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Sixty-odd tools is a drawer, not a course. This page is the course: three tracks, one tool at a time, in the order the arithmetic builds. Each step says why it comes next and gives you one problem to try. Type your answer and the page checks it — and when you miss, it tells you which mistake it thinks you made, because on a job site the mistake is always one of the same four or five.
None of this is code. Every number in a problem is stated in the problem; where a real job has a limit — a slab thickness, a drop percentage, a riser height — that comes from your plans and your authority, and the tools leave a blank for you to type it.
Track 1 — Concrete & site
Everything on a site starts as an area, becomes a volume the moment you add a depth, and turns into an order once you know what a truck or a bag holds. Seven tools, and by the end the ÷27 will be reflex.
- Square footage
Why first: every takeoff begins with length × width. Get the habit of writing the unit next to the number — 720 sq ft, not 720 — and half the later mistakes never happen.
- Concrete
Why next: add a thickness to that area and you have a volume. This is where inches sneak in beside feet and where the cubic yard (27 cubic feet) lives — the two errors that put a truck in the wrong place.
- Concrete bags
Why next: a small pour is the same volume bought in bags, and a bag is just a yield: divide what you need by what one bag makes. The number to hold on to is the yield printed on the bag — not the weight.
- Gravel
Why next: the base under that slab is the same length × width × depth — but the pit sells it by weight, so a density turns yards into tons. The density is the supplier's number; the multiplication is yours.
- Excavation
Why last: the hole you dig is bank volume; the spoil that comes out of it is bigger, because loose material swells. The truck count comes from the loose figure, and that catches everyone once.
- Post hole concrete
Why next: the first volume with something already sitting in it. A hole full of concrete is one cylinder; a hole with a post down the middle is that cylinder minus the post. Forget the subtraction and you buy bags you will carry home again.
- Trench
Why last: a trench is the whole track in one dig — a volume, a subtraction, a swell and an order, stacked in layers. Bedding under the pipe, backfill over it, and spoil that will not all fit back in the hole.
Done the seven? Next on this shelf: footings, round columns (a cylinder, not a box), cut & fill, which is excavation with a plus and a minus column, and ramp slope when the grade has to come out at a ratio somebody else set.
Track 2 — Framing & finish
Framing is counting and triangles; finishing is area divided by what a sheet, a box or a can covers. The one skill under all of it is reading a tape as a number and a number as a tape, so that is where this track starts.
- Fraction to decimal
Why first: the tape speaks in sixteenths, the calculator speaks in decimals, and you have to translate both ways without thinking. Sixteenths are 0.0625 each — that one fact carries the whole tape.
- Studs
Why next: a wall is a count. Length ÷ spacing gives you the spaces; a stud stands at both ends of the run, so there is always one more stud than spaces. Corners, openings and partitions add to that.
- Wall framing
Why next: the stud count was one line of a material list. The whole wall is that count plus the kings, jacks and cripples at each opening, the plates, the blocking and the sheathing — and every one of them is an addition you can lose track of standing at a lumber counter.
- Stairs
Why next: the first division that has to come out as a whole number. Rise ÷ target riser, round it, then divide the rise back by that count — every riser identical, which is what feet notice.
- Rafter length
Why next: the stair stringer was a hypotenuse, and so is a rafter. Run and rise are the two legs; √(run² + rise²) is the board. Pitch is just rise per foot of run.
- Roofing
Why next: the rafter told you a roof is longer than the building under it. Roofing sells that in squares, and a square is a hundred square feet — so the footprint has to be stretched by the pitch factor before anything gets ordered.
- Drywall
Why next: finishing starts with wall area, and wall area is perimeter × height — not the floor. Divide by a sheet, and always round up: a 0.1 of a sheet is still a sheet.
- Paint
Why last: the same 416 sq ft, divided by what a gallon covers — except coats multiply the area first. Coverage is the number on the can; the tool leaves it as a field for that reason.
From here: board feet for the lumber order, tile and flooring for the floor, 3-4-5 for squaring a corner with the same triangle you just used. Keep units & fractions open beside all of it — the tape chart in sixteenths and the exact factors, on one page.
Track 3 — Electrical basics
Five relationships, each one line long, each feeding the next. These tools do arithmetic on numbers you bring — none of them holds a table, and none of them tells you what is allowed. That is deliberate: the arithmetic is the part you can practise here.
- Ohm's law
Why first: V = I × R is the one relationship everything else is built on. Type any two, get the other two — then cover the answer and predict it before you look.
- kVA
Why next: volts × amps is apparent power. Divide by 1000 for kVA; multiply by √3 only when it is three phase. Those two factors are the whole tool — and the two things people forget.
- Motor amps
Why next: horsepower becomes watts (746 each), and the motor's efficiency and power factor both make the current larger than the watts alone would say. Both are numbers off the nameplate — you type them.
- AWG to mm²
Why next: the next tool wants a cross-section, and a gauge number is a size by definition, not by chart: the diameter is 0.005 × 92^((36 − n)/39) inches, and the area is a circle. You can compute any gauge from that one line.
- Voltage drop
Why last: everything above meets here. Resistance per km comes from the metal and that cross-section; the run is doubled because the current comes back; times the amps is the volts lost. The limit you compare it to is your job's — the tool has a blank for it.
The voltage-drop page carries on from here — the working written out, three more worked runs, and a drill that hands you random runs to estimate. Conduit fill and derating are on the shelf too; both take your book's figures and only divide.
How to use the tracks
Do the problem before you open the tool. A calculator that agrees with a number you already worked out teaches you the arithmetic; a calculator you copy from teaches you nothing. When a step goes wrong, the feedback line names the mistake it thinks you made — read it, fix the one step, and try again rather than starting over. Then open the tool, type the same figures in, and watch it land on your answer. That agreement is the whole point.
Each track is about twenty minutes. Nothing is saved, nothing is scored, and no one is watching — the only person who needs to know you got the drywall count wrong is you, and only until you get it right.
One more habit
Where somebody actually signs the work off — concrete and masonry, framing, site and excavation, drywall and insulation, the electrical tools — the tool carries a What an inspector looks for panel. Read it before you start, not after: a lot of what an inspector turns down is work that had to be done in an order — covered before it was looked at, poured before it was tied — and that is cheap to get right the first time and expensive afterwards. What is deliberately not in those panels is the numbers: rise limits, cover depths, fill percentages and ampacities all live in the code your jurisdiction has adopted, and every tool here leaves a blank for you to type yours into.
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