Most jobs come down to a handful of calculations: area, volume (for concrete), board feet, roof pitch and rafter length, and squaring a corner. Get these five right and you order the right amount, cut the right length, and stop paying for material you did not need. Here they are in plain form, with the units that trip people up called out. The on-site calculators do these for you, but knowing the math means you can sanity-check the number before you order.
Area, and the waste factor
Area is length times width, in the same units. A 12 ft by 15 ft room is 180 square feet. The catch is always waste: add roughly 10% for square layouts and 15% or more for diagonal tile, complex cuts, or patterned material. Never order exactly to the calculated area.
Handy area conversions:
- 1 square yard = 9 square feet (carpet and some flooring price per square yard)
- 1 "square" of roofing = 100 square feet
- 1 acre = 43,560 square feet
Volume, and concrete by the yard
Concrete is sold by the cubic yard, and the number one ordering mistake is mixing units. The formula:
Cubic yards = (length in feet x width in feet x thickness in feet) / 27
The thickness is the one people get wrong. A 4-inch slab is 0.33 feet (4 divided by 12), not 4. So a 10 ft x 10 ft slab at 4 inches is 10 x 10 x 0.33 / 27 = about 1.23 cubic yards. Add about 10% for spillage and uneven subgrade, and round up, because coming up short on a pour is a bad day. For small patches by the bag, an 80 lb bag yields roughly 0.6 cubic foot and a 60 lb bag about 0.45 cubic foot (27 cubic feet to the yard, so it takes a lot of bags).
Board feet (lumber by volume)
Lumber is often priced by the board foot, which is a volume, not a length:
Board feet = (thickness in inches x width in inches x length in feet) / 12
So a 2 x 6 that is 12 feet long is 2 x 6 x 12 / 12 = 12 board feet. Use nominal sizes (what it is called, the 2x6) for pricing, even though the actual dressed size is smaller.
Roof pitch and rafter length
Pitch is written as rise over 12 of run, so a "6/12" roof climbs 6 inches for every 12 inches horizontal. To get the actual rafter length from the horizontal run, multiply the run by the pitch's length multiplier:
- 4/12 pitch: run x 1.054
- 6/12 pitch: run x 1.118
- 8/12 pitch: run x 1.202
- 12/12 pitch: run x 1.414
So a common rafter over an 8 ft run on a 6/12 roof is about 8 x 1.118 = 8.94 feet before the ridge and overhang adjustments. That same multiplier turns a roof's flat plan area into its actual sloped surface area for ordering shingles.
Squaring a corner: the 3-4-5
To check a corner is a true 90 degrees, measure 3 feet along one side and 4 feet along the other. If the diagonal between those two marks is exactly 5 feet, the corner is square. Any multiple works and bigger is more accurate: 6-8-10, 9-12-15. It is the fastest layout check in the trade and it costs nothing.
Stairs, quickly (and where the code comes in)
The math of a stair is simple: divide the total rise (finished floor to finished floor) by your target riser height to get the number of risers, then the run is the number of treads times the tread depth. The math is universal, but the legal limits on riser height, tread depth, and how much they can vary are set by code and change by adopted edition and jurisdiction. So calculate the layout here, but get the actual limits from Do I need a permit and the per-state codes before you build. Do not eyeball stairs.
Units that catch people out
- 1 yard = 3 feet, 1 cubic yard = 27 cubic feet, 1 square yard = 9 square feet
- 1 foot = 12 inches, and inch fractions add in sixteenths (1/8 = 2/16, 1/4 = 4/16)
- Circle: area = 3.1416 x radius squared, circumference = 3.1416 x diameter
- 1 gallon of water is about 0.134 cubic foot (roughly 7.48 gallons to the cubic foot)
The move
Do the math first, add your waste factor, then round up on anything you cannot easily buy more of mid-job (concrete especially). Use the on-site Calculators to check yourself, and keep a tape, a framing square, and a calculator on you. The cost of measuring twice is a minute. The cost of measuring once is a return trip or a short pour.
Common questions
How many bags of concrete do I need for a cubic yard?
Roughly 45 80-pound bags, or about 60 60-pound bags, make one cubic yard. An 80-pound bag yields about 0.6 cubic foot and a 60-pound bag about 0.45 cubic foot, and there are 27 cubic feet in a yard, so you divide 27 by the bag yield. Bags are fine for small patches and post holes, but once you are past roughly half a yard, ordering ready-mix is usually cheaper and far less work. Always confirm the yield printed on the bag, since it varies by product.
How do I convert inches to a decimal of a foot?
Divide the inches by 12. So 4 inches is 4 divided by 12, which is 0.33 feet, 6 inches is 0.5 feet, and 9 inches is 0.75 feet. This matters most on concrete, where a 4-inch slab thickness has to go into the volume formula as 0.33 feet, not 4. Putting the inches in raw is the most common ordering mistake there is, and it overstates the order by a factor of twelve.
What is a "square" in roofing?
A square is 100 square feet of roof area. Roofing material, labor, and estimates are all quoted by the square, so a roof with 2,000 square feet of surface is 20 squares. Use the actual sloped area, not the flat footprint of the house, which means multiplying the plan area by the pitch multiplier first. Shingles are sold in bundles, and it usually takes three bundles to cover a square, but confirm that against the specific product.
How many square feet are in an acre?
An acre is 43,560 square feet. That is the number to memorize for site and lot math. For a quick mental check, a square parcel about 209 feet on each side is close to one acre. If you are working in square yards, an acre is 4,840 square yards, since there are 9 square feet in a square yard.
The honest bit
- These formulas are standard, but always confirm supplier coverage rates (bag yields, mortar and adhesive spread rates) against the bag, since those vary by product.
- Code limits for stairs, guards, and openings are not printed here on purpose, because they depend on the edition your jurisdiction adopted. Get them from Do I need a permit and Working in Your State.
- This is general guidance, not engineering. Structural spans and loads need the code tables or an engineer, not a rule of thumb.
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