Moving Box Calculator (How Many Boxes Do I Need?)

Choose how to estimate (add up from what you have, or a rough range from people or rooms) and enter the quantities. The boxes per unit, extra allowance, box sizes and tape can stay at their defaults, and the price and truck cargo volume can be left blank.

Units

How to estimate

Item (what to count)	Qty	Boxes per unit
Small box Books (bookshelf shelves)
Small box Dishes (cabinet shelves)
Medium box Folded clothes (dresser drawers or bins)
Medium box Hanging clothes (hangers)
Medium box Kitchenware (cabinet shelves or drawers)
Medium box Household items (storage shelves)
Small box Papers and files (file boxes)
Medium box Shoes (pairs)

Other (enter boxes directly, optional)

Small box

Medium box

Extra allowance (%)

Box size (width × depth × height, cm)

Small box × ×

Medium box × ×

Packing tape (per box and per roll, m)

Price per box ($, optional)

Truck cargo volume (m³, optional)

Items with a quantity of 0 (or blank) are left out. Blank boxes-per-unit, size and tape fields use the defaults.

Result and figure

Enter what you have to pack (or the number of people) on the left and press "Calculate". The result 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 what you have, such as the number of bookshelf shelves, cabinet shelves, dresser drawers and hangers, and the calculator adds up the small boxes (for heavy items such as books and dishes) and medium boxes (for lighter items such as clothes)
Every "boxes per unit" value, such as "1 bookshelf shelf = 1 small box", is an input field, so you can match it to the way you pack
Before you count your things, you can get a rough range (minimum to maximum) from the number of people or rooms × boxes per person (or per room)
It also works out the boxes with an extra allowance (10 to 20% is typical), the total volume in cubic feet and its share of a truck's cargo space, and the length and rolls of packing tape
Enter the price per box (0 if you get boxes for free) to see the estimated cost. A plain-language explanation of the formulas and copy-and-paste formulas for Excel, Google Sheets and Python are all on this page

The box count is an estimate made with common rules of thumb such as "1 box per shelf", and the real number depends on the size of your books, how you pack and the size of the boxes. The range from the number of people or rooms is only a rough guide and does not guarantee an exact count. The number usually grows once you start packing, so it is safer to allow plenty of extra boxes.

What is this calculation used for?

Getting ready to pack (how many boxes to have on hand)

Say you are moving on your own and count 3 bookshelf shelves, 2 cabinet shelves of dishes, 4 dresser drawers, 10 hangers, 2 kitchen cabinet shelves and 3 storage shelves. The net count is $3 + 2 = 5$ small boxes and $4 + 1 + 2 + 3 = 10$ medium boxes. With a 15% extra allowance and rounding up, that is $\lceil 5.75 \rceil = 6$ small boxes and $\lceil 11.5 \rceil = 12$ medium boxes, 18 boxes in total.
With "how many more boxes do I need" as a number, it is quick to decide whether to buy only what the moving company does not provide or to buy a moving kit at a home center. Packing usually takes more than planned, so it is safer to allow plenty of extra.

Knowing how much you have before getting a quote from movers

In-home and online moving quotes often ask "about how many boxes will you have?" If you can give a count built up from what you own, the moving company can more easily plan the truck size and crew.
Divide the total volume by the truck's cargo volume from the company to see what share of the truck the boxes alone take up, as a guide to whether your furniture and appliances will fit in the rest (it is only a guide, because of gaps and how things are loaded).

Moving for college or a new job (with a moving container or by shipping)

With a portable moving container, where you move only what fits in one container, or when you ship boxes one by one, the total volume matters as well as the number of boxes. For the single-person example above (6 small and 12 medium boxes), the total volume is $6 \times 1.333 + 12 \times 3 \approx 44$ ft³.
Compare it with the container size or the carrier's size limits to choose how to move (sizes and limits differ by company, so always check the service you use).

Clearing out a family home or organizing without a move

When clearing out a parent's home, sorting an estate or putting things in storage, count them the same way ("8 bookshelf shelves, 4 cabinet shelves, 10 dresser drawers") and the same formulas give the boxes and total volume you need.
Self-storage units are rented by floor size, such as 5 × 10 ft, so knowing the total volume helps you choose the size: a 5 × 10 ft unit with an 8 ft ceiling holds $5 \times 10 \times 8 = 400$ ft³ at most. Things cannot be stacked with no gaps, so allow more than the total volume.

Shopping for packing supplies (tape and packing material)

Once the number of boxes is set, the rolls of tape follow right away. Taping 30 boxes with 8 ft each takes $30 \times 8 = 240$ ft, so with 165 ft rolls you need $\lceil 240 \div 165 \rceil = 2$ rolls.
The number of small boxes for dishes is also a guide to how much packing paper or bubble wrap to get (the amount of packing material depends a lot on the size of the dishes and how you wrap them, so it is not calculated here; get plenty, using the number of boxes as a guide).

Formulas and figures

Boxes for each item

Standard notation (the usual math form)

$x$ $=$ $q$ $\times$ $c$

In words (symbols replaced with words)

③ $x$: boxes for the item $=$ ① $q$: quantity $\times$ ② $c$: boxes per unit

The formula in words

① Multiply the $q$: quantity (bookshelf shelves, hangers and so on) by the

② $c$: boxes per unit (1 box per shelf, 0.1 box per hanger and so on) to get the

③ $x$: boxes for the item

Quick example

With 20 hangers of clothes and 0.1 medium box per hanger (10 hangers per box), the boxes for this item are

$x$: boxes for the item $=$ quantity (20 hangers) $\times$ per hanger (0.1 box)

$20 \times 0.1 = 2$

Key idea

Set a "boxes per easy-to-count unit" for each item, such as "the books on one bookshelf shelf fit in about one small box" or "10 hangers of clothes fill about one medium box". Then you only need to walk around your home counting, and the boxes add up. The boxes-per-unit values on this page are common rules of thumb; they change with the size of your books and the bulk of your clothes, so adjust them in the input fields to fit your things. The basic rule of packing is to put heavy things such as books, dishes and papers in small boxes (so the bottom does not give out and you can still lift them), and light, bulky things such as clothes, kitchenware and household items in medium boxes.

Boxes with the extra allowance (small and medium boxes separately)

Figure

Standard notation (the usual math form)

$B$ $=$ $\sum x$

$N$ $=$ $\lceil$ $B$ $\times$ $($ $1$ $+$ $r$ $)$ $\rceil$

In words (symbols replaced with words)

② $B$: net count of boxes $=$ ① $\sum x$: sum of the boxes for each item $x$

⑤ $N$: boxes with the extra allowance $=$ $\lceil$ $B$: net count of boxes $\times$ $($ $1$ $+$ ③ $r$: extra allowance $)$ ④ $\rceil$

The formula in words

① Adding up the $\sum x$: boxes for each item separately for small and medium boxes gives the

② $B$: net count of boxes . Multiply it by 1 plus the

③ $r$: extra allowance (1.15 times for 15%),

④ and round up to a whole number (the sign $\lceil\ \rceil$ stands for rounding up) to get the

⑤ $N$: boxes with the extra allowance

Quick example

If the medium-box items come to "dresser drawers 6 boxes, hangers 2, kitchen 3, household items 4, shoes 2" and the extra allowance is 15%, the medium boxes with the extra allowance are

$N$: boxes with the extra allowance $=$ $\lceil$ net count (17 boxes) $\times$ $($ $1$ $+$ extra allowance (0.15) $)$ $\rceil$

$6 + 2 + 3 + 4 + 2 = 17$

$17 \times (1 + 0.15) = 17 \times 1.15 = 19.55$

$\lceil 19.55 \rceil = 20$

Key idea

The extra allowance follows a form widely used when estimating materials: "amount needed = net amount × (1 + extra rate)". When packing, you usually end up needing more than the net count: the books turn out thicker than you thought, or packing material in the bottom of a box leaves less room. So people often allow 10 to 20% extra. Boxes come only in whole numbers, so round up. Small and medium boxes hold different things, so add up and round up each size separately (rounding up only the combined total can let the leftover fractions of the two sizes cancel out and leave you short).

Rough range of boxes from the number of people (minimum to maximum)

Standard notation (the usual math form)

$N_{\min}$ $=$ $n$ $\times$ $a$

$N_{\max}$ $=$ $n$ $\times$ $b$

In words (symbols replaced with words)

④ $N_{\min}$: low estimate of boxes $=$ ① $n$: number of people $\times$ ② $a$: minimum boxes per person

$N_{\max}$: high estimate of boxes $=$ $n$: number of people $\times$ ③ $b$: maximum boxes per person

The formula in words

① Multiply the $n$: number of people by the

② $a$: minimum boxes per person to get the low estimate, and by the

③ $b$: maximum boxes per person to get the high estimate. The span between them is the

④ rough range of boxes ($N_{\min}$ to $N_{\max}$)

Quick example

For a household of 2, with 10 to 25 boxes per person, the rough range is

rough range $=$ people (2) $\times$ minimum (10 boxes) $\sim$ people (2) $\times$ maximum (25 boxes)

$2 \times 10 = 20$

$2 \times 25 = 50$

Key idea

An estimate from the number of people just multiplies by an average "boxes per person", so it cannot reflect whether you own a lot or a little. That is why this page does not give one number but a range, like "20 to 50 boxes", from a minimum and a maximum value. The default of 10 to 25 boxes per person is a rough rule of thumb, not a standard; raise the maximum if you know you have a lot of things. The estimate from rooms has the same form (rooms × minimum to maximum boxes per room). Count the bedrooms plus the living room, kitchen and other main rooms; a 2-bedroom apartment with a living room and kitchen counts as 4 rooms, which gives 40 to 60 boxes at the default of 10 to 15 per room. Enter both to compare the two ranges. Once you can count your things, switch to "Add up from what you have" for a more accurate count.

Volume of one box

Figure

Standard notation (the usual math form)

$v$ $=$ $w$ $\times$ $d$ $\times$ $h$

In words (symbols replaced with words)

④ $v$: volume of one box $=$ ① $w$: width $\times$ ② $d$: depth $\times$ ③ $h$: height

The formula in words

① Multiply the $w$: width ,

② the $d$: depth and

③ the $h$: height to get the

④ $v$: volume of one box (the formula for the volume of a rectangular prism)

Quick example

The volume of a small box (16 in × 12 in × 12 in) is

$v$: volume of one box $=$ width (16 in) $\times$ depth (12 in) $\times$ height (12 in)

$16 \times 12 \times 12 = 2304\,\mathrm{in^3}$

$2304 \div 1728 \approx 1.333\,\mathrm{ft^3}$

Key idea

A box is a rectangular prism, so its volume is width × depth × height. Multiplying in inches gives cubic inches (in³), so divide by 1,728 to get cubic feet (ft³). 1 ft = 12 in, so 1 ft³ = 12 × 12 × 12 = 1,728 in³. In the US, moving boxes usually come in a few standard sizes: small boxes of about 1.3 to 1.5 ft³ (for example 16 × 12 × 12 in) for books, dishes and other heavy things; medium boxes of about 3 ft³ (18 × 18 × 16 in) for kitchenware, toys and clothes; and large boxes of about 4.5 ft³ (18 × 18 × 24 in) for bedding, pillows and other light, bulky things. This page uses two sizes, small and medium. If you already know which boxes you will use, enter their sizes in the input fields (enter large boxes as the medium box). If you ship boxes with a parcel carrier, check the carrier's size and weight limits separately.

Total volume of the boxes

Standard notation (the usual math form)

$V$ $=$ $N_{S}$ $\times$ $v_{S}$ $+$ $N_{M}$ $\times$ $v_{M}$

In words (symbols replaced with words)

⑤ $V$: total volume $=$ ① $N_{S}$: number of small boxes $\times$ ② $v_{S}$: volume of one small box $+$ ③ $N_{M}$: number of medium boxes $\times$ ④ $v_{M}$: volume of one medium box

The formula in words

① Multiply the $N_{S}$: number of small boxes by the

② $v_{S}$: volume of one small box to get the volume of the small boxes. Multiply the

③ $N_{M}$: number of medium boxes by the

④ $v_{M}$: volume of one medium box to get the volume of the medium boxes. Adding the two gives the

⑤ $V$: total volume

Quick example

The total volume of 10 small boxes (1.333 ft³ each) and 20 medium boxes (3 ft³ each) is

$V$: total volume $=$ small boxes (10) $\times$ small box volume (1.333 ft³) $+$ medium boxes (20) $\times$ medium box volume (3 ft³)

$10 \times 1.333 + 20 \times 3 = 13.33 + 60 = 73.33\,\mathrm{ft^3}$

Key idea

The total volume is the volume of the boxes stacked with no gaps. A real truck also carries furniture and appliances, and there are gaps between boxes, so the total volume is not the same as the truck space you need. If you enter the truck's cargo volume (checked with the moving or rental company), the page shows the share of the truck the boxes alone take up, $V \div$ cargo volume $\times 100$, as a guide to how much space is left for furniture. With a portable moving container, where you move only what fits in one container, whether this total volume fits in the container is a key point for deciding.

Rolls of packing tape

Standard notation (the usual math form)

$R$ $=$ $\lceil$ $N$ $\times$ $t$ $\div$ $L$ $\rceil$

In words (symbols replaced with words)

⑤ $R$: rolls of tape $=$ $\lceil$ ① $N$: total boxes $\times$ ② $t$: tape per box $\div$ ③ $L$: length of one roll ④ $\rceil$

The formula in words

① Multiply the $N$: total boxes (small + medium) by the

② $t$: tape per box to get the length needed, divide it by the

③ $L$: length of one roll ,

④ and round up to a whole number to get the

⑤ $R$: rolls of tape

Quick example

To tape 30 boxes with 8 ft of tape each, using 165 ft rolls, the number of rolls is

$R$: rolls $=$ $\lceil$ boxes (30) $\times$ per box (8 ft) $\div$ per roll (165 ft) $\rceil$

$30 \times 8 = 240\,\mathrm{ft}$

$240 \div 165 \approx 1.45$

$\lceil 1.45 \rceil = 2$

Key idea

How much tape a box takes depends on how you tape it. Taping only the center seam on the top and the bottom uses about 5 to 6 ft per box, and an H-tape (center seam plus both edges) about 8 to 10 ft. Heavy boxes of books and dishes are usually H-taped on the bottom so it does not give out, so the default is 8 ft. A common roll of packing tape is 55 yd (165 ft), and 60 yd (180 ft) and 110 yd (330 ft) rolls are also sold. The default is 165 ft; enter the length of the tape you buy. Tape is sold only by the roll, so round up.

Estimated cost of the boxes

Standard notation (the usual math form)

$T$ $=$ $N_{S}$ $\times$ $u_{S}$ $+$ $N_{M}$ $\times$ $u_{M}$

In words (symbols replaced with words)

⑤ $T$: estimated cost $=$ ① $N_{S}$: number of small boxes $\times$ ② $u_{S}$: price of a small box $+$ ③ $N_{M}$: number of medium boxes $\times$ ④ $u_{M}$: price of a medium box

The formula in words

① Multiply the $N_{S}$: number of small boxes by the

② $u_{S}$: price of a small box to get the cost of the small boxes. Multiply the

③ $N_{M}$: number of medium boxes by the

④ $u_{M}$: price of a medium box to get the cost of the medium boxes. Adding the two gives the

⑤ $T$: estimated cost

Quick example

The cost of buying 10 small boxes at $1.50 each and 20 medium boxes at $2.50 each is (the prices are only an example)

$T$: estimated cost $=$ small boxes (10) $\times$ price ($1.50) $+$ medium boxes (20) $\times$ price ($2.50)

$10 \times 1.50 + 20 \times 2.50 = 15.00 + 50.00 = 65.00$

Key idea

Moving companies sometimes include a number of boxes for free, and you can often get boxes free from grocery or liquor stores, friends or online marketplaces. In those cases, set the price to 0. If you buy only the boxes you are missing, think "boxes bought × price". Tape, packing material, wardrobe boxes and mattress bags cost extra. Prices vary by store and company, so this page has no default price; enter the real prices.

The basic way to count moving boxes is to add up "quantity of each item × boxes per unit" separately for small and medium boxes, multiply by 1 plus an extra allowance (10 to 20% is typical) and round up. An estimate from the number of people or rooms is a range (minimum to maximum) found with rough rules of thumb. Once the number of boxes is set, the total volume, rolls of tape and cost follow from it.

Symbols and terms

Symbols

$q$	q	The quantity of an item, counted in an easy unit for that item: bookshelf shelves, cabinet shelves, dresser drawers, hangers, pairs of shoes and so on. It is the first letter of "quantity".
$c$	c	The boxes per unit (a coefficient). It is 1 for "1 bookshelf shelf = 1 small box" and 0.1 for "1 hanger = 0.1 medium box". It is the first letter of "coefficient".
$x$	x	The boxes for each item, found with $x = q \times c$.
$\sum x$	sigma x	The sum of the boxes $x$ for all items. $\sum$ (sigma) is the sign for "add them all up"; it is the Greek letter for S, as in "sum".
$B$	B	The net count of boxes (the total before the extra allowance), found separately for small and medium boxes.
$r$	r	The extra allowance as a rate. For 15%, $r = 0.15$, and you multiply by $1 + r = 1.15$. It is the first letter of "rate".
$N$	N	The number of boxes with the extra allowance, found with $N = \lceil B(1 + r) \rceil$. It is the first letter of "number". In the tape formula, it is the total of small and medium boxes with the extra allowance.
$N_{S},\ N_{M}$	N sub S, N sub M	The numbers of small (S) and medium (M) boxes with the extra allowance. The small letters S and M stand for "small" and "medium".
$n$	lowercase n	The number of people, used in the people mode for "people × boxes per person".
$a,\ b$	a, b	The minimum ($a$) and maximum ($b$) boxes per person. The defaults are 10 and 25, and you can change them to match how much you own.
$N_{\min},\ N_{\max}$	N min, N max	The low and high ends of the rough range of boxes from the number of people (or rooms): $N_{\min} = n \times a$ and $N_{\max} = n \times b$.
$w,\ d,\ h$	w, d, h	The width, depth and height of one box, from the first letters of those words. On this page they are entered in inches.
$v$	lowercase v	The volume of one box: $v = w \times d \times h$, converted to cubic feet. It is the first letter of "volume".
$v_{S},\ v_{M}$	v sub S, v sub M	The volume of one small box and one medium box. With the default sizes they are about 1.333 ft³ and 3 ft³.
$V$	capital V	The total volume of all the boxes, found with $V = N_{S} v_{S} + N_{M} v_{M}$.
$t$	t	The length of tape used per box (ft), from the first letter of "tape". The default is 8 ft.
$L$	L	The length of one roll of tape (ft), from the first letter of "length". The default is 165 ft (55 yd).
$R$	capital R	The number of rolls of tape, from the first letter of "roll". It is found with $R = \lceil N t \div L \rceil$.
$u_{S},\ u_{M}$	u sub S, u sub M	The price of one small box and one medium box ($ per box), from "unit price".
$T$	capital T	The estimated cost of the boxes ($), from the first letter of "total".
$\lceil x \rceil$	ceiling of x	The sign for rounding up to a whole number, called the ceiling function. (Example - $\lceil 19.55 \rceil = 20$, $\lceil 23 \rceil = 23$)

Terms

small box	On this page, the box for heavy things such as books, dishes and papers. A US small moving box is about 1.3 to 1.5 ft³ (for example 16 × 12 × 12 in). If you put heavy things in a big box, it gets too heavy to lift or the bottom gives out, so the heavier the things, the smaller the box.
medium box	On this page, the box for light, bulky things such as clothes, kitchenware and household items. A US medium moving box is about 3 ft³ (for example 18 × 18 × 16 in). For very light things such as bedding, large boxes (about 4.5 ft³) are also used.
cubic foot	A unit of volume: a cube 12 in on each side, which is 1,728 in³. Moving boxes, truck cargo space and storage units are often described in cubic feet (ft³). Boxes with the same total of width, depth and height can have different volumes, so the volume is calculated as width × depth × height.
extra allowance	The percentage added on top of the net count of boxes. Once packing starts, boxes tend to run short ("more books than I thought", "the packing material takes up room"), so 10 to 20% is often allowed. In the formula it is used as $1 + r$ times.
net count	The amount itself, with nothing extra. On this page, it is the number of boxes before the extra allowance, just the quantities times the boxes per unit, added up.
rounding up	Going up to the next whole number whenever there is a decimal part. Boxes and tape come only in whole units, so box and roll counts are always rounded up.
cargo volume	The volume a truck or moving container can hold (ft³). All your belongings, including furniture and appliances, must fit in it. The size depends on the company and the vehicle, so this page takes it as an input.
dresser drawer	A drawer of a dresser, or a plastic storage bin for clothes. On this page, "the clothes in one drawer or bin = 1 medium box" is used as a unit of the rule of thumb. Some movers move light dressers with the clothes still inside, so ask first.
wardrobe box	A tall moving box with a hanging bar, so clothes can travel on their hangers. If you use them, you do not need to fold hanging clothes into boxes, so set the quantity of that item to 0.
packing material	Packing paper, bubble wrap, air pillows and the like used to wrap breakables such as dishes. Wrapping makes each item bigger, so dishes go in small boxes with room to spare, as in "1 cabinet shelf = 1 small box".
number of rooms	For the room-based estimate, count the bedrooms plus the living room, kitchen, dining room, home office and other main rooms. Bathrooms and hallways with little in them can be left out. For example, a 2-bedroom apartment with a living room and kitchen is 4 rooms.

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.

Unit rates (Grade 6)	Knowing that "an amount per 1", such as "1 box per shelf" or "0.1 box per hanger", times a count gives the whole amount Understanding what decimal multiplication such as $20 \times 0.1$ and $17 \times 1.15$ is asking (a calculator can do the arithmetic)
Percents (Grade 6)	Knowing that "15% more" is "× 1.15" (add 15% = 0.15 to 1) Knowing that "50%" is "half" (for the share of small boxes)
Rounding (Grades 3–4)	Knowing the difference between rounding up, rounding down and rounding to the nearest whole number Being able to explain in your own words why the numbers of boxes and rolls of tape are rounded up
Volume of a rectangular prism and its units (Grade 5)	Knowing that the volume of a rectangular prism is length × width × height Knowing that 1 ft = 12 in, so $1\,\text{ft}^3 = 12 \times 12 \times 12 = 1728\,\text{in}^3$ (the length conversion multiplied three times)

How to calculate it in Excel

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

Table for the boxes for each item

Quantity (hangers)	20
Boxes per unit	0.1
Boxes for the item	=B1*B2

Table for the boxes with the extra allowance

Net count (total of medium boxes)	17
Extra allowance (%)	15
Boxes with the extra allowance	=ROUNDUP(B1*(1+B2/100),0)

Table for the rough range of boxes from the number of people

Number of people	2
Minimum boxes per person	10
Maximum boxes per person	25
Low estimate of boxes	=B1*B2
High estimate of boxes	=B1*B3

Table for the volume of one box

Width (in)	16
Depth (in)	12
Height (in)	12
Volume of one box (ft³)	=B1B2B3/1728

Table for the total volume of the boxes

Number of small boxes	10
Volume of one small box (ft³)	1.333
Number of medium boxes	20
Volume of one medium box (ft³)	3
Total volume (ft³)	=B1B2+B3B4

Table for the rolls of packing tape

Total boxes	30
Tape per box (ft)	8
Length of one roll (ft)	165
Rolls of tape	=ROUNDUP(B1*B2/B3,0)

Table for the estimated cost of the boxes

Number of small boxes	10
Price of a small box ($)	1.50
Number of medium boxes	20
Price of a medium box ($)	2.50
Estimated cost ($)	=B1B2+B3B4

After pasting, the upper rows of column B are your inputs and the last row is calculated automatically.
"ROUNDUP(value, 0)" rounds up to a whole number (it matches ⌈ ⌉ in the formulas).
The first table gives 2 boxes, the second rounds "17 × 1.15 = 19.55" up to 20 boxes, and the third gives 20 and 50 boxes.
The fourth table divides "16 × 12 × 12 = 2304 in³" by 1,728 to get about 1.333 ft³, the fifth gives 73.33 ft³, the sixth rounds "240 ÷ 165 ≈ 1.45" up to 2 rolls, and the seventh gives $65.00. Just replace the numbers in column B with your own.

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 for the boxes for each item

Quantity (hangers)	20
Boxes per unit	0.1
Boxes for the item	=B1*B2

Table for the boxes with the extra allowance

Net count (total of medium boxes)	17
Extra allowance (%)	15
Boxes with the extra allowance	=ROUNDUP(B1*(1+B2/100),0)

Table for the rough range of boxes from the number of people

Number of people	2
Minimum boxes per person	10
Maximum boxes per person	25
Low estimate of boxes	=B1*B2
High estimate of boxes	=B1*B3

Table for the volume of one box

Width (in)	16
Depth (in)	12
Height (in)	12
Volume of one box (ft³)	=B1B2B3/1728

Table for the total volume of the boxes

Number of small boxes	10
Volume of one small box (ft³)	1.333
Number of medium boxes	20
Volume of one medium box (ft³)	3
Total volume (ft³)	=B1B2+B3B4

Table for the rolls of packing tape

Total boxes	30
Tape per box (ft)	8
Length of one roll (ft)	165
Rolls of tape	=ROUNDUP(B1*B2/B3,0)

Table for the estimated cost of the boxes

Number of small boxes	10
Price of a small box ($)	1.50
Number of medium boxes	20
Price of a medium box ($)	2.50
Estimated cost ($)	=B1B2+B3B4

The same formulas as in Excel work as is (ROUNDUP has the same name). 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

# For each item: (label, quantity, boxes per unit, size). Size "S" = small box, "M" = medium box
items = [
    ("Books (bookshelf shelves)", 4, 1.0, "S"),
    ("Dishes (cabinet shelves)", 3, 1.0, "S"),
    ("Folded clothes (dresser drawers or bins)", 6, 1.0, "M"),
    ("Hanging clothes (hangers)", 20, 0.1, "M"),
    ("Kitchenware (cabinet shelves or drawers)", 3, 1.0, "M"),
    ("Household items (storage shelves)", 4, 1.0, "M"),
    ("Papers and files (file boxes)", 2, 0.5, "S"),
    ("Shoes (pairs)", 10, 0.2, "M"),
]
extra_rate = 0.15             # extra allowance (15%)
small_box_in = (16, 12, 12)   # small box width, depth, height (in)
medium_box_in = (18, 18, 16)  # medium box width, depth, height (in)
tape_per_box_ft = 8           # packing tape per box (ft)
tape_roll_ft = 165            # length of one roll of tape (ft) = 55 yd
price_small = 1.50            # price of a small box ($), example only
price_medium = 2.50           # price of a medium box ($), example only

# Boxes for each item = quantity x boxes per unit, added up separately for small and medium boxes
net_small = sum(qty * coef for _, qty, coef, size in items if size == "S")
net_medium = sum(qty * coef for _, qty, coef, size in items if size == "M")

# Boxes with the extra allowance = net x (1 + extra rate), rounded up (small and medium separately)
boxes_small = math.ceil(net_small * (1 + extra_rate))
boxes_medium = math.ceil(net_medium * (1 + extra_rate))
boxes_total = boxes_small + boxes_medium

# Volume of one box (in^3 -> ft^3) and the total volume
vol_small = small_box_in[0] * small_box_in[1] * small_box_in[2] / 1728
vol_medium = medium_box_in[0] * medium_box_in[1] * medium_box_in[2] / 1728
total_volume = boxes_small * vol_small + boxes_medium * vol_medium

# Length of tape and rolls needed (rounded up), estimated cost
tape_length = boxes_total * tape_per_box_ft
tape_rolls = math.ceil(tape_length / tape_roll_ft)
cost = boxes_small * price_small + boxes_medium * price_medium

print(f"Small boxes: net {net_small:g} -> with extra {boxes_small}")
print(f"Medium boxes: net {net_medium:g} -> with extra {boxes_medium}")
print(f"Total: {boxes_total} boxes")
print(f"Total volume: {total_volume:.2f} ft³")
print(f"Packing tape: {tape_length:g} ft -> {tape_rolls} rolls")
print(f"Estimated cost: ${cost:.2f}")

Runs with the standard library only. math.ceil() rounds up (the ⌈ ⌉ in the formulas). Replace the quantities and boxes per unit in items, and the extra allowance, box sizes, tape and prices, with your own values and run it. This example gives 10 small boxes, 20 medium boxes, 30 boxes in total, a total volume of 73.33 ft³, 2 rolls of tape and a cost of $65.00.

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

Boxes for each item

x = q × c

x = q \times c

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

x = q * c

q*c

x := q*c;

x = q*c;

x = q × c

Boxes with the extra allowance (small and medium boxes separately)

N = ⌈B × (1 + r)⌉

N = \lceil B(1 + r) \rceil

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>N</mi>
    <mo>=</mo>
    <mo>&#x2308;</mo>
    <mi>B</mi>
    <mo>&#x2062;</mo>
    <mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi>r</mi><mo>)</mo></mrow>
    <mo>&#x2309;</mo>
  </mrow>
</math>

N = |~ B(1 + r) ~|

Ceiling[b*(1 + r)]

N := ceil(B*(1 + r));

N = ceil(B*(1 + r));

N = ⌈B(1 + r)⌉

Rough range of boxes from the number of people (minimum to maximum)

Nmin = n × a,  Nmax = n × b

N_{\min} = n \times a,\quad N_{\max} = n \times b

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <msub><mi>N</mi><mi>min</mi></msub>
    <mo>=</mo>
    <mi>n</mi><mo>&#xD7;</mo><mi>a</mi>
    <mo>,</mo>
    <msub><mi>N</mi><mi>max</mi></msub>
    <mo>=</mo>
    <mi>n</mi><mo>&#xD7;</mo><mi>b</mi>
  </mrow>
</math>

N_min = n * a,  N_max = n * b

{n*a, n*b}

Nmin := n*a;  Nmax := n*b;

Nmin = n*a; Nmax = n*b;

N_min = n × a, N_max = n × b

Volume of one box

v = w × d × h

v = w \times d \times h

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>v</mi>
    <mo>=</mo>
    <mi>w</mi>
    <mo>&#xD7;</mo>
    <mi>d</mi>
    <mo>&#xD7;</mo>
    <mi>h</mi>
  </mrow>
</math>

v = w * d * h

w*d*h

v := w*d*h;

v = w*d*h;

v = w × d × h

Total volume of the boxes

V = Nₛ × vₛ + Nₘ × vₘ

V = N_{S} v_{S} + N_{M} v_{M}

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>V</mi>
    <mo>=</mo>
    <msub><mi>N</mi><mi>S</mi></msub>
    <mo>&#x2062;</mo>
    <msub><mi>v</mi><mi>S</mi></msub>
    <mo>+</mo>
    <msub><mi>N</mi><mi>M</mi></msub>
    <mo>&#x2062;</mo>
    <msub><mi>v</mi><mi>M</mi></msub>
  </mrow>
</math>

V = N_S * v_S + N_M * v_M

nS*vS + nM*vM

V := NS*vS + NM*vM;

V = NS*vS + NM*vM;

V = N_S v_S + N_M v_M

Rolls of packing tape

R = ⌈N × t ÷ L⌉

R = \left\lceil \frac{N t}{L} \right\rceil

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>R</mi>
    <mo>=</mo>
    <mo>&#x2308;</mo>
    <mfrac><mrow><mi>N</mi><mo>&#x2062;</mo><mi>t</mi></mrow><mi>L</mi></mfrac>
    <mo>&#x2309;</mo>
  </mrow>
</math>

R = |~ (N t) / L ~|

Ceiling[n*t/l]

R := ceil(N*t/L);

R = ceil(N*t/L);

R = ⌈(N t)/L⌉

Estimated cost of the boxes

T = Nₛ × uₛ + Nₘ × uₘ

T = N_{S} u_{S} + N_{M} u_{M}

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>T</mi>
    <mo>=</mo>
    <msub><mi>N</mi><mi>S</mi></msub>
    <mo>&#x2062;</mo>
    <msub><mi>u</mi><mi>S</mi></msub>
    <mo>+</mo>
    <msub><mi>N</mi><mi>M</mi></msub>
    <mo>&#x2062;</mo>
    <msub><mi>u</mi><mi>M</mi></msub>
  </mrow>
</math>

T = N_S * u_S + N_M * u_M

nS*uS + nM*uM

T := NS*uS + NM*uM;

T = NS*uS + NM*uM;

T = N_S u_S + N_M u_M

How to have ChatGPT do the calculation

You are a calculation assistant for counting packing supplies for a move. 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).

Here is what there is to pack (quantity × boxes per unit):
For small boxes: 4 bookshelf shelves (1 box per shelf), 3 cabinet shelves of dishes (1 box per shelf), 2 file boxes (0.5 box each)
For medium boxes: 6 dresser drawers (1 box each), 20 hangers (0.1 box each), 3 kitchen cabinet shelves (1 box per shelf), 4 storage shelves (1 box per shelf), 10 pairs of shoes (0.2 box per pair)
The extra allowance is 15%. A small box is 16 × 12 × 12 in and a medium box is 18 × 18 × 16 in. Use 8 ft of tape per box and 165 ft per roll.

Find each of the following:
1. The net count of small boxes and of medium boxes (the sum of the boxes for each item)
2. The boxes with the extra allowance (net × 1.15, rounded up separately for small and medium boxes) and the total
3. The total volume of the boxes (ft³, with 1 ft³ = 1,728 in³)
4. The length of tape needed (ft) and the number of rolls (rounded up)

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

How to Use

1

Enter your numbers

Type the numbers you want to calculate with into the input fields
2

Calculate

Press the "Calculate" button
3

Check the result

The result appears on the spot. The same page also explains the idea behind the calculation and the formula

DataChef Features

Easy and Free

Unlimited conversions for free.
No technical knowledge required.
Intuitive and user-friendly operation.

No Registration Required

Available immediately after access.
Can be used without registering personal information.

Safe and Secure

Fully SSL encrypted communication.
Automatic file deletion by clicking "download".

Fast

High-speed site access
and rapid file conversion.

No Watermark

No watermark.
No attribution required.

Commercial Use Available

Free for commercial use.
No need to contact us for commercial use permission.

\(q\)	q	The quantity of an item, counted in an easy unit for that item: bookshelf shelves, cabinet shelves, dresser drawers, hangers, pairs of shoes and so on. It is the first letter of "quantity".
\(c\)	c	The boxes per unit (a coefficient). It is 1 for "1 bookshelf shelf = 1 small box" and 0.1 for "1 hanger = 0.1 medium box". It is the first letter of "coefficient".
\(x\)	x	The boxes for each item, found with \(x = q \times c\).
\(\sum x\)	sigma x	The sum of the boxes \(x\) for all items. \(\sum\) (sigma) is the sign for "add them all up"; it is the Greek letter for S, as in "sum".
\(B\)	B	The net count of boxes (the total before the extra allowance), found separately for small and medium boxes.
\(r\)	r	The extra allowance as a rate. For 15%, \(r = 0.15\), and you multiply by \(1 + r = 1.15\). It is the first letter of "rate".
\(N\)	N	The number of boxes with the extra allowance, found with \(N = \lceil B(1 + r) \rceil\). It is the first letter of "number". In the tape formula, it is the total of small and medium boxes with the extra allowance.
\(N_{S},\ N_{M}\)	N sub S, N sub M	The numbers of small (S) and medium (M) boxes with the extra allowance. The small letters S and M stand for "small" and "medium".
\(n\)	lowercase n	The number of people, used in the people mode for "people × boxes per person".
\(a,\ b\)	a, b	The minimum (\(a\)) and maximum (\(b\)) boxes per person. The defaults are 10 and 25, and you can change them to match how much you own.
\(N_{\min},\ N_{\max}\)	N min, N max	The low and high ends of the rough range of boxes from the number of people (or rooms): \(N_{\min} = n \times a\) and \(N_{\max} = n \times b\).
\(w,\ d,\ h\)	w, d, h	The width, depth and height of one box, from the first letters of those words. On this page they are entered in inches.
\(v\)	lowercase v	The volume of one box: \(v = w \times d \times h\), converted to cubic feet. It is the first letter of "volume".
\(v_{S},\ v_{M}\)	v sub S, v sub M	The volume of one small box and one medium box. With the default sizes they are about 1.333 ft³ and 3 ft³.
\(V\)	capital V	The total volume of all the boxes, found with \(V = N_{S} v_{S} + N_{M} v_{M}\).
\(t\)	t	The length of tape used per box (ft), from the first letter of "tape". The default is 8 ft.
\(L\)	L	The length of one roll of tape (ft), from the first letter of "length". The default is 165 ft (55 yd).
\(R\)	capital R	The number of rolls of tape, from the first letter of "roll". It is found with \(R = \lceil N t \div L \rceil\).
\(u_{S},\ u_{M}\)	u sub S, u sub M	The price of one small box and one medium box ($ per box), from "unit price".
\(T\)	capital T	The estimated cost of the boxes ($), from the first letter of "total".
\(\lceil x \rceil\)	ceiling of x	The sign for rounding up to a whole number, called the ceiling function. (Example - \(\lceil 19.55 \rceil = 20\), \(\lceil 23 \rceil = 23\))

Moving Box Calculator (How Many Boxes Do I Need?)

Table of Contents

What you can do on this page

What is this calculation used for?

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

How to Use

DataChef Features

Related Features

Rectangular Prism Volume Calculator (Length × Width × Height)

Find the volume of one box (width × depth × height) with unit conversions

Room Volume and Ventilation Calculator (Air Changes per Hour, CFM)

Find the volume of a room and compare it with the total volume of your belongings

Furniture Fit Calculator (Through a Door, Around a Hallway Corner, Into an Elevator)

Check from the sizes whether furniture fits through the doors, hallway corners and elevator of your new home

Storage Capacity Calculator (Cubic Feet, How Many Books and Bins Fit)

Find how many bins or books fit in the storage of your new home from its inside dimensions

Recommended

Probability and random number

Averages and statistics

Percentage and ratio

Speed

Density and concentration

Physics and electricity

Unit conversion

Integer and signed number

Fraction, decimal and rounding

Equation and inequality

Polynomial

Square root and nth root

Exponent and logarithm

Complex number

Function and graph

Sequence

Vector

Matrix

Plane geometry

Solid geometry

Date and time

Finance and economics

Web marketing and ad metric

Health and fitness

Sports

Weather

Computer

Household energy and budget

Car

Solar power and battery

Home and DIY

Remove Ads