Volume Calculator

Four shapes, one exact chain

Every shape reduces to cubic feet first, and every other unit is derived from that one unrounded figure. The box is V = L × W × H: 4 × 3 × 2 ft = 24 cu ft = 0.8889 cu yd. The cylinder is V = πr²h: a 3 ft radius by 5 ft tall gives 141.37 cu ft. The sphere is V = 4/3 πr³ (3 ft radius → 113.1 cu ft), and the cone is V = πr²h ÷ 3 — exactly one third of its cylinder, 47.12 cu ft for the same 3 × 5 ft dimensions; the build checks that ratio (3 to one) and fails if it drifts. Every figure on this page is computed when the page is built by the same engine behind the form, so the copy and the tool cannot disagree.

The volume units themselves — why a cubic yard holds exactly 27 cubic feet, how cubic meters relate to both, and what happens to a volume once it becomes a concrete order — are the subject of the guide Cubic feet, cubic yards, and ordering concrete. Read it if the conversions are new to you. The rest of this page explains what this calculator does with the numbers you give it, why it stops where it does, and how to read what comes back.

Where this page sits in the pipeline

Every estimator on this site follows the five-stage pipeline documented on the methodology page: geometry, coverage, waste, package rounding, and user-priced cost. This calculator runs the first stage and deliberately stops there. It turns dimensions into a volume and reports that volume in five units; it does not divide by a coverage figure, does not add a waste allowance, does not round up to a whole bag or a quarter yard, and does not take a price. Those four stages need to know what material is going into the shape and how it is sold, and this page does not ask. That is what makes it general: the same cylinder is a tank of water, a column of concrete, or a drum of sand, and the geometry is identical for all three.

Because nothing is divided, padded, or rounded, the cubic-yard line here is the net geometry — the figure the methodology page describes as the quantity to compare against a drawing, not the quantity to buy. When the volume is going to be filled, the material tools linked at the end of this page pick the chain up at stage two. And the boundary every estimator here shares applies in full: this tool computes quantities only. Whether a tank, footing, or container is adequate for what it holds, and whether the shape you enter is the right shape to build, are questions for a qualified engineer or contractor, as the note under the form says.

Why each input matters

The shape picks the formula, and the formula decides how hard each dimension pushes the result. In a box every dimension is linear: doubling the length, the width, or the height doubles the volume. In a cylinder and a cone the height is linear but the radius is squared, so doubling the radius quadruples the volume — the 3 ft radius, 5 ft cylinder holds 141.37 cu ft, the same cylinder with a 6 ft radius holds 565.49, 4 times as much, while doubling the height instead gives 282.74 cu ft, 2 times. In a sphere the radius is cubed: the 3 ft sphere holds 113.1 cu ft and the 6 ft sphere 904.78, 8 times as much. A small error in a radius is therefore a larger error in the volume than the same error in a height, which is why the radius fields are the ones to measure twice.

Radius, not diameter. The round shapes ask for the radius, half the distance across, because that is what the formulas use. A tape laid across a tank reads the diameter; halve it before you type. The misreadings section below shows what happens when the diameter goes in unhalved.

Feet and the inches box. Every imperial dimension has a feet field and an optional "+ inches" field. The inches are divided by 12 and added to the feet before the engine runs — 2 ft 6 in becomes 2.5 ft, 6 ft 8 in becomes 6.6667 ft — the mixed-measurement convention every tool on the site follows. Decimal feet typed straight into the feet field work too; the inches box exists so a tape reading need not be converted by hand. It is meant for the remainder under a foot: carry whole feet into the feet field.

The units toggle changes what the fields expect and which unit leads the result, not what is computed. In metric mode each field takes meters, and the entry is divided by 0.3048 — the international foot, exact by definition — to get the feet the engine works in; the result then leads with cubic meters and liters. The arithmetic is identical in both systems. Metric and imperial in the estimators documents the toggle across the site.

The figures this page relies on

No manufacturer figure, coverage figure, or trade convention enters this page: the site's materials-data module, where every sourced coverage constant lives with its citation, holds nothing for it. The constants here are all definitions, or arithmetic on definitions, and the geometry engine stores each one once.

• Cubic feet per cubic yard, 27 — definition: a yard is three feet, cubed. The cubic-yard line divides by it.
• Inches per foot, 12 — definition. The inches boxes divide by it, and cubed it gives the 1,728 cubic inches in a cubic foot that the gallon factor needs.
• US gallons per cubic foot, 7.480519 — exact ratio. The US liquid gallon is defined as 231 cubic inches (the definition the engine cites from NIST Handbook 44, Appendix C), so the factor is 1,728 ÷ 231, stored as that single division rather than as a typed approximation. These are US liquid gallons, the only gallon the engine defines.
• Meters per foot, 0.3048 — the international foot, exact by definition. Metric entries are divided by it on the way in.
• Cubic meters per cubic foot, 0.028316846592 — that foot cubed, an exact decimal. The m³ line multiplies by it; from it follow 0.764554857984 m³ per cubic yard and 35.3147 cu ft per cubic meter.
• Liters per cubic meter, 1,000 — definition: a liter is 0.001 m³, so a cubic foot is 28.316846592 L.
• π — the one irrational number in the chain, used by the three round shapes as the closest double-precision value to pi. Everything else is exact.

Nothing is rounded between units. The engine carries every value at full precision and only the digits on screen are trimmed — a two-decimal cubic-feet figure is a display copy of the unrounded number that produced the cubic-yard, gallon, and liter lines beside it.

Worked examples

Every figure in this table was produced at build time by the engine behind the form. The inputs are chosen to show different behaviours: the four anchor shapes, a slab-shaped box with its height in inches, a tape-measured box in feet and inches, round shapes measured across rather than by radius, and two metric entries converted exactly before the engine ran, which is what the toggle does.

The slab-shaped box. The methodology page's example slab, 10 × 10 ft at 4 in, is a box whose height goes in as 0 in the feet field and 4 in the inches box. The inches become 0.3333 ft — one third of a foot — and the volume is 33.33 cu ft, 1.2346 cu yd, 0.9439 m³. That is the same net volume the concrete slab calculator starts from; the difference is that the slab tool then adds a waste allowance and rounds to a quarter yard, and this page does not.

The planter bed in feet and inches. A raised bed measured as 6 ft 8 in long, 2 ft 6 in wide, and 1 ft 3 in deep reaches the engine as 6.6667 × 2.5 × 1.25 ft and holds 20.83 cu ft — 0.7716 cu yd, or 589.93 L. The fraction of a yard is the figure to carry to the topsoil calculator, which adds the bulk-material allowance and rounds to how soil is sold.

The tank measured across. A round tank 8 ft across and 4 ft tall has a radius of 4 ft. π × 4² × 4 gives 201.06 cu ft, and the gallon line reads 1,504.05 US gal — the cubic feet times 7.480519. That is the geometric capacity of the shape to the brim: the model has no notion of a fill line, an outlet height, or the thickness of the tank wall, so measure the inside if the inside is what you want.

The sphere measured across. A ball 2 ft in diameter has a 1 ft radius and holds 4.1888 cu ft, 31.33 US gal. A cylinder that just encloses it — the same radius, 2 ft tall — holds 6.2832 cu ft, and the sphere is 0.6667 of that: two thirds, a ratio the engine reproduces for any radius.

The stockpile. A conical pile of loose material 12 ft across at the base and 4 ft high has a 6 ft base radius: π × 6² × 4 ÷ 3 = 150.8 cu ft, or 5.5851 cu yd. The cylinder of the same base and height holds 452.39 cu ft, 3 times the cone. A real pile is rarely a clean cone, and a volume is not a weight — converting it to tons needs a density the gravel calculator asks you to supply — so treat the figure as the geometry of the shape you described.

The metric box. In metric mode, 1.2 × 0.9 × 0.6 m reaches the engine as 3.937 × 2.9528 × 1.9685 ft, each meter divided by 0.3048. The result leads with 0.648 m³ and 648 L, with 22.88 cu ft, 0.8476 cu yd, and 171.18 US gal beneath. Multiplying the three meter figures directly gives 0.648 m³ — the same number, because the conversions in and out are exact and cancel.

The metric drum. A cylinder with a 0.3 m radius and a 0.9 m height is 0.2545 m³, or 254.47 L — the cubic meters times 1,000. Beneath it the panel still lists 8.99 cu ft and 67.22 US gal, so a metric measurement can be handed to a supplier who sells in either system.

How to read the result

In imperial mode the headline is cubic feet, the unit every formula produces first. Beneath it, Cubic yards is the cubic feet divided by 27, the unit bulk material and ready-mix are sold in; US gallons is the liquid capacity; and Also carries the cubic meters and liters. In metric mode the headline is cubic meters, Litres follows, and the Also line carries cubic feet, cubic yards, and US gallons. Every line comes from the same unrounded cubic-feet figure, so the lines agree with each other to more digits than are shown: the panel displays cubic feet, gallons, and liters to two decimals and cubic yards and cubic meters to four. The copy button puts the headline and its companions on the clipboard as plain text, ready for the material tool that comes next.

A unit cube makes the relationships visible. A 1 × 1 × 1 ft box is 1 cu ft, 0.037037 cu yd, 7.480519 US gal, 0.028316846592 m³, and 28.316846592 L — each line is the conversion factor itself.

Common misreadings

Inches in the feet field. The classic slip on every volume tool is a thickness or depth entered in the wrong unit. The 10 × 10 ft slab-shaped box above is 4 in high; type that 4 into the Height (ft) field instead of the inches box and the engine sees a box 4 ft high: 400 cu ft and 14.81 cu yd instead of 33.33 cu ft and 1.2346 cu yd — 12 times the real volume, because there are 12 inches to the foot. If the cubic-yard figure looks wildly high for a slab, a bed, or a footing, check which box the small dimension went into before anything else.

Diameter typed as radius. The tank above is 8 ft across. Enter 8 as the radius and the cylinder becomes 804.25 cu ft, 6,016.19 US gal — 4 times the true 1,504.05, because the radius is squared. For a sphere the error is larger: the 2 ft ball entered with a 2 ft radius comes out at 33.5103 cu ft, 8 times its real 4.1888, because the radius is cubed. A round result that is 4 or 8 times what the container plausibly holds usually means an unhalved diameter.

Metric figures with the toggle on Imperial. The metric box is 1.2 × 0.9 × 0.6 m. Type those numbers with the toggle still on Imperial and the engine sees a box of the same numbers in feet: 0.648 cu ft, against the correct 22.88. The volume is 35.31 times too small — the cube of the 3.2808 feet in a meter — and nothing on the panel warns you, because a 1.2 ft box is a perfectly valid entry. If a result looks implausibly small for the object, check the toggle.

The displayed digits as the working figure. The panel shows cubic feet to two decimals; the cubic-yard, gallon, and liter lines were computed from the unrounded value, not from the two decimals you can see. Converting the displayed 141.37 cu ft by hand lands a hair away from the displayed 5.236 cu yd. The engine is right; the copied display is the approximation.

The cubic-yard line as an order. This page reports net geometry. A cubic-yard figure handed straight to a supplier carries no allowance for spillage, settlement, or an uneven bottom and no round-up to the increment the material is sold in. The material tools add both; this page intentionally adds neither.

Where the model stops

The engine models four ideal solids and assumes the shape you describe is the shape that exists. It does not model a tapered tank, a domed or dished end, a sloped bottom, a wall thickness that makes the inside smaller than the outside, a fill line below the rim, or a pile that has slumped away from a true cone; for any of those, measure the part that matters and, if necessary, split the object into pieces this page can compute and add them. It computes no weight — mass needs a density, which the aggregate tools take from you as an input — and no coverage, waste, rounding, or cost, for the reasons given above. It accepts any dimension up to 1,000,000 ft and refuses zero, negative, and larger values with a message rather than a number. And it decides nothing about structure: whether a container, column, or footing of the volume you computed is adequate for its contents is a question for a qualified engineer or contractor, and the dimensions you enter should already carry that review. The methodology page lists the simplifications every estimator on the site shares.

From geometry to a shopping list

This page measures; it does not order. When the volume is destined to be filled with something, hand it to the estimator that knows how that material is sold: the concrete slab calculator, concrete footing calculator, and concrete column calculator for pours with waste and quarter-yard ordering or bag counts; the gravel calculator, sand calculator, or topsoil calculator for bulk material by the whole yard or bag; and the square footage calculator when the job starts from a floor plan rather than a solid. The feet & inches calculator turns awkward tape readings into decimal feet, and the construction unit converter moves any single figure between units. For the units behind the cubic-yard line and what happens to it next, read cubic feet, cubic yards, and ordering concrete; for the stages this page leaves to the material tools, how material estimates are calculated; or browse all guides.

Frequently asked questions

Dimensions are computed locally and never leave your device. The exactness rules for every conversion factor are documented on the methodology page.