the Same Area
Question: Do gable roofs and hip roofs that cover the same footprint and have the same pitch have the same surface area?
Answer: Yes. It feels counterintuitive because a hip roof slopes down on all four sides while a gable roof has vertical gable ends. That difference does not change the total surface area of the combined roof planes when the footprint and pitch are the same.
(Related, but not relevant here: Gable roofs and hip roofs do produce different attic volumes.)
How to think about it:
- One roof pitch multiplier applies to all roof planes with the same pitch. For a uniform pitch with angle θ, the roof surface area simply equals the horizontal footprint area multiplied by the roof pitch multiplier, which is sec θ.
Roof Surface Area = Footprint Area × sec θ - A gable roof has two main planes. A hip roof has four smaller planes. If the footprint is the same and every plane has the same pitch, the total horizontal plan area that those planes cover is still the same rectangle. Adding hips and shortening the ridge only changes how many roof planes cover that rectangle, not the total plan area (or the total area of the roof planes).
- Ridges, hips, and valleys are lines where planes meet. Lines have length, not area. They affect layout and the roofing contractor’s waste factor, but they do not change surface area.
Example:
- Footprint: 30 ft × 50 ft = 1,500 ft²
- Pitch: 6 in 12, so the multiplier is √(1 + (6/12)²) = √1.25 ≈ 1.1180
- Roof surface area: 1,500 × 1.1180 ≈ 1,677 ft²
That roof can be either a gable roof or a hip roof. As long as the footprint and the pitch stay the same, you still get 1,677 ft² of roof surface area.
Assumptions:
- Same rectangular footprint
- Same pitch on every plane
- Counting only the roof planes, not any vertical wall surfaces
More Roof Calculators
These calculators provide more detailed measurement information, including surface area, but also other key dimensions specific to that roof type, such as hip length and attic volume. Some of them cover roof types that don’t have flat roof planes or uniform pitches.
- Barrel Roof Calculator: Area, Arc Length, Volume, and More
- Conical Roof Surface Area Calculator and Math
- Dome Roof Area Calculators (Spherical, Ellipsoid, Onion)
- Gable Roof Calculator: Area, Slope, Volume, Rakes & More
- Hip Roof Calculator: Area, Slope, Volume, Ridge, Hips & More
- Pyramid Roof Calculator: Area, Slope, Hips & More
- Saltbox Roof Calculator: Area, Slopes, Volume, Rakes & More
About the Author
Jack Gray spent 20 years as a principal roof consultant with the Moriarty Corporation, an award-winning building enclosure consultant firm founded in 1967. Mr. Gray has worked in the roofing industry for over 25 years, with training and practical experience in roof installation, roof inspection, roof safety, roof condition assessment, construction estimating, roof design & specification, quality assurance, roof maintenance & repair, and roof asset management. He was awarded the Registered Roof Observer (RRO) professional credential in 2009. He also served as an infantry paratrooper in the 82nd Airborne Division and has a B.A. from Cornell University.