Box / room
Also: rectangular prism, bed, trench, room
V = L × W × H
L = length, W = width, H = height or depth.
Example: A raised bed 12 ft long, 4 ft wide and 1.5 ft deep: 12 × 4 × 1.5 = 72 cu ft (2.67 cu yd).
Quick answer: cubic feet = length × width × height, with every measurement in feet. Divide the result by 27 to get cubic yards. Measured in inches? Multiply the three numbers and divide by 1,728.
How to calculate cubic feet
A cubic foot is the space inside a cube that measures one foot on every side. When you calculate cubic feet, you are simply asking how many of those little cubes would fit into your space. For anything with straight sides and square corners, such as a raised bed, a trench, a moving box or a room, it takes three steps:
- Measure the length, width and height (or depth) of the space.
- Make sure all three are in feet. If one is in inches, divide it by 12 first. Six inches is 0.5 ft, three inches is 0.25 ft.
- Multiply them together. The answer is the volume in cubic feet (written cu ft, ft³ or cf).
Cubic feet = length (ft) × width (ft) × height (ft)
Worked example: filling a raised garden bed
Your raised bed is 10 ft long, 8 ft wide and 2 ft deep.
10 × 8 × 2 = 160 cubic feet. Divide by 27 and you get 5.93 cubic yards.
Soil usually comes in 2 cu ft bags, so you need 160 ÷ 2 = 80 bags. Soil settles after watering, so most gardeners add about 10%, which makes 88 bags. At that size, a bulk delivery of 6 cubic yards is usually cheaper than bags.
Volume formulas for 17 shapes, with examples
Every shape in the calculator has its own formula. Here they all are, with a drawing, what each letter means and a worked example in feet. Use all your measurements in the same unit; if they are in feet, the answer is in cubic feet. The radius (r) is always half of the diameter you measure across.
Cube
V = a³
a = length of one side.
Example: A storage cube 2.5 ft on each side: 2.5 × 2.5 × 2.5 = 15.63 cu ft.
Cylinder
Also: round hole, post hole, tank, planter
V = π × r² × h
r = radius (half the diameter), h = height.
Example: A post hole 12 in (1 ft) wide and 3 ft deep: r = 0.5 ft, so π × 0.5² × 3 = 2.36 cu ft.
Area × depth
Also: square feet to cubic feet
V = A × d
A = area, d = depth or thickness.
Example: Mulch for a 240 sq ft bed, 3 in (0.25 ft) deep: 240 × 0.25 = 60 cu ft (2.22 cu yd).
Triangular prism
Also: wedge, A-frame, gable attic
V = ½ × b × h × L
b = base of the triangle, h = height of the triangle, L = length of the prism.
Example: An attic under a gable 20 ft wide and 6 ft high, 30 ft long: ½ × 20 × 6 × 30 = 1,800 cu ft.
Trench / trapezoid
Also: ditch, berm, swale, trapezoidal prism
V = (a + b) ÷ 2 × h × L
a = top width, b = bottom width, h = depth, L = length.
Example: A drainage trench 3 ft wide at the top, 1.5 ft at the bottom, 2 ft deep, 40 ft long: (3 + 1.5) ÷ 2 × 2 × 40 = 180 cu ft (6.67 cu yd).
Sphere
Also: ball
V = 4⁄3 × π × r³
r = radius.
Example: A ball 18 in (1.5 ft) across: r = 0.75 ft, so 4⁄3 × π × 0.75³ = 1.77 cu ft.
Cone
Also: pile, mound, heap
V = 1⁄3 × π × r² × h
r = base radius, h = height.
Example: A gravel pile 10 ft across and 4 ft high: r = 5 ft, so 1⁄3 × π × 5² × 4 = 104.72 cu ft (3.88 cu yd).
Hollow cylinder
Also: pipe, tube, ring, annulus
V = π × (R² − r²) × h
R = outer radius, r = inner radius, h = height.
Example: A concrete ring 4 ft outside, 3 ft inside, 2 ft tall: π × (2² − 1.5²) × 2 = 11.00 cu ft of concrete.
Half cylinder
Also: trough, gutter, tunnel
V = ½ × π × r² × L
r = radius, L = length.
Example: A trough 2 ft across and 10 ft long: ½ × π × 1² × 10 = 15.71 cu ft (117.5 gallons).
Pyramid
V = 1⁄3 × L × W × H
L, W = base length and width, H = height to the tip.
Example: A pyramid with an 8 × 8 ft base, 5 ft high: 8 × 8 × 5 ÷ 3 = 106.67 cu ft.
Conical frustum
Also: tapered planter, bucket, cut cone
V = 1⁄3 × π × h × (R² + R·r + r²)
R = bottom radius, r = top radius, h = height.
Example: A tapered planter 2 ft across the top, 1.5 ft across the bottom, 1.5 ft tall: R = 1, r = 0.75, so 1⁄3 × π × 1.5 × (1 + 0.75 + 0.5625) = 3.63 cu ft.
Hemisphere
Also: dome, bowl
V = 2⁄3 × π × r³
r = radius.
Example: A dome 8 ft across: r = 4 ft, so 2⁄3 × π × 4³ = 134.04 cu ft.
Capsule
Also: propane tank, pill
V = π × r² × (4⁄3 × r + a)
r = radius, a = length of the straight middle part.
Example: A tank 3 ft across with a 6 ft straight middle: π × 1.5² × (4⁄3 × 1.5 + 6) = 56.55 cu ft (423 gallons).
Oval tank
Also: elliptical cylinder, stock tank, oval pool
V = π × a × b × h
a = half the long width, b = half the short width, h = height.
Example: An oval stock tank 8 ft long, 4 ft wide and 2 ft deep: π × 4 × 2 × 2 = 50.27 cu ft (376 gallons).
Partly filled tank
Also: horizontal cylinder, fuel tank, oil tank
V = L × [r² × acos((r − f) ÷ r) − (r − f) × √(2rf − f²)]
r = radius, f = fill depth, L = length.
Example: A tank 4 ft across and 8 ft long with 1 ft of fuel in it: 19.65 cu ft, about 147 gallons.
Sloped slab
Also: ramp, uneven depth, tapered bed
V = L × W × (h₁ + h₂) ÷ 2
L = length, W = width, h₁ and h₂ = depth at each end.
Example: A slab 20 × 10 ft, 6 in deep at one end and 4 in at the other: 20 × 10 × (0.5 + 0.333) ÷ 2 = 83.33 cu ft (3.09 cu yd).
How to measure cubic feet correctly
When you measure cubic feet, most mistakes don’t come from the math. They come from the tape measure. A few habits make your numbers much more reliable:
- Measure the inside, not the outside. For a planter, crate or trailer bed, the walls take up space. Measure from inside wall to inside wall.
- Use the real depth. If you only want to fill a bed to 2 inches below the rim, measure to that line, not to the top edge.
- Check uneven depth in several spots. For a sloping yard or a dug hole, measure the depth in three to five places and use the average.
- Write feet and inches as decimals. 5 ft 6 in is 5.5 ft, not 5.6 ft. Divide the inches by 12: 6 ÷ 12 = 0.5.
- Round up, not down, when you are buying material. Running short halfway through a job costs you a second trip and often a second delivery fee.
Calculating cubic feet from inches, yards or meters
You don’t have to convert by hand. Just switch the unit in the calculator above. If you want to do it yourself, here are the numbers to use:
| You measured in | Multiply L × W × H, then… | Example |
|---|---|---|
| Inches | divide by 1,728 | 24 × 18 × 12 in = 5,184 ÷ 1,728 = 3 cu ft |
| Yards | multiply by 27 | 2 × 1 × 1 yd = 2 × 27 = 54 cu ft |
| Meters | multiply by 35.315 | 1 × 1 × 1 m = 35.31 cu ft |
| Centimeters | divide by 28,317 | 100 × 50 × 40 cm = 7.06 cu ft |
The most common case is converting cubic inches to cubic feet for a box measured in inches. Why 1,728? A cubic foot is 12 inches long, 12 inches wide and 12 inches high, and 12 × 12 × 12 = 1,728. So every 1,728 cubic inches add up to one cubic foot.
Square feet to cubic feet
Square feet measure a flat area; cubic feet measure volume. You can’t convert one straight into the other, but you can multiply an area by a depth. This is how you work out mulch, gravel, topsoil or concrete for a bed, path or slab: cubic feet = square feet × depth in feet. Choose “Area × depth” in the calculator if you already know the square footage.
| Depth | Per 100 sq ft | Cubic yards | 2 cu ft bags |
|---|---|---|---|
| 1 in | 8.33 cu ft | 0.31 | 5 |
| 2 in | 16.67 cu ft | 0.62 | 9 |
| 3 in | 25.00 cu ft | 0.93 | 13 |
| 4 in | 33.33 cu ft | 1.23 | 17 |
| 6 in | 50.00 cu ft | 1.85 | 25 |
| 12 in | 100.00 cu ft | 3.70 | 50 |
Going the other way, divide cubic feet by the depth in feet to find how much area a volume covers. A 2 cu ft bag of mulch spread 3 inches deep covers 2 ÷ 0.25 = 8 sq ft.
Odd shapes: split them into rectangles
Few gardens or rooms are perfect rectangles. The trick is to cut the shape into simple pieces, work out each one, and add the results. An L-shaped bed, for example, is just two rectangles that share the same depth.
The calculator does this for you: enter the first piece and press “Add this shape to a project total”, then switch shape (or change the sizes) for the next piece and add it too. The project total lists every part, adds them up, applies your waste allowance and counts the bags for the whole job. You can mix shapes, for example a rectangular patio, a round fire-pit area and a sloped path, in one list and send it to your supplier.
For a curved border, measure it as a rectangle along its longest length and average width. The small error is usually less than the 5–10% extra you would add for settling anyway. If you have several identical pieces, such as four matching planters, enter one of them and set “How many?” to 4.
Cubic feet to cubic yards (and back)
Bulk materials like topsoil, mulch, gravel and concrete are sold by the cubic yard, often just called a “yard”. One cubic yard is a cube 3 feet on each side, so it holds 3 × 3 × 3 = 27 cubic feet.
- Cubic feet to cubic yards: divide by 27. This is the conversion behind every how many cubic feet in a yard question. 160 cu ft ÷ 27 = 5.93 cu yd.
- Cubic yards to cubic feet: multiply by 27. 3 cu yd × 27 = 81 cu ft.
- A yard of mulch or soil (people often search how many cubic feet in a yard of mulch) is 27 cubic feet, which is 13.5 bags of 2 cu ft. You would buy 14 bags.
As a rule of thumb, once you need more than about 3 cubic yards, bulk delivery tends to cost less than bags, and it saves you a lot of lifting. Below that, bags are easier to handle and store.
Cubic feet to gallons, liters and quarts
Liquids and some garden products are measured in gallons, liters or quarts instead of cubic feet. These are the conversions you will actually use, from cubic feet to gallons and liters to quarts to cubic feet for potting soil:
| 1 cubic foot equals | Handy to know |
|---|---|
| 7.48 US gallons | A 5-gallon bucket holds about 0.67 cu ft |
| 28.32 liters | A 50 L bag of compost is about 1.77 cu ft |
| 25.71 US dry quarts | 50 dry quarts of potting soil ≈ 1.94 cu ft |
| 29.92 US liquid quarts | 50 liquid quarts ≈ 1.67 cu ft |
| 1,728 cubic inches | A 12-inch cube |
Cubic feet conversion table
Use this table to convert cubic feet to other volume units, or back again. The factors use the exact definitions (1 in = 2.54 cm, 1 US gallon = 231 cubic inches).
| 1 cubic foot equals | To convert back to cu ft | Example: 10 cu ft |
|---|---|---|
| 1,728 cubic inches | divide by 1,728 | 17,280 cu in |
| 0.037037 cubic yards | multiply by 27 | 0.37 cu yd |
| 0.0283168 cubic meters | multiply by 35.3147 | 0.28 m³ |
| 28.3168 liters | divide by 28.3168 | 283.17 L |
| 28,316.8 cubic centimeters | divide by 28,316.8 | 283,168 cm³ |
| 7.48052 US gallons | divide by 7.48052 | 74.81 gal |
| 6.22884 UK (imperial) gallons | divide by 6.22884 | 62.29 UK gal |
| 29.9221 US liquid quarts | divide by 29.9221 | 299.22 qt |
| 25.7143 US dry quarts | divide by 25.7143 | 257.14 dry qt |
| 59.8442 US pints | divide by 59.8442 | 598.44 pt |
| 957.506 US fluid ounces | divide by 957.506 | 9,575.06 fl oz |
| 0.803564 US bushels | divide by 0.803564 | 8.04 bu |
| 12 board feet | divide by 12 | 120 board ft |
A board foot is a piece of lumber 12 × 12 × 1 inches, so there are 12 in every cubic foot. Lumber yards price hardwood by the board foot.
How much does a cubic foot weigh?
Volume tells you how much space a material takes up; its weight decides whether your truck, trailer or wheelbarrow can carry it. Choose a material under “Estimate the weight of” to see the weight with your result. These are typical figures. Wet material is heavier, and suppliers can give you the exact density of what they sell.
| Material | Per cubic foot | Per cubic yard |
|---|---|---|
| Water | 62.4 lb | 1,685 lb (0.84 tons) |
| Concrete, wet | ≈ 150 lb | ≈ 4,050 lb (2.0 tons) |
| Gravel | ≈ 105 lb | ≈ 2,835 lb (1.4 tons) |
| Sand, dry | ≈ 100 lb | ≈ 2,700 lb (1.35 tons) |
| Topsoil | ≈ 80 lb | ≈ 2,160 lb (1.1 tons) |
| Wood mulch | ≈ 22 lb | ≈ 600 lb (0.3 tons) |
Check your vehicle’s payload before you load it: a cubic yard of gravel weighs more than many half-ton pickups are rated to carry.
How big is a cubic foot? Everyday sizes
Rough sizes help you picture the volume and catch a wrong decimal point before you order. Product sizes vary, so check the label or spec sheet for exact numbers.
| Thing | Typical volume |
|---|---|
| 5-gallon bucket | ≈ 0.67 cu ft |
| 80 lb bag of concrete mix (yield) | ≈ 0.6 cu ft |
| Bag of mulch or garden soil | 1.5–3 cu ft (2 cu ft is most common) |
| Small / medium / large moving box | ≈ 1.5 / 3 / 4.5 cu ft |
| Wheelbarrow | ≈ 4–8 cu ft (6 cu ft is common) |
| Full-size refrigerator | ≈ 18–28 cu ft of storage |
| One cubic yard | 27 cu ft |
| Cord of firewood (4 × 4 × 8 ft stack) | 128 cu ft |
| 10 × 10 ft storage unit, 8 ft high | 800 cu ft |
Real-life examples
Moving and storage
Moving companies and storage units quote in cubic feet. A medium moving box of 18 × 18 × 16 inches is 5,184 ÷ 1,728 = 3 cu ft. A 10 × 10 ft storage unit with 8 ft ceilings has 800 cubic feet of space, although you can realistically fill around three quarters of it once you leave room to walk and stack safely.
Refrigerators and freezers
Fridge capacity is listed in cubic feet of usable inside space, which is why a fridge’s outside measurements always give a bigger number. If you want to check a chest freezer, measure the inside: 40 × 20 × 24 inches = 19,200 ÷ 1,728 = 11.1 cu ft.
Concrete footings and post holes
A round post hole 10 inches wide and 3 ft deep is a cylinder: 3.1416 × (0.4167)² × 3 = 1.64 cu ft. For bagged concrete, check the yield on the bag: an 80 lb bag of standard mix typically makes about 0.6 cubic feet, so that hole takes 3 bags.
Rooms and air volume
Heating, ventilation and dehumidifier sizing sometimes uses room volume. A bedroom of 12 × 14 ft with an 8 ft ceiling holds 12 × 14 × 8 = 1,344 cubic feet of air.
Notes for engineers, estimators and contractors
Exact constants. The calculator works internally in feet using exact definitions: 1 in = 2.54 cm, so 1 ft = 0.3048 m and 1 ft³ = 0.028316846592 m³. 1 US gallon = 231 in³ exactly, giving 7.480519 gal per ft³. 1 US dry quart = 67.200625 in³; 1 US liquid quart = 57.75 in³.
Bank, loose and compacted volume. Volume calculated from dimensions is in-place (“bank”) volume. Excavated soil swells when dug, and aggregate compacts when placed, so order quantities should allow for the material’s swell or compaction factor from your supplier.
Precision. Results display to two decimals; bag counts are rounded up after the waste allowance. Keep input precision in line with your measurements: a tape read to the nearest ½ inch on a 2 ft depth already carries about ±2% uncertainty.
Cylinder input. Enter the inside diameter for tanks and forms (e.g. Sonotube inside diameter), not the outside.
Tips before you buy
- Add 5–10% for loose materials. Soil, mulch, sand and gravel settle and spill.
- Compare bags and bulk by the cubic yard. Divide the bag price by its cubic feet and multiply by 27 to see the price per yard.
- Check the bag label. Bags list their volume in cubic feet, quarts or liters; use the table above to compare them fairly.
- Send your list. Use WhatsApp, Email or Print under the result to send the quantities to your supplier. “Copy link” saves the calculator with your numbers filled in, so you can come back to it later.
- Measured in feet and inches? Choose “Feet + inches” as the unit and type each part in its own box, fractions included (6 3/4).
Frequently asked questions
How do I calculate cubic feet?
Measure the length, width and height in feet, then multiply them: length × width × height = cubic feet. A space 10 ft long, 8 ft wide and 2 ft deep holds 10 × 8 × 2 = 160 cubic feet.
How many cubic feet are in a cubic yard?
There are 27 cubic feet in one cubic yard, because a yard is 3 feet and 3 × 3 × 3 = 27. Divide cubic feet by 27 to get cubic yards, or multiply cubic yards by 27 to get cubic feet.
How many cubic feet are in a yard of mulch, soil or gravel?
A "yard" of landscaping material always means one cubic yard, which is 27 cubic feet. That equals 13.5 bags of 2 cu ft mulch or soil, so you would buy 14 bags.
How do I calculate cubic feet from inches?
Multiply length × width × height in inches, then divide by 1,728 (12 × 12 × 12). A 24 × 18 × 12 inch box is 5,184 cubic inches, which is exactly 3 cubic feet.
How many gallons are in a cubic foot?
One cubic foot holds about 7.48 US gallons (28.32 liters). A 5-gallon bucket therefore holds about 0.67 cubic feet.
How many cubic feet is 50 quarts of potting soil?
Potting soil is usually sold in dry quarts. 50 dry quarts is about 1.94 cubic feet. If the bag means liquid quarts, 50 quarts is about 1.67 cubic feet.
Can I convert square feet to cubic feet?
Not on their own: square feet measure area and cubic feet measure volume. Multiply the square footage by the depth in feet. For example, 100 sq ft at 3 inches (0.25 ft) deep is 25 cubic feet.
How do I calculate the cubic feet of a pile of gravel or soil?
Treat the pile as a cone. Measure across the base and the height, then use 1/3 × π × r² × h. A pile 10 ft across and 4 ft high holds about 105 cubic feet, or 3.9 cubic yards. Choose “Cone” in the calculator.
How do I find the cubic feet of an irregular shape?
Split it into simple shapes such as boxes, cylinders and triangles. Work out each one, press “Add this shape to a project total”, and the calculator adds them up and counts the bags for the whole job.
How many gallons are in a partly full horizontal tank?
Pick “Partly filled tank”, enter the diameter, length and the depth of the liquid. A 4 ft × 8 ft tank with 1 ft of fuel holds about 19.65 cubic feet, which is 147 US gallons.
Should I add extra for waste?
For loose materials such as soil, mulch, sand or gravel, add 5–10% for settling, uneven ground and spills. For a container you are filling exactly, no extra is needed.