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Roofing Calculator

Find your roof's real area from the house's size and roof pitch. Then see how many squares and shingle bundles to buy, plus an optional cost.

Level: Grade 8

  • Common Core standard 8.G.B.7Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
Printable worksheet

Roofing Calculator

Know the answer you need? Pick an input to work backward.

Inputs
Measured in

Outside wall to outside wall, measured on the ground.

How far the roof sticks out past the walls. Enter 0 if your footprint already includes it.

Roof pitch given as

A 6/12 roof climbs 6 inches for every 12 inches across. Use 0 for a flat roof.

About 10% for a simple gable roof, 15% or more for hips, valleys and dormers.

Check the wrapper: most three-tab and architectural shingles take 3 bundles per 100 ft²; some heavy styles take 4 or 5.

Material or installed price for 100 ft² of roof.

Result

Roof surface area

1,502.64 ft²

About 1,503 ft² of roof: 16.5 squares with waste, or 50 bundles.

In square meters
139.6 m²
Roofing squares (no waste)
15.03
Squares including 10% waste
16.53
Shingle bundles to buy
50
Footprint with overhang
1,344 ft²
Slope factor
1.118
Roof angle
26.57 °

See the step-by-step solution ↓

Step-by-step solution

  1. Add the overhang to both ends of the length

    40+2×1=42 ft

  2. Add the overhang to both sides of the width

    30+2×1=32 ft

  3. Find the flat area the roof covers, seen from above: length times width

    42×32=1,344 ft²

  4. Find the slope factor, how much bigger a 6/12 sloped roof is than its flat area

    1+(612)2=1.118034

  5. Multiply the flat area by the slope factor to get the real roof surface

    1,344×1.118034=1,502.637681 ft²

  6. Divide by 100 to get roofing squares, since one square covers 100 ft²

    1,502.637681100=15.026377

  7. Add 10% extra for shingles cut off at edges, ridges and valleys

    15.026377×1+0.1=16.529014

  8. Multiply by 3 bundles per square, and round up because you can only buy whole bundles

    16.529014×3=49.587043=→ =50

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

What this calculator does

Find out how much roof you have to cover, and how many shingle bundles to buy for it. Roofing is sold by the square, which means 100 square feet of roof surface. You need that surface area to order shingles or underlayment (the sheet laid under them), or to check a contractor's quote. It's bigger than the floor area of the house, because the roof slopes and hangs past the walls.

You can take every measurement from the ground: the house's length and width, and the eave overhang (how far the roof sticks out past the walls). Add the roof pitch (how steep it is). The calculator then finds the real sloped area, the number of squares with some extra for waste, and the bundles to buy. Enter a price per square to estimate the cost.

Where it's used

Why this math matters outside the classroom:

  • Slope factor. A 6/12 roof has a slope factor of √(1 + 0.5²) ≈ 1.118, so 2,000 ft² of plan area becomes about 2,236 ft² of roof.
  • Roofing squares. Roofers divide roof area by 100, so 2,236 ft² is about 22.4 squares.
  • Shingle bundles. With three bundles to a square, as is common for shingles, 23 squares means 69 bundles before waste.
  • Overhangs. A 40 × 30 ft house with 1 ft eaves on every side has a plan area of 42 × 32 = 1,344 ft².
  • Comparing bids. Homeowners check a roofing quote by estimating the squares themselves from the footprint and pitch.

Grade level and standards: Grade 8; Common Core State Standards for Mathematics 8.G.B.7. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. Measure the outside length and width of the house, and choose feet or meters. For an L-shaped house, run the calculator once for each rectangle and add the results.
  2. Enter the eave overhang, the distance the roof sticks out past each wall. Use 0 if your measurements already include it.
  3. Enter the pitch as rise per 12 (such as 6/12) or as an angle. A pitch gauge, a level and tape measure, or the roof plans will tell you.
  4. Set a waste allowance and the bundles per square printed on the shingle package. Then read the area, squares and bundles.

What the inputs mean

House length (footprint)
Outside wall to outside wall, measured on the ground.
Eave overhang on each side
Eaves usually stick out 1 to 2 feet past the walls. The calculator adds the overhang to both ends of the length and both sides of the width.
Pitch: rise for every 12 of run
Pitch is how many inches the roof climbs for every 12 inches across. 4/12 is a gentle slope, 6/12 is common, and 12/12 is a 45° roof. 0 means a flat roof.
Waste allowance
Covers pieces cut off at the edges, valleys, hips, ridges and the first (starter) rows. A simple two-sided (gable) roof needs about 10%. Roofs with many hips, valleys or dormers need 15% or more.
Shingle bundles per square
Most shingles come 3 bundles to a square, but some heavy architectural shingles need 4 or 5. The package will tell you.
Price per square (optional)
Material or installed price for 100 ft² of roof.

Formula and method

plan area = (length + 2 × overhang) × (width + 2 × overhang)
slope factor = √(1 + (rise ÷ 12)²) = 1 ÷ cos(roof angle)
roof area = plan area × slope factor
squares = roof area in ft² ÷ 100
bundles = squares × (1 + waste % ÷ 100) × bundles per square, rounded up

Seen from above, a roof covers the house's footprint plus the overhang. That's the plan area. But the roof slopes, so it's longer along its surface than it looks from above. In the formula, rise is how many inches the roof climbs for every 12 inches across. The slope factor, √(1 + (rise ÷ 12)²), is how many times bigger the sloped surface is than the plan area. (√ means square root.) If you enter an angle instead, the same factor is 1 ÷ the cosine of that angle.

The slope factor is the same for gable, hip and shed roofs, as long as every section of the roof has the same pitch. Squares and bundles are measured in square feet. So metric areas are converted with the exact value 1 ft² = 0.09290304 m². Bundles are rounded up at the end, since you can't buy part of a bundle.

Worked example

A 40 ft × 30 ft house has a 1 ft overhang all around and a 6/12 roof. Shingles come 3 bundles per square, and you allow 10% for waste.

  1. With overhang: 40 + 2 × 1 = 42 ft and 30 + 2 × 1 = 32 ft.
  2. Plan area: 42 × 32 = 1,344 ft².
  3. Slope factor for 6/12: √(1 + 0.5²) = √1.25 ≈ 1.118034.
  4. Roof area: 1,344 × 1.118034 ≈ 1,502.64 ft², or 15.03 squares.
  5. With 10% waste: 15.03 × 1.1 ≈ 16.53 squares.
  6. Bundles: 16.53 × 3 ≈ 49.59, rounded up to 50 bundles.

Result: You have about 1,503 ft² of roof. That's 16.53 squares including waste, or 50 bundles of shingles.

Understanding the result

Order by the bundle count. When you get quotes for underlayment or labor, round squares up to whole squares. Leftover bundles are handy for future repairs, so many roofers keep one or two.

Steep roofs need much more material than their footprint suggests. A 12/12 roof has about 41% more surface than its plan area, while a 4/12 roof has only about 5% more.

Assumptions and limitations

  • Every section of the roof has the same pitch, so one slope factor works for all of it.
  • The footprint is a rectangle, and the overhang is the same on every side.
  • A square is 100 ft² of roof surface. Bundles per square comes from the shingle package.
  • Ridge caps, starter strips, drip edge, flashing and underlayment aren't counted separately. The waste allowance only partly covers them.
  • For roofs with mixed pitches, dormers or complicated shapes, measure each section separately, or use roof plans, for an accurate number.
  • Costs vary a lot with materials, removing the old roof (tear-off) and how easy the roof is to reach. Treat the cost line as a rough budget, not a quote.

Frequently asked questions

How many bundles of shingles are in a square?

Most standard and architectural shingles come 3 bundles per square, so each bundle covers about 33.3 ft². Some heavier or designer shingles come 4 or 5 to a square. Always check the wrapper, and set the bundles-per-square box to match.

Does a hip roof need more shingles than a gable roof?

For the same footprint and pitch, the surface area is the same. The slope factor doesn't depend on the roof's shape. But a hip roof does create more cut-off waste along its hips. So use a higher waste allowance, often 15% instead of 10%.

How do I find my roof pitch?

Go into the attic, or up a ladder at the gable end (the triangle-shaped wall). Hold a level flat against the rafter or roof. Measure 12 inches along the level, then measure straight up to the roof. That height is the rise, so 6 inches means a 6/12 pitch.

Can I use the floor area of my house instead?

Only as a starting point. The floor area in a listing may count several floors or leave out a garage. It also ignores the overhang and the slope. You'll get a much better answer by measuring the outside walls of the floor that sits under the roof.

How this calculator is checked

Method: Pythagorean slope factor √(1 + (rise/12)²); roofing square = 100 ft²; exact conversion 1 ft = 0.3048 m. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

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