"What is a cubic foot" is asked by children in grades 5 to 8 meeting volume for the first time, and by adults buying a fridge, a bag of mulch or a moving truck, which is why the question is searched more than almost any other unit question in the United States. The answer is simple, the measuring is simple once you know the one division to do, and the useful part is knowing what 1, 2, 5 and 10 cubic feet look like so that a number on a label means something. This page gives the definition, the formula, the conversions, a set of worked examples from real objects, and practice questions with answers; the printable sheet has all of it on two pages.
Download the cubic feet formula and conversion sheet (PDF) (the formula, the conversion chart, what each size looks like, seven worked examples, eight practice questions with answers and a measure-something-at-home box; two pages, free).
What a cubic foot is
A cubic foot is the volume of a cube that measures one foot on each side: one foot long, one foot wide, one foot high. Because a foot is 12 inches, that cube holds 12 × 12 × 12 = 1,728 cubic inches. It is a unit of volume, which means it measures how much space something takes up or how much a container holds, and it is written cu ft, ft³ or "cubic feet".
For a sense of size: a cubic foot is about the box a basketball comes in, a milk crate, or a small moving box. It holds about 7.5 US gallons of water, which weighs 62 pounds. The United States uses cubic feet for the capacity of refrigerators, freezers, microwaves, washing machines and dryers, for moving boxes and truck space, for bags of mulch, soil and gravel, and for shipping; most of the rest of the world uses litres and cubic metres for the same things.
How to measure cubic feet
The formula: cubic feet = length (in feet) × width (in feet) × height (in feet).
Measure the three sides, multiply them, and the answer is in cubic feet. The only thing that goes wrong is units: if any side is in inches, convert it to feet first (divide by 12), or measure all three in inches, multiply, and divide the total by 1,728.
| Measured in | Do this |
|---|---|
| Feet | Multiply the three sides. Done |
| Inches | Multiply the three sides, then divide by 1,728 |
| Feet and inches (6 ft 3 in) | Turn the inches into a decimal of a foot first: 3 in is 0.25 ft, so 6.25 ft |
| Centimetres | Multiply the three sides, then divide by 28,317 |
| Metres | Multiply the three sides, then multiply by 35.3 |
A cylinder (a tank, a bucket, a round planter): volume = π × radius² × height, with everything in feet. A tank 1 foot in radius and 3 feet tall is 3.14 × 1 × 1 × 3 = 9.42 cubic feet, about 70 gallons.
An irregular shape (a room with an alcove, an L-shaped space): split it into boxes, work out each, add them.
What 1, 2, 5 and 10 cubic feet look like
| Cubic feet | About the size of |
|---|---|
| 1 | A small moving box (16 × 12 × 9 in), a milk crate, a basketball's box |
| 1.5 | A medium moving box |
| 2 | A standard bag of mulch or potting soil; the inside of a large countertop microwave (about 17 × 19 × 11 in); a mini fridge |
| 3 | A large moving box; a bag of soil conditioner |
| 4 to 5 | A front-load washing machine drum; a dorm fridge |
| 7 | A small chest freezer |
| 10 | A chest freezer; the trunk of a small car |
| 18 to 25 | A full-size refrigerator, inside |
| 27 | One cubic yard: a pickup truck bed filled level |
The two numbers most people actually need: a bag of mulch is 2 cubic feet, and a cubic yard is 27 cubic feet (so 13 or 14 bags).
The conversion chart
| 1 cubic foot equals | |
|---|---|
| Cubic inches | 1,728 |
| Cubic yards | 0.037 (there are 27 cubic feet in a cubic yard) |
| Cubic metres | 0.0283 (there are 35.3 cubic feet in a cubic metre) |
| Litres | 28.3 |
| US gallons | 7.48 |
| UK (imperial) gallons | 6.23 |
| Weight of water | 62.4 lb, or 28.3 kg |
| To convert | Do this |
|---|---|
| Cubic inches to cubic feet | Divide by 1,728 |
| Cubic feet to cubic yards | Divide by 27 |
| Cubic yards to cubic feet | Multiply by 27 |
| Cubic feet to cubic metres | Multiply by 0.0283 |
| Cubic metres to cubic feet | Multiply by 35.3 |
| Cubic feet to litres | Multiply by 28.3 |
| Cubic feet to US gallons | Multiply by 7.48 |
Worked examples
| The job | The working | The answer |
|---|---|---|
| A moving box 24 in × 18 in × 12 in | 24 × 18 × 12 = 5,184 cubic inches; ÷ 1,728 | 3 cubic feet |
| A bedroom 12 ft × 10 ft with an 8 ft ceiling | 12 × 10 × 8 | 960 cubic feet (what an air conditioner or dehumidifier label means by room size) |
| A fridge 30 in wide, 28 in deep, 60 in tall, outside | 30 × 28 × 60 = 50,400; ÷ 1,728 | 29.2 cubic feet outside; the inside is about 20 because of the walls and the compressor |
| Mulch for a bed 10 ft × 4 ft, 3 inches deep | 3 in is 0.25 ft; 10 × 4 × 0.25 = 10 cubic feet; bags are 2 cubic feet | 5 bags |
| A concrete slab 10 ft × 10 ft, 4 inches thick | 4 in is one third of a foot; 10 × 10 × 0.333 = 33.3 cubic feet; ÷ 27 | 1.23 cubic yards (order 1.5 with waste) |
| A cylindrical rain barrel, 1 ft radius, 3 ft tall | 3.14 × 1² × 3 | 9.42 cubic feet, about 70 gallons |
| What a "2.0 cubic foot" microwave means in inches | 2 × 1,728 | 3,456 cubic inches: about 17 × 19 × 11 in inside |
Two habits prevent most errors: write the unit on every number, and ask whether the answer is sensible (a bedroom of 96 cubic feet is a cupboard; the ceiling height was left out).
Where it sits in school maths
Volume of a rectangular prism is a grade 5 topic in the US (Common Core 5.MD), where children build boxes from unit cubes and discover the formula; grade 6 extends it to fractional sides, grade 7 to composite shapes and grade 8 to cylinders, cones and spheres. In England it is Year 6 and Year 7; in India, CBSE Class 8 (Mensuration) and Class 9; in Australia, Year 7 and 8. The cubic foot specifically is a US unit, but the method is the same in cubic centimetres, and the one division (by 1,728 in inches, by 1,000 from cm³ to litres) is the step children forget.
The practice questions, with answers, are in the PDF; the most useful homework is to measure three things in the house in inches and work out the cubic feet of each, because a child who has measured the fridge never forgets what a cubic foot is.
Practice: eight questions
- A box is 3 ft by 2 ft by 2 ft. How many cubic feet?
- A box is 36 in by 24 in by 24 in. How many cubic feet?
- A sandbox 6 ft by 4 ft is filled 6 inches deep. How many cubic feet of sand?
- How many 2-cubic-foot bags fill 15 cubic feet?
- A pool 20 ft by 10 ft by 4 ft deep: how many cubic feet, and how many gallons?
- Convert 2 cubic metres to cubic feet.
- A moving truck holds 400 cubic feet. How many 3-cubic-foot boxes fit?
- A cube has a volume of 27 cubic feet. How long is each side?
Answers: 1) 12. 2) 36 × 24 × 24 = 20,736 ÷ 1,728 = 12. 3) 6 × 4 × 0.5 = 12. 4) 7.5, so buy 8. 5) 800 cubic feet; × 7.48 = 5,984 gallons. 6) 70.6. 7) 133. 8) 3 ft.
Download the cubic feet sheet (PDF)
Where to get help
A 1-on-1 online maths class with a tutor who holds a master's in mathematics, for grades 5 to 8 in the US curriculum and the equivalent years in England, Australia and CBSE: measurement and volume taught with real objects on the shared screen, then the formula, then the word problems the tests use. The recording and notes after every class, the same tutor every week, US$10 to $13 an hour. The grade 6 math page has the grades; the free 30-minute first class is a real lesson, usually on the homework the child brings.
Questions parents ask
1What is a cubic foot?
2How do you measure cubic feet?
3What does 2 cubic feet look like?
4How many cubic feet are in a cubic yard?
5How many cubic feet are in a cubic metre?
See how we teach this, 1-on-1 online →
Shobha
Founder and lead tutor, Science with Shobha
Teaching maths, science and English to children online since 2018. 500+ students, 20+ tutors, families in nine countries.