Cubic Yard Calculator

Turn a shape’s dimensions into cubic yards and a material cost.

Nine shapes, seven length units and twenty currencies, solved in either direction.

Updated October 19, 2026

CreatorFrank Zhao

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Introduction

A cubic yard is a volume, and it is the unit bulk material is often ordered in: concrete, gravel, sand, topsoil, mulch. This calculator turns the dimensions of the hole, pad or container you are dealing with into that volume for nine common shapes, then multiplies it by whatever your supplier charges so you can see the bill before you pick up the phone.

The shape does more work than most people expect. A cone and a cylinder with the same base and the same height do not hold the same amount — the cone holds exactly one third — and a rectangular tube holds only the material in its walls, not the space inside it. Choose the shape that matches what you are filling or building and the arithmetic follows; choose the wrong one and the number can be out by a factor of three.

It is a working tool for pads and footings, driveways and drainage trenches, raised beds and planters, and any excavation where the invoice arrives in cubic yards. It also runs the other way: if you already know the yardage — a delivery note, a mixer drum, a bag count — type it with the area or the other dimensions and read back the depth it will spread to.

9 shapes

From a box to a hollow cylinder

7 length units

Inches to yards, or feet / inches in one box

Both directions

Dimensions to yardage, or yardage back to a dimension

Quick start

Pick the shape that matches the job

Nine options cover the shapes material is normally measured in. Two are easy to mix up: a hollow cylinder is a pipe, described by an outer radius, an inner radius and a depth; a hollow cuboid is a rectangular tube, described by its outer length and width, the wall thickness and the depth. Choose Other shape when you measured a cross-section instead of a regular solid.

Type the dimensions, each in its own unit

Every box has its own unit menu, so a pad can be 12 feet long, 8 feet wide and 6 inches deep without any conversion by hand. The feet / inches entry takes a measurement the way a tape gives it to you, and you can change any box's unit afterwards without retyping the number.

Read the Volume box

The Yardage group shows the volume in cubic yards by default. Switch it to cubic feet, cubic metres or cubic inches if that is how your supplier quotes; no price is needed for this number to appear. The volume is the same quantity in every unit, so switching the menu never changes the job.

Add the price, if you want the cost

Enter what the material costs per cubic yard — or switch the price box to per cubic metre, per cubic foot and so on — and pick your currency. The total appears underneath, rounded to cents. The price and the total each carry their own currency menu: changing the price currency only re-expresses that price in the equivalent amount, while the total box keeps the currency you chose for it.

Check the working against a pad you can picture

A 12 ft × 8 ft pad, 6 inches thick, with concrete at 165 US dollars per cubic yard. Six inches is half a foot, so the thickness enters as $0.5$ ft:

V

=

12\ \mathrm{ft} \times 8\ \mathrm{ft} \times 0.5\ \mathrm{ft}

=

48\ \mathrm{ft^3}

=

1.77778\ \mathrm{yd^3}

The total then reads 293.33 US dollars for that yardage. If the pad were half as thick, the volume would halve with it, because nothing else in the recipe changed.

The formulas behind each shape

Every option is the same idea in a different dress: the area of the footprint multiplied by the depth it is pushed to. What changes between shapes is how that footprint is computed, and whether a geometric factor of one third or two thirds comes with it.

Footprint times depth

Box

V = \mathrm{L} \times \mathrm{W} \times \mathrm{D}

Two footprint sides and a depth. The plainest case, and the shape most pads and trenches are.

Cube

V = a^{3}

One side only; the same value fills the length, the width and the depth.

Cylinder

V = \pi \, r^{2} \times \mathrm{D}

A round footprint of area $\pi r^{2}$ carried down to a depth: sonotubes, drilled piers, round planters.

Cone

V = \frac{1}{3}\,\pi \, r^{2} \times \mathrm{D}

The same cylinder with a point on it, so exactly one third of the volume.

Pyramid

V = \frac{1}{3}\,\mathrm{A} \times \mathrm{D}

A base of any shape, tapering to a point: one third of the prism that would contain it.

Hemisphere

V = \frac{2}{3}\,\pi \, r^{3}

Half of a sphere, so no separate depth box — the radius sets everything.

Hollow cylinder

V = \pi \left(R^{2} - r^{2}\right) \times \mathrm{D}

A pipe: the outer disc minus the hollow core, carried down to a depth.

Hollow cuboid

V = 2\,b\,\mathrm{D}\left(\mathrm{L} + \mathrm{W} - 2b\right)

A rectangular tube's walls only — see below for where that compact form comes from.

Other shape

V = \mathrm{A} \times \mathrm{D}

Any cross-section you measured yourself, multiplied by the depth.

The tube is walls, not the hole inside it

A rectangular tube holds only the material of its four walls. Subtract the hollow middle from the outer rectangle and the bracket collapses into a shorter formula that needs no inner dimensions at all:

\left[\mathrm{L}\mathrm{W} - (\mathrm{L} - 2b)(\mathrm{W} - 2b)\right]\mathrm{D}

=

2\,b\,\mathrm{D}\left(\mathrm{L} + \mathrm{W} - 2b\right)

The wall thickness $b$ is what you type, not the inner size: a 6 ft × 3 ft planter with 6-inch walls is not a 6 ft × 3 ft box. The same idea drives the hollow cylinder, where the hollow core is described by its own radius.

Working backwards

The volume and the dimensions are one relationship, not a one-way recipe. Fill in all but one box and the remaining one is solved for you — a known yardage with the length and width of a pad gives its depth, and a known depth with the area of a bed gives whatever yardage you have bought. The price behaves the same way: with two of volume, unit price and total, the third follows.

It needs exactly one unknown, though. Each shape is a single relationship between its boxes, so filling in all of them but one leaves the last one solvable — three dimensions give the volume of a box, but a volume plus one dimension cannot find the other two at once. A solve with no real answer stays blank rather than inventing one: ask for a wall thickness on a tube whose volume is larger than the whole outer box and there is no wall to find.

Units, and the exact size of a cubic yard

Each box is converted to a common base — metres, square metres, cubic metres — before anything is multiplied, then the answer is shown back in the unit you picked. The yard is defined metrically: it has been exactly 0.9144 m since 1959, as NIST SP 811, Appendix B records. Cubing it gives the factor behind every yardage on this page:

1\ \mathrm{yd}

=

3\ \mathrm{ft}

=

0.9144\ \mathrm{m}

1\ \mathrm{yd^3}

=

27\ \mathrm{ft^3}

=

0.764554857984\ \mathrm{m^3}

So a cubic yard is a little under three quarters of a cubic metre, and a cubic metre is about 1.31 cubic yards. Neither conversion needs to be done by hand: the volume menu switches the display, and the stored quantity stays the same.

V

Volume — the yardage, in whichever volume unit the box is set to

\mathrm{L},\ \mathrm{W}

Length and width of the footprint

\mathrm{D}

Depth or height: the dimension the footprint is carried through

a

Side of a cube

b

Wall thickness of a rectangular tube

r

Radius — half the diameter — of a circle, pipe core or hemisphere

R

Outer radius of a pipe

\mathrm{A}

Area of a base or a measured cross-section

P

Material price per volume unit

C

Total price of the volume

What survives a shape change

Switching shape keeps the measurements the shapes share — length, width, depth, radius, area — and keeps the material price, so you can compare a cylinder and a cone on the same footprint without retyping anything. The previous yardage and total are cleared, because they belonged to the shape you just left.

Worked examples

Concrete for three round pier footings

Situation: Three sonotubes for a deck, each 18 inches across and 3 ft deep. The tube supplier sells concrete by the cubic yard, and the hardware store by the bag, so the yardage is the number that matters.

Inputs

ShapeCylinder

Radius

0.75\ \mathrm{ft}

Depth / Height

3\ \mathrm{ft}

Volume unitcubic yards (cu yd)

Result

V

=

\pi \,(0.75)^{2} \times 3

=

5.30144\ \mathrm{ft^3}

=

0.19635\ \mathrm{yd^3}

An 18-inch tube has a 0.75 ft radius, not a 1.5 ft one: the diameter goes in halved. That slip alone would make the answer four times too large.

In practice: Multiply by the three piers and round up: about 0.59 cubic yard in total, so a single cubic yard covers all three with room to spare for spillage and an uneven base.

Material for a rectangular planter wall

Situation: A raised planter with outer dimensions of 6 ft by 3 ft, 6-inch walls and an 18-inch height, built from a cast material. The order is for the walls; the soil inside is a separate purchase.

Inputs

ShapeHollow cuboid / Rectangular tube

Length × width

6\ \mathrm{ft} \times 3\ \mathrm{ft}

Border width

6\ \mathrm{in}

Depth / Height

18\ \mathrm{in}

Result

V

=

2\,(0.5)(1.5)(6 + 3 - 1)

=

12\ \mathrm{ft^3}

=

0.444444\ \mathrm{yd^3}

Both thicknesses went in as 0.5 ft and 1.5 ft, the page converting the inches for you. The compact form is already doing the subtraction: the hollow middle is 5 ft by 2 ft, so what remains in the formula is the four walls.

In practice: The walls take 0.44 cubic yard. For the soil, switch to Box and enter the inside dimensions (5 ft × 2 ft at the same height) — the page keeps the shared measurements but solves the new shape from scratch.

How deep two cubic yards will spread

Situation: A landscaper has two cubic yards on the truck and a 100 square foot bed prepared. The question is the opposite of the usual one: not how much material, but how far it goes.

Inputs

ShapeOther shape

Area

100\ \mathrm{ft^2}

Volume

2\ \mathrm{yd^3}

Depth unitinches (in)

Result

2\ \mathrm{yd^3}

=

54\ \mathrm{ft^3}

\Rightarrow

\mathrm{D} = \frac{54}{100}

=

0.54\ \mathrm{ft} = 6.48\ \mathrm{in}

The relation is linear both ways: double the area and the depth halves, so the same two yards would give 3.24 in over 200 square feet.

In practice: About 6.5 inches at the volume delivered. Settling and compaction take some of that back, so treat it as a ceiling rather than a promise, and expect less over an uneven bed.

Measuring and ordering advice

Take the depth in several places

Ground is rarely flat and a pad is rarely exactly one thickness. Measure the depth at the corners and in the middle and enter the average; a two-inch difference across a 12 ft pad is already a noticeable slice of the volume. Length and width are easy — the depth is where estimates drift.

A tube wants the wall, not the inside

For a rectangular tube enter the outer length and width plus the wall thickness; for a pipe enter the outer radius and the inner radius. Entering the inside size as if it were the outside quietly inflates the order, because the material volume is only the ring or the walls.

No sphere? Use the hemisphere twice

A hemisphere is half a sphere, so a full round dome is the hemisphere result doubled. The same trick works the other way: a shape you are only building halfway can be halved from the closest option.

Price the whole job, then add your margin

The total is the theoretical quantity at your unit price. Add your own allowance on top of it for waste, spillage on a rough base, and the way the material sits once it is placed, rather than shaving the measurements to make the order look smaller.

If your supplier prices by weight

Concrete, gravel and crushed stone are often sold by the ton rather than the yard. The volume here is the starting point, not the answer: the cubic yards to tons calculator converts that same yardage into mass using the material's density, which is the figure the ticket at the quarry is written in. If you are buying bagged garden material instead of a bulk load, the mulch calculator turns the volume into bags of a given size.

Questions

How many cubic feet are in a cubic yard?

Twenty-seven. A yard is three feet, so a cubic yard is $3 \times 3 \times 3 = 27$ cubic feet, and working the other way you divide cubic feet by 27. In metric terms one cubic yard is 0.764554857984 cubic metres, and one cubic metre is about 1.31 cubic yards. The volume box on this page switches between all of them without any arithmetic on your part.

How much ground does one cubic yard cover?

It depends entirely on the depth, because $V = \mathrm{A} \times \mathrm{D}$ . A cubic yard is 27 cubic feet; spread over 100 square feet that is $27/100 = 0.27\ \mathrm{ft}$ , or about 3.24 inches. Over 50 square feet the same yard buys 6.48 inches. Enter your own area and volume with the Other shape option and read the depth directly: it is the volume divided by the area.

\mathrm{D} = \frac{\mathrm{V}}{\mathrm{A}}

so a bigger area spreads the same volume thinner, in exact proportion.

Why does the total not change when I switch the price currency?

Because the currency menu re-expresses the same price in a different currency — it does not change what the material costs. The price box converts its own number to the equivalent amount and the calculation continues from the unchanged price, so the total stays where it was. The total has a separate currency menu: switch that one if you want the bill shown in another currency.

Why is a box blank, or red?

A blank box usually means the shape still has more than one unknown: fill in every box of the shape except one, and that last box is solved for you. A red box is a rule that did not hold — a wall thickness larger than half of the outer length or width, an inner radius that is not smaller than the outer one, a volume too large to fit inside the tube you described, or a value outside the range the field accepts. The number stays visible in the red box so you can see what the solver produced and judge the input that caused it.

How far the number goes

This is a quantity estimate, not a design. It gives the volume of an idealised shape. Concrete grade, reinforcement, subgrade preparation, formwork and local building rules sit outside the model, and a footing or slab that carries a real load should be sized by a qualified engineer rather than by the volume of its hole.
The shape is treated as perfect. A dug hole has sloped sides and an uneven base, a bed is not a rectangle, and a planter is not cast to the millimetre. Measure an average depth, and prefer a cross-section you actually measured for the Other shape option over a nominal length and width.
Loose, compacted and in-place volumes differ. Material that arrives loose settles and compacts; material that is excavated bulks up. The number here is the volume of the finished space, so the delivered quantity and the depth a load actually covers will not match it exactly.
The total is a material cost only. It excludes tax, delivery and any labour, and prices differ by region, supplier and season, so an average is not a quote. Use your own figure, and confirm the unit your supplier actually invoices in — the yard, the ton and the bag are all in use for the same material.
Check any number you are about to order against. For a large pour, a structural element, or anything where a shortfall stops the job, confirm the quantity with the supplier or the engineer responsible for the work — and note that a cubic yard of different materials weighs very different amounts, so a volume is not yet a load.
Order the size that can be delivered. Loads arrive in fixed truck sizes and many suppliers set a minimum, so a calculated 0.4 cubic yard may still be billed as a full load. Ask before the pour, not after.

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