Every takeoff formula, and where each one gets its number
Six quantities, one room. What separates a takeoff that survives a dispute from one that does not is knowing which openings come off which line — and none off some.
The room is a walk, and everything else falls out of it
Before any quantity there is one thing: the walk. A run, a turn, a run, a turn, back to where you started. Every corner is where the previous run left you, and the polygon that closes is the room.
Floor area is the shoelace formula over those corners — not width times depth, which is only right when the room happens to be a box. Perimeter is the runs added up. Everything below is those two numbers with something taken off.
If the walk does not close, none of it means anything, and that is worth finding out first. The odd-shaped room calculator walks a room and says how far out it finished.
The four a room produces on its own
| Quantity | Derivation | Unit |
|---|---|---|
| Floor | the shoelace formula over the corners the walk lands on | sq ft |
| Ceiling | follows the floor outline exactly | sq ft |
| Wall face | built walls × their height, less every door, window and cased opening | sq ft |
| Baseboard | built walls less doors and cased openings; it runs under a window | lf |
Two things in that table are doing more work than they look like they are.
"Built walls." A side of a room with nothing across it — a garage door opening, a wide span into the next room — bounds the floor and the ceiling and closes the polygon, and it carries no drywall, no paint and no baseboard. It is an open span, it is priced at nothing, and it appears on the sheet as its own line so that nobody finds out about it from a delivery.
"Less every door, window and cased opening" — but not the same ones on each line. That is the sentence this whole page exists for.
Which openings come off which
| Wall face | Baseboard | Floor and ceiling | |
|---|---|---|---|
| Door | Comes off — width × height | Comes off — its width | No effect |
| Cased opening | Comes off — width × height | Comes off — its width | No effect |
| Window | Comes off — width × height | Stays — base runs underneath it | No effect |
Subtracting windows from the base run is the second commonest arithmetic error in a takeoff, and it always goes the same way: short. The commonest is pricing board off the floor area.
On a room 12' × 14' at 8', with one 3' × 6' 8" door and one 3' × 5' window, that is the difference between four numbers:
| Figure | |
|---|---|
| Floor, and ceiling | 168.0 sq ft |
| Perimeter | 52.00 lf |
| Wall face before any deduction | 416.0 sq ft |
| Wall face, door and window off | 381.0 sq ft |
| Baseboard — door off, window not | 49.00 lf |
Quote the floor figure for board and you are short by a factor of more than two. Subtract the window from the base and you are short by its width, on every room in the house.
Every way the app measures a surface
These are the app’s own measures, and the sentence beside each one is the sentence it prints under that line on a takeoff. This table is generated from the engine rather than written here, so it cannot describe a quantity differently from the way the app derives it.
| Measure | Unit | On | What comes off it |
|---|---|---|---|
| the face of the wall, less its openings | sq ft | wall | the wall face, its height less every door and window in it |
| how long the wall is, corner to corner | lf | wall | the whole run of the wall, openings included |
| the run along the floor, less doors and cased openings | lf | wall | the wall at the floor, less doors and cased openings; base runs under a window |
| doors in the wall | ea | wall | counted off the wall |
| windows in the wall | ea | wall | counted off the wall |
| cased openings in the wall | ea | wall | counted off the wall |
| every opening in the wall — doors, windows and cased | ea | wall | every opening in the wall, whatever kind |
| the floor | sq ft | floor | the floor outline |
| the ceiling | sq ft | ceiling | follows the floor |
| a number you type | ea | wall, floor, ceiling | a number typed by hand — it does not move when the room does |
The last row is the honest one. Some things on a job are not measured off a room at all — a dumpster, a day, a permit — and a number typed by hand does not move when the room does. The sheet says so on that line rather than letting it pass for a quantity somebody derived.
The quantities that need a wall thickness
Four more come out of the room only once somebody has said how thick the walls are, and every one of them is unorderable without it:
- Jamb depth — the wall thickness plus a sixteenth. One per wall thickness rather than one per room: an average would be right for some openings and send the wrong pre-hung unit for the rest.
- Opening wrap — the board that returns into the reveal. Its area is the reveal’s perimeter times the thickness. Two jambs and a head on a door; a sill as well on a window, because a door has the floor running through it.
- Plates and studs — three times the framed run for plates, one bottom and two top, and field studs at the spacing plus one at each end of each wall.
- Outside footprint — the inside area plus the wall thickness all the way round, which is what a slab, a roof and a permit sketch are measured on.
A wall with no thickness given contributes to none of those, and the takeoff names it rather than assuming four and a half inches. That matters more than it sounds: a block garage priced as stud framing reconciles perfectly and is wrong, and a sheet missing the framing for three walls also adds up perfectly.
Where the errors actually live
The perimeter, four inches out
Four inches over four walls moves the wall face by more than ten square feet, and nothing about the resulting number looks wrong. It is as authoritative as a correct one.
The ceiling height, taken once
It multiplies the perimeter, so it multiplies the error, and in an old house it is different in the next room.
A window taken off the base run
Short by the window width, every time, on every room with glass in it.
An opening deducted with no return added
The wall face is right and the board order is short by the wrap. On a job with a lot of doors this is real money.
Two collinear walls entered as one
A wall written twice, or a real angle recorded as square. Either way the walk stops closing, which is the one error a takeoff can catch on its own.
Why the sheet says where the numbers came from
Every formula above is exact arithmetic on exact integers — lengths in whole nanometres, areas in whole square nanometres, money in whole cents — so nothing is ever rounded until the moment it is printed for a person to read. That removes one class of error completely.
It does nothing at all about the other one. A perfectly derived quantity from a wall nobody measured is a perfectly derived guess, and by the time it is a line on a client’s proposal nothing on the paper says which it was. Which is why every length in Trueline carries how it was arrived at — scanned, drawn, or measured with a tape — right through onto the document somebody signs.
Run any of these on your own room: the calculators use this exact code, in your browser, on figures you type.
Free download: Room takeoff sheet — a blank PDF to print, generated by the same code that produces the app’s own documents. All the templates.
Questions people ask
- What is the formula for wall face area?
- The perimeter of the built walls times the ceiling height, less the area of every door, window and cased opening. Floor area has nothing to do with it, and a side of the room with no wall built across it contributes nothing.
- Do windows come off the baseboard run?
- No. Baseboard runs underneath a window, so only doors and cased openings interrupt it. Windows do come off the wall face, which is why the two lines deduct different openings from the same perimeter.
- How is floor area calculated for a room that is not rectangular?
- By the shoelace formula over the corners the walk lands on. It handles an L, a U, a bay and an angled wall without being told which of them it has, and it is exact — width times depth is only correct when the room is genuinely a box.
- What is an opening return, and why does it need a wall thickness?
- It is the board or trim that wraps through the wall into the jamb. Its area is the perimeter of the reveal times the thickness of the wall, so without a thickness there is no number — and guessing one would price a block wall as stud framing while the sheet still reconciled.
- Why keep the ceiling separate from the walls?
- Because they are boarded differently, finished differently and frequently hung by different people. A combined figure cannot be priced against either trade’s rate, and once combined it cannot be taken apart again.
Where this fits with Trueline
Trueline is an iPhone app that measures a room, takes it off, prices it from your own rate book and turns it into a proposal — with every length carrying whether it was scanned, drawn or measured, right onto the document a client reads. See how it works, or take the free templates and use them with whatever you already have.