Sheet Vinyl and Carpet Roll Calculator (Length Needed, Seams, Offcuts and Cost)

Enter the room size, the roll width, the trim allowance, the pattern repeat and the increment the store cuts in. The price can be left blank (then no cost is calculated).

Units

Room size

Length × width

Room length (m)

Room width (m)

Roll width

Trim allowance per strip (cm)

Pattern repeat (cm, 0 if solid)

Cut in increments of

Price ($, optional)

The room length and width are in meters, the trim allowance and pattern repeat in cm, and the roll width in the unit chosen on the right (cm or m). For a solid color, set the pattern repeat to 0.

Result and figure

Enter the room size and the roll width in the fields on the left and press "Calculate". The length needed for running the roll lengthwise and widthwise will appear here.

[ CLOSE ]

What you can do on this page
What is this calculation used for?
How to Use
Formulas and figures
Symbols and terms
- Symbols
- Terms
Good to know before you start
How to calculate it in Excel
How to calculate it in Google Sheets
How to calculate it in Python
How to write it in LaTeX and other math languages (copy and paste)
How to have ChatGPT do the calculation
DataChef Features
Related Features
NumberChef Calculators List

What you can do on this page

Enter the room length and width and the roll width (sheet vinyl is usually 12 ft wide), and you get the number of strips, the length of each strip and the total length for running the roll lengthwise and widthwise. The page recommends the direction that needs less
Measure in feet and inches by default, or switch "Units" to Metric to work in meters and centimeters
Enter the trim allowance (the extra length for each strip) and the pattern repeat, and the extra length for pattern matching is added to each strip
The length needed is rounded up to the increment the store cuts in (6 in, 1 ft or 1 yd) to give the length to buy, along with the offcut area and the waste rate
Enter a price (per linear foot or per square foot), and the estimated cost for each direction is calculated too
A plain-language explanation of the formulas, a layout drawing and copy-and-paste formulas for Excel, Google Sheets and Python are all on this page

This page is for roll goods: flooring cut to length from a roll of fixed width, such as sheet vinyl, linoleum, roll carpet (broadloom) and commercial sheet flooring. For plank flooring laid piece by piece, such as hardwood, laminate or vinyl plank, use the "Flooring Calculator" page, and for wallpaper use the "Wallpaper Calculator" page. The length needed assumes a rectangular room. In an L-shaped room, or with closets, columns or doorways, the actual layout may need a different number of strips or lengths.

What is this calculation used for?

Laying sheet vinyl yourself in a kitchen or a family room

Sheet vinyl is a popular DIY floor for kitchens, laundry rooms and basements. For a 15 ft × 13 ft room with a 12 ft wide roll, running it widthwise takes 2 strips × 13.5 ft = 27 ft, while running it lengthwise takes 2 strips × 15.5 ft = 31 ft. Pick the wrong direction and you buy 4 ft more.
Working out both directions before you buy saves money on material, and it also saves you from running short and buying more later from a different dye lot, whose color may not quite match.

Covering a room with no seam

Sheet vinyl also comes 13.2 ft (13 ft 2 in) wide, and carpet 15 ft wide. In the same 15 ft × 13 ft room, a 13.2 ft roll run lengthwise covers the room in one strip of 16 ft, with no seam. A 15 ft carpet run lengthwise also covers it in one piece. In a bedroom or a family room, where the feel and the look matter, being able to go seamless can decide which product you choose.
Change the roll width on this page to 13.2 or 15 and you can see right away whether one direction needs only one strip.

Checking the quantity in a flooring quote

Flooring quotes often list carpet and sheet vinyl in square yards rather than in feet of roll. The material is bought as "roll width × length", so the quantity comes from strips × strip length, as in these formulas. For example, 27 ft of a 12 ft roll is $27 \times 12 = 324$ ft², which is $324 \div 9 = 36$ square yards.
Knowing the formulas, you can follow which layout the quote is based on and how much trim and pattern allowance it includes (a real quote also covers labor, floor preparation and removal of the old floor, so the quantity alone does not tell you whether the price is fair).

Laying commercial sheet flooring in a long hallway

In a long, narrow space such as a 5 ft × 40 ft hallway, a 6 ft wide roll run down the length covers it in one strip of 41 ft with no seam. Running it across the hallway takes $\lceil 40 \div 6 \rceil = 7$ strips × 5.5 ft = 38.5 ft, bought as 39 ft. That is a little shorter, but it makes 6 seams. When the lengths are close, stores and offices usually choose the direction by also weighing the number of seams and the installation work.
This page recommends the direction by the length to buy, so if you want fewer seams, also check "Strips (seams)" in the result.

Allowing for pattern matching with patterned sheet vinyl

Wood-look and tile-look sheet vinyl has a pattern repeat, such as 18 in, and to line up the pattern at a seam, each strip is rounded up to a multiple of the repeat. For a 15 ft room with the roll run lengthwise, a 15.5 ft strip for a solid color becomes 16.5 ft for a pattern, so 2 strips need 2 ft more.
If you calculate as if the product were solid and then buy a pattern, you may run short, so always enter the repeat for a patterned product.

Formulas and figures

Number of strips (how many widths side by side)

Figure

Standard notation (the usual math form)

$n$ $=$ $\lceil$ $b$ $\div$ $w$ $\rceil$

In words (symbols replaced with words)

④ $n$: number of strips $=$ ③ $\lceil$ ① $b$: room side across the roll $\div$ ② $w$: roll width $\rceil$

The formula in words

① Take the $b$: room side across the roll

② divide it by the $w$: roll width to see how many roll widths it takes

③ round up to the next whole number (the symbol $\lceil\ \rceil$ means "round up")

④ and you get the $n$: number of strips

Quick example

For a 15 ft × 13 ft room with 12 ft wide sheet vinyl run lengthwise (the 13 ft width is covered by roll widths), the number of strips is

$n$: number of strips $=$ $\lceil$ width (13 ft) $\div$ roll width (12 ft) $\rceil$

$13 \div 12 \approx 1.08$

$\lceil 1.08 \rceil = 2$

Key idea

With roll flooring, the number of strips is how many roll widths you lay side by side. If the roll runs along the room length (lengthwise), the side to cover is the width, so $b$ is the width. If it runs widthwise, $b$ is the length. Even if 1.08 roll widths would do, you cannot buy "a little more than one" strip, so you round up to 2. Two strips side by side make 1 seam (the number of seams is $n-1$). If the roll is wider than the room, $n=1$ and there is no seam. When the room is almost exactly "roll width × number of strips" wide (for example, a 12 ft wide room with a 12 ft roll), there is no slack across the width. Crooked walls or a small measuring error can leave you short. Measure the room and check that you have at least a few inches to spare, and if in doubt, plan for one more strip or a wider roll.

Length of each strip (with trim and pattern matching)

Figure

Standard notation (the usual math form)

$l$ $=$ $a$ $+$ $m$

$l$ $=$ $p$ $\times$ $\lceil$ $($ $a$ $+$ $m$ $)$ $\div$ $p$ $\rceil$

In words (symbols replaced with words)

③ $l$: strip length (solid color) $=$ ① $a$: room side along the roll $+$ ② $m$: trim allowance

⑥ $l$: strip length (patterned) $=$ ④ $p$: pattern repeat $\times$ ⑤ $\lceil$ $($ $a$: room side along the roll $+$ $m$: trim allowance $)$ $\div$ $p$: pattern repeat $\rceil$

The formula in words

① Take the $a$: room side along the roll

② add the $m$: trim allowance

③ and you get the $l$: strip length for a solid color

④ For a patterned product, find how many times the $p$: pattern repeat goes into that length,

⑤ round it up to a whole number (the symbol $\lceil\ \rceil$),

⑥ and multiply by the pattern repeat to get the $l$: strip length for a patterned product

Quick example

For a room 15 ft long with the roll run lengthwise, the strip length for a solid color with a 6 in (0.5 ft) trim allowance, and for a pattern with an 18 in (1.5 ft) repeat, is

$l$: strip length (solid color) $=$ length (15 ft) $+$ trim allowance (0.5 ft)

$15 + 0.5 = 15.5$

$1.5 \times \lceil 15.5 \div 1.5 \rceil = 1.5 \times \lceil 10.33 \rceil = 1.5 \times 11 = 16.5$

Key idea

Walls are rarely perfectly straight, and doorways and columns get in the way, so a strip cut to the exact room length can come up short. It is common to leave about 3 in extra at each end (the trim allowance) and trim the strip to the wall after laying it. With a pattern (wood grain, tile look and so on), strips must be placed so the pattern runs on across the seams. Lining it up means shifting the strips, so each strip is rounded up to a multiple of the pattern repeat. A solid color needs no pattern matching, so you just add the trim allowance. Strictly speaking, the first strip has nothing to match to, but so that any strip can go first, this page rounds every strip up when two or more are laid side by side. When one strip covers the room (no seam), no pattern matching is needed, so even a patterned product only gets the trim allowance added. How much extra a pattern match needs differs by product, and some manufacturers give their own guideline, such as "add one repeat per strip". Check the product's installation instructions before ordering.

Length needed and length to buy

Standard notation (the usual math form)

$M$ $=$ $n$ $\times$ $l$

$M'$ $=$ $\lceil$ $M$ $\div$ $u$ $\rceil$ $\times$ $u$

In words (symbols replaced with words)

③ $M$: length needed $=$ ① $n$: number of strips $\times$ ② $l$: strip length

⑤ $M'$: length to buy $=$ $\lceil$ $M$: length needed $\div$ ④ $u$: cutting step $\rceil$ $\times$ $u$: cutting step

The formula in words

① Take the $n$: number of strips

② multiply it by the $l$: strip length

③ and you get the $M$: length needed

④ Then divide the length needed by the $u$: cutting step , round up, and multiply by the step again

⑤ and you get the $M'$: length to buy

Quick example

For a 15 ft × 13 ft room, a 12 ft wide solid-color roll, a 0.5 ft trim allowance and a 1 ft cutting step, the length needed lengthwise (2 strips × 15.5 ft) and widthwise (2 strips × 13.5 ft) is (the first line of the steps is lengthwise, the second is widthwise)

$M$: length needed $=$ strips (2) $\times$ strip length (15.5 ft)

$2 \times 15.5 = 31$

$2 \times 13.5 = 27$

Key idea

In this example, both directions need 2 strips, but the strips are 15.5 ft and 13.5 ft long, so the length needed is 31 ft one way and 27 ft the other, a clear difference. When you choose the direction, always work out the length for both ways and compare. This page recommends the direction with the shorter length to buy (or, if they are equal, the one with fewer seams). The number of seams is shown too, so when the difference in length is small, choosing the direction with fewer seams is also a sensible choice. You cannot always buy exactly the length needed. Many stores cut sheet vinyl and carpet from the roll by the linear foot, so the length needed rounded up to the cutting step is what you actually buy (for example, 26.4 ft cut in 1 ft steps is $\lceil 26.4 \div 1 \rceil \times 1 = 27$ ft).

Offcut area and waste rate

Standard notation (the usual math form)

$E$ $=$ $M'$ $\times$ $w$ $-$ $S$

$r$ $=$ $E$ $\div$ $($ $M'$ $\times$ $w$ $)$

In words (symbols replaced with words)

④ $E$: offcut area $=$ ① $M'$: length to buy $\times$ ② $w$: roll width $-$ ③ $S$: floor area

⑥ $r$: waste rate $=$ $E$: offcut area $\div$ $($ $M'$: length to buy $\times$ ⑤ $w$: roll width $)$

The formula in words

① Take the $M'$: length to buy

② multiply it by the $w$: roll width to get the area bought, then

③ subtract the $S$: floor area

④ and you get the $E$: offcut area

⑤ Divide the offcut area by the area bought (length to buy × roll width)

⑥ and you get the $r$: waste rate

Quick example

For a 15 ft × 13 ft room (195 ft² of floor), with a 12 ft wide roll run widthwise and 27 ft bought, the offcuts are

$E$: offcut area $=$ length to buy (27 ft) $\times$ roll width (12 ft) $-$ floor area (195 ft²)

$27 \times 12 - 195 = 324 - 195 = 129\,\mathrm{ft^2}$

$129 \div 324 \approx 0.398\ \ (39.8\%)$

Key idea

The offcuts are "area bought − floor area". The area bought is the length to buy times the roll width (the area of the roll when unrolled). In the same room, running the roll lengthwise means buying 31 ft × 12 ft = 372 ft², with 177 ft² of offcuts (47.6%), while running it widthwise leaves 129 ft² (39.8%). The direction alone changes the waste a lot. Most of the waste is the extra width (two 12 ft strips are 24 ft wide for a 13 ft room), followed by the trim and pattern allowances. When the waste rate is high, you can turn the roll the other way, choose a product in a different width (a 13.2 ft wide roll covers this room in one strip), or reuse the offcuts in a small space such as a bathroom or a laundry room.

Estimated cost

Standard notation (the usual math form)

$T$ $=$ $c$ $\times$ $Q$

In words (symbols replaced with words)

③ $T$: estimated cost $=$ ① $c$: unit price $\times$ ② $Q$: quantity

The formula in words

① Take the $c$: unit price (per linear ft or per ft²)

② multiply it by the $Q$: quantity (the length to buy or the area bought, to match the price)

③ and you get the $T$: estimated cost

Quick example

The cost of buying 27 ft of sheet vinyl (run widthwise) at $18 per linear foot is

$T$: estimated cost $=$ unit price ($18 per linear ft) $\times$ length to buy (27 ft)

$18 \times 27 = 486$

Key idea

The key is to match the units of the price and the quantity. If the price is per linear foot (1 ft of length at the full roll width), multiply by the length to buy $M'$. If it is per square foot, multiply by the area bought $M' \times w$. A price per square yard divided by 9 gives the price per square foot. Here $18 per linear foot on a 12 ft roll is the same as $1.50 per ft², and 27 ft costs $486 either way ($1.5 \times 324 = 486$). Running the roll lengthwise (31 ft) would cost $558, so the direction changes the cost too. Adhesive, seam sealer, tools and labor are extra.

The length of roll flooring you need is "the number of strips across, ⌈b ÷ w⌉, × the strip length (a + trim allowance, rounded up to a multiple of the pattern repeat for patterned products)". Work it out for both lengthwise and widthwise, and the basic rule is to pick the direction with the shorter length to buy.

Symbols and terms

Symbols

$a$	a	The room side along the roll (ft). It is the room length when the roll runs lengthwise, and the width when it runs widthwise. Think of "a" for "along".
$b$	b	The room side across the roll (ft), the side covered by roll widths. It is the width when the roll runs lengthwise, and the length when it runs widthwise.
$w$	w	The roll width (ft), from "width". Sheet vinyl is usually 12 ft wide.
$m$	m	The trim allowance (ft), the total extra length per strip, from "margin". About 3 in at each end, 6 in (0.5 ft) in total, is typical.
$p$	p	The pattern repeat (ft), the length after which the pattern repeats along the roll, from "pattern". A solid color counts as 0.
$n$	n	The number of strips (how many roll widths side by side), from "number". Found with $n = \lceil b \div w \rceil$. The number of seams is $n - 1$.
$l$	l	The strip length (ft), from "length". For a solid color it is $a + m$. For a pattern with two or more strips it is $p \times \lceil (a + m) \div p \rceil$ (with one strip, even a pattern uses $a + m$).
$M$	M	The length needed (ft). $M = n \times l$, the length before rounding up to the cutting step.
$M'$	M prime	The length to buy (ft). The length needed rounded up to the cutting step, which is the length you order at the store.
$u$	u	The cutting step (ft), from "unit". It is 1 for 1 ft steps and 3 for 1 yd steps.
$S$	S	The floor area (ft²), found from length × width.
$E$	E	The offcut area (ft²). The area bought (length to buy × roll width) minus the floor area.
$r$	r	The waste rate, the share of the area bought that becomes offcuts, from "rate". $r = E \div (M' \times w)$.
$c$	c	The unit price (per linear ft or per ft²), from "cost".
$Q$	Q	The quantity that matches the price unit (the length to buy or the area bought), from "quantity".
$T$	T	The estimated cost (the flooring only, without adhesive or labor), from "total".
$\lceil x \rceil$	ceiling of x	The ceiling function: rounds up to the next whole number. (Examples: $\lceil 1.08 \rceil = 2$, $\lceil 2 \rceil = 2$)

Terms

sheet vinyl	Vinyl flooring that comes in large sheets on a roll, with a printed wood or tile look on the surface, often with a cushioned backing. It is usually 12 ft wide and cut to the length you need. Popular for kitchens, bathrooms and laundry rooms.
broadloom carpet	Wall-to-wall carpet sold on wide rolls, usually 12 ft and also 15 ft wide, and cut to fit the room. A 15 ft roll covers many rooms without a seam.
commercial sheet flooring	Heavy-duty vinyl sheet flooring used in stores, offices, schools and hallways. It also comes on rolls, and the length you need is worked out the same way.
roll width	The width of the roll. Sheet vinyl is usually 12 ft (also 6 ft and 13.2 ft), and carpet 12 ft or 15 ft. If the room is narrower than the roll, one strip covers it without a seam.
seam	The joint between strips laid side by side when one roll width is not enough. There is one fewer seam than strips. Fewer seams look better and are easier to install. Seams are said to show less when they run in the same direction as the light from the main window.
trim allowance	The extra length, beyond the room length, kept for trimming the strip to the walls at both ends. It covers crooked walls and doorways. About 3 in at each end, 6 in in total, is typical.
pattern repeat	The length after which the pattern repeats along the roll, shown on the product as "pattern repeat: 18 in" or similar. When strips are laid side by side, each strip is rounded up to a multiple of this length to line up the pattern at the seams. A solid color counts as 0.
pattern matching	Laying the strips so the pattern runs on across the seams. The shift needed to line it up takes extra material. Not needed when one strip covers the room (no seam).
layout	Deciding which way the roll runs and where the strips are joined. Installers plan the layout before ordering and work out the length from it. "Lengthwise" and "widthwise" on this page are the two most basic layouts.
offcut	The part of the purchased roll that is cut away and not laid in the room. The extra width (the combined strip width minus the room width) is usually the largest part, followed by the trim and pattern allowances. Offcuts can often be reused in a small room such as a bathroom or a closet.
waste rate	The share of the area bought that ends up as offcuts. It tells you how well the direction and the roll width were chosen.
wall to wall	Measured from the inside face of one wall to the inside face of the opposite wall. Flooring is calculated from these inside measurements. Plans are often dimensioned to the center of the walls, so the inside measurement is shorter by the wall thickness.
linear foot	One foot of length cut from the roll at its full width. Stores that cut sheet vinyl and carpet to order often sell by the linear foot, and each store has its own cutting step.
square yard	A unit of area often used for carpet and sheet vinyl prices and quotes in the US. 1 sq yd = 3 ft × 3 ft = 9 ft². To get square yards from square feet, divide by 9.
dye lot	A batch of product made at the same time. Colors can differ slightly between dye lots, so it is best to buy all the flooring for a room at once.
rounding up	Changing a value with a decimal part to the next whole number. For the number of strips and the number of cutting steps, always round up so you do not run short.

Good to know before you start

Here is what helps you use the calculation on this page with real understanding, not just by pressing the button.

Area of a rectangle (Grades 3–4)	Knowing that the area of a rectangle is "length × width" Seeing that an unrolled roll is also a rectangle, so "length × width" is the area you buy
Converting units of length (Grades 4–5)	Knowing that 1 ft = 12 in, so 6 in is 0.5 ft and 18 in is 1.5 ft
Multiplying and dividing decimals (Grades 5–6)	Understanding what decimal calculations such as $13 \div 12$ and $2 \times 15.5$ mean (a calculator is fine for the arithmetic)
Rounding (Grades 3–4)	Knowing the difference between rounding up, rounding down and rounding to the nearest Being able to explain in your own words why you round up the number of strips and the length you order
Percentages (Grades 6–7)	Being able to find "what share of the whole" something is, such as the waste rate, with part ÷ whole

How to calculate it in Excel

Copy the whole table below and paste it into cell A1 in Excel. It works as is.

Table to find the number of strips

Room side across the roll b (ft)	13
Roll width w (ft)	12
Number of strips n	=ROUNDUP(B1/B2,0)

Table to find the strip length

Room side along the roll a (ft)	15
Trim allowance m (in)	6
Pattern repeat p (in, 0 if solid)	0
Strip length l (ft)	=IF(B3>0,B3/12*ROUNDUP((B1+B2/12)/(B3/12),0),B1+B2/12)

Table to find the length needed and the length to buy

Number of strips n	2
Strip length l (ft)	13.5
Cutting step u (ft)	1
Length needed M (ft)	=B1*B2
Length to buy M' (ft)	=ROUNDUP(B4/B3,0)*B3

Table to find the offcut area and the waste rate

Length to buy M' (ft)	27
Roll width w (ft)	12
Floor area S (ft²)	195
Offcut area E (ft²)	=B1*B2-B3
Waste rate r	=B4/(B1*B2)

Table to find the estimated cost

Unit price c ($)	18
Quantity Q (ft or ft²)	27
Estimated cost T ($)	=B1*B2

After pasting, the upper rows in column B are your inputs and the last rows are calculated automatically.
"ROUNDUP(value, 0)" rounds up to a whole number (the ⌈ ⌉ in the formulas).
B3 in the first table shows 2 strips. The second table takes the trim allowance and pattern repeat in inches and turns them into feet with "/12", and the IF function rounds up to a multiple of the repeat only when the repeat is more than 0 (15.5 in the solid-color example, 16.5 if you enter a repeat of 18).
In the third table B4 and B5 show 27 (27 ft is a whole number of 1 ft steps). In the fourth table B4 shows 129 and B5 about 0.398 (39.8%), and B3 in the fifth table shows 486.
The first two tables use the lengthwise numbers (the 13 ft width is covered by roll widths, and each strip is the 15 ft length plus trim), and the tables from the third on use the widthwise numbers (2 strips × 13.5 ft = 27 ft). To get the widthwise strips and strip length, enter the length 15 in B1 of the first table and the width 13 in B1 of the second table (2 strips, 13.5 ft). If a patterned product needs only one strip (no seam), no pattern matching is needed, so set B3 (the pattern repeat) in the second table to 0.

How to calculate it in Google Sheets

Copy the whole table below and paste it into cell A1 in Google Sheets. It works as is.

Table to find the number of strips

Room side across the roll b (ft)	13
Roll width w (ft)	12
Number of strips n	=ROUNDUP(B1/B2,0)

Table to find the strip length

Room side along the roll a (ft)	15
Trim allowance m (in)	6
Pattern repeat p (in, 0 if solid)	0
Strip length l (ft)	=IF(B3>0,B3/12*ROUNDUP((B1+B2/12)/(B3/12),0),B1+B2/12)

Table to find the length needed and the length to buy

Number of strips n	2
Strip length l (ft)	13.5
Cutting step u (ft)	1
Length needed M (ft)	=B1*B2
Length to buy M' (ft)	=ROUNDUP(B4/B3,0)*B3

Table to find the offcut area and the waste rate

Length to buy M' (ft)	27
Roll width w (ft)	12
Floor area S (ft²)	195
Offcut area E (ft²)	=B1*B2-B3
Waste rate r	=B4/(B1*B2)

Table to find the estimated cost

Unit price c ($)	18
Quantity Q (ft or ft²)	27
Estimated cost T ($)	=B1*B2

The same formulas as in Excel (including the ROUNDUP and IF functions) work as is. Copy the whole table, paste it into cell A1, and replace the numbers in column B with your own.

How to calculate it in Python

import math

room_length_ft = 15      # room length (ft)
room_width_ft = 13       # room width (ft)
roll_width_ft = 12       # roll width (ft). Sheet vinyl is usually 12 ft wide
margin_ft = 6 / 12       # trim allowance per strip (6 in, in feet)
repeat_ft = 0            # pattern repeat (ft). 0 for a solid color
sale_unit_ft = 1         # cutting step (ft). 1 for 1 ft steps
price_per_ft = 18        # price per linear foot ($)

floor_area_ft2 = room_length_ft * room_width_ft

def one_direction(along_ft, across_ft):
    """Amounts when the roll runs along along_ft and across_ft is covered by roll widths"""
    strips = math.ceil(across_ft / roll_width_ft)                         # number of strips (rounded up)
    strip_len_ft = along_ft + margin_ft                                  # strip length with trim allowance
    if repeat_ft > 0 and strips > 1:
        strip_len_ft = repeat_ft * math.ceil(strip_len_ft / repeat_ft)   # patterned with 2+ strips: round up to a multiple of the repeat (one strip has no seam, so no matching)
    total_ft = strips * strip_len_ft                                     # length needed
    purchase_ft = math.ceil(round(total_ft / sale_unit_ft, 9)) * sale_unit_ft   # rounded up to the cutting step
    waste_ft2 = purchase_ft * roll_width_ft - floor_area_ft2             # offcut area
    waste_rate = waste_ft2 / (purchase_ft * roll_width_ft)               # waste rate
    cost = price_per_ft * purchase_ft                                    # estimated cost ($)
    return strips, strip_len_ft, total_ft, purchase_ft, waste_ft2, waste_rate, cost

for name, along_ft, across_ft in (("Lengthwise", room_length_ft, room_width_ft), ("Widthwise", room_width_ft, room_length_ft)):
    strips, strip_len_ft, total_ft, purchase_ft, waste_ft2, waste_rate, cost = one_direction(along_ft, across_ft)
    print(f"{name}: {strips} strips × {strip_len_ft:.2f} ft = {total_ft:.2f} ft needed → buy {purchase_ft} ft, "
          f"offcuts {waste_ft2:.1f} ft² ({waste_rate * 100:.1f}%), estimated cost ${cost:,.2f}")

Runs with the standard library only. math.ceil() rounds up (the ⌈ ⌉ in the formulas). one_direction() does the calculation for one direction, and it is called twice, lengthwise and widthwise, to compare. round(…, 9) keeps a floating-point error (such as 27.000000001) from rounding up one extra step. Replace the sizes, widths and price at the top with your own numbers and run it.

How to write it in LaTeX and other math languages (copy and paste)

Number of strips (how many widths side by side)

n = ⌈b ÷ w⌉

n = \left\lceil \frac{b}{w} \right\rceil

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>n</mi>
    <mo>=</mo>
    <mo>&#x2308;</mo>
    <mfrac><mi>b</mi><mi>w</mi></mfrac>
    <mo>&#x2309;</mo>
  </mrow>
</math>

n = |~ b / w ~|

Ceiling[b/w]

n := ceil(b/w);

n = ceil(b/w);

n = ⌈b/w⌉

Length of each strip (with trim and pattern matching)

l = a + m (solid),  l = p × ⌈(a + m) ÷ p⌉ (patterned)

l = a + m,\quad l = p \left\lceil \frac{a + m}{p} \right\rceil

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>l</mi>
    <mo>=</mo>
    <mi>a</mi><mo>+</mo><mi>m</mi>
    <mo>,</mo>
    <mi>l</mi>
    <mo>=</mo>
    <mi>p</mi>
    <mo>&#x2062;</mo>
    <mo>&#x2308;</mo>
    <mfrac><mrow><mi>a</mi><mo>+</mo><mi>m</mi></mrow><mi>p</mi></mfrac>
    <mo>&#x2309;</mo>
  </mrow>
</math>

l = a + m,  l = p |~ (a + m) / p ~|

If[p > 0, p*Ceiling[(a + m)/p], a + m]

l := piecewise(p > 0, p*ceil((a + m)/p), a + m);

if p > 0, l = p*ceil((a + m)/p); else, l = a + m; end

l = a + m, l = p⌈(a + m)/p⌉

Length needed and length to buy

M = n × l,  M' = ⌈M ÷ u⌉ × u

M = n l,\quad M' = \left\lceil \frac{M}{u} \right\rceil u

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>M</mi>
    <mo>=</mo>
    <mi>n</mi><mo>&#x2062;</mo><mi>l</mi>
    <mo>,</mo>
    <msup><mi>M</mi><mo>&#x2032;</mo></msup>
    <mo>=</mo>
    <mo>&#x2308;</mo>
    <mfrac><mi>M</mi><mi>u</mi></mfrac>
    <mo>&#x2309;</mo>
    <mo>&#x2062;</mo>
    <mi>u</mi>
  </mrow>
</math>

M = n l,  M' = |~ M / u ~| u

{n*l, Ceiling[n*l/u]*u}

M := n*l;  Mp := ceil(M/u)*u;

M = n*l; Mp = ceil(M/u)*u;

M = nl, M' = ⌈M/u⌉u

Offcut area and waste rate

E = M' × w − S,  r = E ÷ (M' × w)

E = M' w - S,\quad r = \frac{E}{M' w}

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>E</mi>
    <mo>=</mo>
    <msup><mi>M</mi><mo>&#x2032;</mo></msup><mo>&#x2062;</mo><mi>w</mi>
    <mo>&#x2212;</mo>
    <mi>S</mi>
    <mo>,</mo>
    <mi>r</mi>
    <mo>=</mo>
    <mfrac><mi>E</mi><mrow><msup><mi>M</mi><mo>&#x2032;</mo></msup><mo>&#x2062;</mo><mi>w</mi></mrow></mfrac>
  </mrow>
</math>

E = M' w - S,  r = E / (M' w)

{mp*w - s, (mp*w - s)/(mp*w)}

E := Mp*w - S;  r := E/(Mp*w);

E = Mp*w - S; r = E/(Mp*w);

E = M'w − S, r = E/(M'w)

Estimated cost

T = c × Q

T = c \times Q

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>T</mi>
    <mo>=</mo>
    <mi>c</mi>
    <mo>&#xD7;</mo>
    <mi>Q</mi>
  </mrow>
</math>

T = c * Q

c*q

T := c*Q;

T = c*Q;

T = c × Q

How to have ChatGPT do the calculation

You are a quantity calculation assistant for flooring jobs. Do the following calculation by actually running Python code, and base your answer only on the numbers from the execution result (do not answer by mental math or guessing).

I am installing solid-color sheet vinyl, 12 ft wide, in a 15 ft × 13 ft room. The trim allowance is 6 in per strip, and the store cuts in 1 ft steps.
For running the roll lengthwise (the 13 ft width is covered by roll widths) and widthwise (the 15 ft length is covered by roll widths), find each of the following:
1. The number of strips (room side across the roll ÷ roll width, rounded up)
2. The strip length (room side along the roll + trim allowance)
3. The length needed (strips × strip length) and the length to buy, rounded up to 1 ft steps
4. The offcut area (length to buy × roll width − floor area) and the waste rate
Finally, tell me which direction needs the shorter length to buy.

Show the formulas you used and the numbers from the execution result.

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Enter your numbers

Type the numbers you want to calculate with into the input fields
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Press the "Calculate" button
3

Check the result

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\(a\)	a	The room side along the roll (ft). It is the room length when the roll runs lengthwise, and the width when it runs widthwise. Think of "a" for "along".
\(b\)	b	The room side across the roll (ft), the side covered by roll widths. It is the width when the roll runs lengthwise, and the length when it runs widthwise.
\(w\)	w	The roll width (ft), from "width". Sheet vinyl is usually 12 ft wide.
\(m\)	m	The trim allowance (ft), the total extra length per strip, from "margin". About 3 in at each end, 6 in (0.5 ft) in total, is typical.
\(p\)	p	The pattern repeat (ft), the length after which the pattern repeats along the roll, from "pattern". A solid color counts as 0.
\(n\)	n	The number of strips (how many roll widths side by side), from "number". Found with \(n = \lceil b \div w \rceil\). The number of seams is \(n - 1\).
\(l\)	l	The strip length (ft), from "length". For a solid color it is \(a + m\). For a pattern with two or more strips it is \(p \times \lceil (a + m) \div p \rceil\) (with one strip, even a pattern uses \(a + m\)).
\(M\)	M	The length needed (ft). \(M = n \times l\), the length before rounding up to the cutting step.
\(M'\)	M prime	The length to buy (ft). The length needed rounded up to the cutting step, which is the length you order at the store.
\(u\)	u	The cutting step (ft), from "unit". It is 1 for 1 ft steps and 3 for 1 yd steps.
\(S\)	S	The floor area (ft²), found from length × width.
\(E\)	E	The offcut area (ft²). The area bought (length to buy × roll width) minus the floor area.
\(r\)	r	The waste rate, the share of the area bought that becomes offcuts, from "rate". \(r = E \div (M' \times w)\).
\(c\)	c	The unit price (per linear ft or per ft²), from "cost".
\(Q\)	Q	The quantity that matches the price unit (the length to buy or the area bought), from "quantity".
\(T\)	T	The estimated cost (the flooring only, without adhesive or labor), from "total".
\(\lceil x \rceil\)	ceiling of x	The ceiling function: rounds up to the next whole number. (Examples: \(\lceil 1.08 \rceil = 2\), \(\lceil 2 \rceil = 2\))

Sheet Vinyl and Carpet Roll Calculator (Length Needed, Seams, Offcuts and Cost)

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How to have ChatGPT do the calculation

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