Volume Calculator

What Is Volume?

Volume answers one question — how much fits — and it answers it with a count. A volume of 60 cubic feet means that sixty cubes measuring one foot on every edge would exactly fill the space. Nothing about the shape changes that meaning; the formulas differ only in how they arrive at the count without stacking the cubes by hand.

The Units Volume Is Measured In

A volume unit is always a length unit cubed, which is why the answer carries a small ³ and why the arithmetic multiplies three measurements rather than two. Feet give cubic feet, inches give cubic inches, meters give cubic meters, centimeters give cubic centimeters. The calculator prints the unit you selected back to you as part of the headline so the answer is never a bare number.

The capacity units people actually buy things in are defined against those cubes rather than invented separately. NIST names the liter as a special name for the cubic decimeter, so a cube 10 cm on each edge is exactly one liter — enter a cube of side 10 in centimeters and the tool returns 1,000 cm³ and 1.000 liters, which is the same statement twice. The US liquid gallon is fixed at 231 cubic inches in NIST Handbook 44's general tables, and that number is checkable here: a cube of side 6.1358 in inches returns 231 in³ and 1.00 US gallons.

Cubic yards are the third family, and they exist because concrete and aggregate are sold that way. A cube of side 3 feet returns 27 ft³ and exactly 1.000 yd³, which is the conversion in its shortest possible form.

Volume, Capacity and Area Are Not the Same Thing

Three measurements get used interchangeably in ordinary speech, and only the first is what this page computes.

• Volume is the geometric space enclosed by a surface — the theoretical maximum, wall thickness and fittings ignored. It is what every formula below returns.
• Capacity is how much a container actually holds in use, which is always less. A tank measuring 48 × 13 × 21 inches inside returns 13,104 in³, or 56.73 gallons, yet nobody fills a tank to the rim.
• Area is two measurements multiplied, not three, and it is measured in square units. A 10 × 10 ft slab has an area of 100 ft²; only once you add a depth of 4 inches does it become a volume of 33.33 ft³.

Running the relationship backwards — knowing the volume you need and asking what side length produces it — is a cube root, which is waiting in the Cube Root Calculator.

The area-to-volume step is where most real jobs start, because floors, patios and beds are measured flat and then given a depth. Enter that depth as a decimal of your chosen unit: 4 inches of a foot is 0.3333, 6 inches is 0.5.

The Five Solids, and Which Fields Each One Reads

The Shape menu changes which of the three dimension fields matter. The unused ones are ignored outright rather than treated as zero, which is why a sphere still returns an answer with the lower boxes left empty.

Because the extra fields are ignored rather than validated, a leftover number in a box you are no longer using cannot corrupt the answer. Running a sphere of radius 3 in feet with 99 sitting in both lower fields still returns 113.1 ft³, exactly as it does with those fields empty.

• Box — reads all three: Length / Radius / Side, Width / Height (if needed), and Height (box only). It is the only shape that uses the third field.
• Cube — reads the first field only, as the side length. Everything else is ignored.
• Sphere — reads the first field only, as the radius.
• Cylinder — reads the first field as the radius and the second as the height.
• Cone — reads the first field as the base radius and the second as the vertical height, not the slant.

Shapes the list does not name are usually two of these added together. A silo is a cylinder plus a cone: run the barrel as a cylinder of radius 5 and height 20 feet for 1,570.8 ft³, run the roof as a cone of radius 5 and height 6 feet for 157.08 ft³, and add them for 1,727.88 ft³.

How Do You Calculate Volume?

Measure in one unit, feed the shape the dimensions it asks for, multiply. The multiplying is what the five formulas differ over, and for four of the five shapes it reduces to the same sentence: work out the area of the flat face, then push that face through the height.

The One Idea Behind Four of the Five Formulas

A box, a cube and a cylinder are all a base area carried through a height. The box's base is a rectangle, so the base area is L × W; the cube's base is a square of side s; the cylinder's base is a circle of area π r². Multiply any of those by the height and you have the volume. A cone shares the cylinder's base and height and holds exactly one third as much, because it tapers to a point instead of keeping its width.

BASE AREA × HEIGHT
Box        (L × W) × H
Cube       (s × s) × s
Cylinder   (π × r²) × h
Cone       (π × r²) × h ÷ 3

THE ODD ONE OUT
Sphere     4⁄3 × π × r³

The sphere is the exception because it has no flat face and no height to push anything through — its width changes continuously from pole to pole. Its 4⁄3 factor comes out of integration rather than out of any stacking argument, and MathWorld gives the result as V = 4/3 πR³.

That is also why the sphere needs only one measurement while the cylinder needs two. A sphere's radius fixes its entire shape; a cylinder's radius fixes only its cross-section, leaving the height free.

Step by Step With This Calculator

Five steps, and the third is the one people get wrong.

Mixed units are the single most common error and the calculator cannot detect them, because 12 and 0.5 are both perfectly legal numbers. A slab entered as 12 × 12 × 6 in the Feet unit returns 864 ft³ instead of the 72 ft³ that 12 × 12 ft at 6 inches deep actually is — a twelvefold overshoot that looks entirely plausible on screen.

• Pick the Shape. Box, Cube, Sphere, Cylinder or Cone — this decides which fields below are read.
• Pick the Unit: Feet, Inches, Meters or Centimeters. This is a label, not a converter, so every dimension you type must already be in it.
• Convert anything that is not in that unit before typing. Inches into feet is ÷ 12, so 4 in of depth is 0.3333 ft; centimeters into meters is ÷ 100.
• Fill Length / Radius / Side. For round shapes this is the radius — half the diameter — and for a cube or sphere it is the only field you need.
• Fill Width / Height (if needed) for a box, cylinder or cone, then Height (box only) for a box. The fields show 4, 3 and 5 as placeholder hints; they start empty and the answer appears once the shape has what it needs.

The Unit choice also decides which capacity conversions you get back, so it is worth choosing for the answer you want rather than for the tape measure you used. Inches return gallons and cubic feet; feet return gallons and cubic yards; meters return liters and cubic feet; centimeters return liters and milliliters.

Worked Example: A 4 × 3 × 5 ft Box

Shape Box, Unit Feet, then 4, 3 and 5 in the three dimension fields — the three placeholder values, run for real.

V = L × W × H
V = 4 × 3 × 5
V = 60 ft³

Capacity   60 × 7.48052 = 448.8 US gallons
Concrete   60 ÷ 27 = 2.222 yd³

What the result panel returns

60 ft³ · Rectangular box: 4 × 3 × 5 · = 448.8 US gallons = 2.222 yd³ · Dimensions not used by this shape are ignored — sphere needs only the radius

The second line is worth reading every time. It echoes the three numbers the calculator actually took from the fields, which is the fastest way to catch a digit that landed in the wrong box. The order of the three makes no difference to the answer: 4 × 3 × 5, 5 × 4 × 3 and 3 × 5 × 4 are the same 60 ft³.

The gallons figure uses 7.48052 gallons per cubic foot, which is not an estimate — it is 1,728 cubic inches divided by the 231 cubic inches in a gallon.

Worked Example: A Cylinder Read in Gallons

Shape Cylinder, Unit Feet, radius 2 in the first field and height 5 in the second. The third field stays empty; a cylinder never reads it.

V = π × r² × h
V = π × 2² × 5
V = π × 4 × 5
V = 62.83 ft³

Capacity   62.83 × 7.48052 = 470 US gallons

What the result panel returns

62.83 ft³ · Cylinder: π × 2² × 5 (radius² × height) · = 470 US gallons = 2.327 yd³ · Dimensions not used by this shape are ignored — sphere needs only the radius

Now repeat it with 4 in the radius field, as though the tank's 4 ft diameter had been typed straight in. The answer becomes 251.33 ft³ and 1,880.1 US gallons — four times too big, because the radius is squared before anything else happens to it. Doubling a radius always quadruples a cylinder of fixed height, and the tool prints no warning because 4 is a legitimate radius.

Height behaves gently by comparison. Doubling it from 5 to 10 ft moves the same cylinder from 62.83 ft³ to 125.66 ft³ — twice, not four times, because height appears once in the formula and radius appears twice.

Worked Example: A Room in Cubic Meters

Shape Box, Unit Meters, 5 by 4 by 2.5 — a room five meters long, four wide, with a 2.5 m ceiling.

What the result panel returns

50 m³ · Rectangular box: 5 × 4 × 2.5 · = 50,000 liters = 1765.74 ft³ · Dimensions not used by this shape are ignored — sphere needs only the radius

Metric is the friendlier system here because the conversion is definitional rather than arithmetic: one cubic meter is one thousand liters, so 50 m³ is 50,000 liters with no factor to remember. The cubic-feet figure on the same line, 1765.74, is what the room would read as if you had measured it in feet instead.

That second figure is also a check on your unit discipline. If you meant meters and the cubic-feet number looks like the size you expected, you probably typed feet into a metric page.

The Volume Formula for Each Shape

Five formulas, each with the trap that catches people using it. Every figure quoted below came out of the calculator at the top of the page with the inputs stated beside it.

Box        V = L × W × H
Cube       V = s³
Sphere     V = 4⁄3 × π × r³
Cylinder   V = π × r² × h
Cone       V = π × r² × h ÷ 3

Rectangular Box: V = L × W × H

Three measurements multiplied, and the only formula here with no constant in it. It is also the only shape that reads the third field. Leave that field empty and the calculator refuses the job with "Enter the third dimension" rather than assuming a height.

The trap is depth expressed in the wrong unit. A 12 × 12 ft slab poured 6 inches deep is 12 × 12 × 0.5 in feet, returning 72 ft³ and 2.667 yd³. Poured 4 inches deep on a 10 × 10 ft footprint it is 10 × 10 × 0.3333, returning 33.33 ft³ and 1.234 yd³ — and that cubic-yard figure is the number a concrete supplier will ask for.

Because multiplication does not care about order, the field labels are advisory. A moving box entered as 2 × 1.5 × 1.5 ft returns 4.5 ft³ whichever way round the three numbers go in.

Cube: V = s³

A box with all three sides equal, so the formula collapses to one measurement cubed — MathWorld writes it as V = a³. Enter a side of 3 in feet and the tool returns 27 ft³, 202 US gallons and exactly 1.000 yd³.

The cube setting is the quickest way to interrogate a unit, because a cube of side one is a unit volume by definition. Side 1 in feet returns 1 ft³; side 12 in inches returns 1,728 in³ and 1.000 ft³; side 10 in centimeters returns 1,000 cm³ and 1.000 liters; side 1 in meters returns 1 m³ and 1,000 liters. Four ways of writing the same idea.

There is no separate field to get wrong on a cube, which makes it the shape least likely to produce a wrong answer and the one most useful for checking that you understand the units before moving to something harder.

Sphere: V = 4⁄3 × π × r³

One measurement, cubed, times π, times four thirds. MathWorld gives it as V = 4/3 πR³, and the R is emphatically a radius. A sphere of radius 3 in feet returns 113.1 ft³ and 846 US gallons; the same radius in meters returns 113.1 m³ and 113,097 liters.

Diameter entered instead of radius is the costliest mistake on the page, because the error is cubed rather than squared. A ball 4 ft across has radius 2 and volume 33.51 ft³; type 4 and you get 268.08 ft³ — eight times too much. Halving works the same way in reverse: radius 1 ft returns 4.19 ft³, exactly one eighth of the radius-2 answer.

Sports balls are the easiest sanity check available. Radius 4.7 in returns 434.89 in³ for a basketball, radius 4.35 in returns 344.79 in³ for a soccer ball, and radius 1.45 in returns 12.77 in³ for a baseball — three objects whose sizes you can picture, in an order that matches the numbers.

Cylinder: V = π × r² × h

The area of the circular end, π r², carried through the height — MathWorld writes it as V = πr²h. Radius 3 and height 8 in feet returns 226.19 ft³ and 1,692.1 US gallons; radius 0.5 and height 3 returns 2.36 ft³ and 0.087 yd³, which is one concrete pier.

Round containers are almost always described by their diameter, so the halving step is where the errors enter. A round pool sold as 18 ft across and 4 ft deep is radius 9, height 4: it returns 1,017.88 ft³ and 7,614.2 US gallons. Entered as radius 18 it would return four times that, and the figure would still look like a swimming pool.

The height field is the second one, labeled Width / Height (if needed). A cylinder ignores the third field entirely, so anything left sitting there from a previous box calculation is harmless.

Cone: V = π × r² × h ÷ 3

The cylinder formula with a division by three on the end, and MathWorld states the same result as V = 1/3 πr²h. The division is exact rather than an approximation: three cone-fulls fill their matching cylinder precisely. Radius 2 and height 5 in feet returns 20.94 ft³ against the cylinder's 62.83 ft³ on identical dimensions.

The height must be the vertical height from base to tip, not the slant height measured along the sloping side. Slant is always the longer of the two, so using it inflates the answer. A cone of radius 1 and height 2 in feet returns 2.09 ft³ and 15.7 US gallons; a funnel of radius 4 and height 6 in inches returns 100.53 in³.

Loose material piled on the ground settles into a cone, which makes this the formula for a gravel or mulch heap. A pile 12 ft across and 4 ft high is radius 6, height 4: it returns 150.8 ft³ and 5.585 yd³.

Radius and height are not interchangeable, even when the two numbers are. Radius 4 with height 3 returns 50.27 ft³; radius 3 with height 4 returns 37.7 ft³ — the same pair of numbers, a quarter of the volume apart, because only one of them gets squared.

The 1 : 2 : 3 Ladder Hiding in Three of Them

Take a sphere and the shortest cylinder that would contain it — same radius, height equal to the sphere's diameter — and add the cone on the same base. Run all three at radius 2 feet, with height 4 for the two that need one.

The three readouts stand in a 1 : 2 : 3 relationship, and the last digits move only because each line is rounded on its own — 16.76 tripled is 50.28 against the cylinder's printed 50.27. Archimedes considered the sphere-to-cylinder result his finest and asked for the figure to be carved on his tomb.

The practical use of the ladder is estimation without a calculator. If you know the cylinder that would enclose something, the sphere inside it holds two thirds as much and the cone on the same base holds a third.

Volume Examples, Worked Out

Every row below was produced by this calculator, with the shape, the unit and the dimensions shown so you can reproduce it. The last column is the conversions line the tool prints underneath the headline figure.

Everyday Objects

Small things are easiest in inches or centimeters, because feet turn them into awkward decimals.

Cooking volumes travel in cups, tablespoons and milliliters rather than cubic centimeters, and the conversion between those is a different job handled by the Recipe Conversion Calculator.

The mug row is the one worth arguing with. A cylinder of radius 4 cm and height 9.5 cm holds 478 mL to the brim, which is why a mug that measures like that pours a 350 mL drink — the last centimeter and a half of height is headroom you never use.

Building and Garden Jobs

Feet are the working unit here, because the conversions line then hands back cubic yards — the unit concrete and aggregate are ordered in.

The two slab rows show why depth deserves care rather than rounding. Two inches of extra depth on a 10 × 10 ft pour is only 0.1667 in the third field, and it moves the order from 1.234 to about 1.85 cubic yards — most of a wheelbarrow's difference in what turns up on site.

Things That Hold Water

For anything that gets filled, the conversions line is usually the answer you actually wanted and the cubic figure is just the route there.

The drum and bucket rows both come out larger than the number on the label — 57.66 against a nominal 55, and 6.52 against a nominal 5 — and neither is an error. A drum is never filled to the closure, and a bucket tapers toward its base while this calculator treats it as a straight cylinder at its widest. Geometric volume is the ceiling; the rating on the side is what the maker will stand behind.

Volume Chart: Cubic Units and Capacity

Two reference tables. The first is a ladder of unit cubes run through this calculator; the second is the conversion factors those results rest on, taken from NIST's published tables.

What Each Cubic Unit Is Worth

Every row is the Cube shape with a single side length. Reading down, each step is a factor of a thousand in the metric column and a factor of 1,728 or 27 in the customary one.

Three pairs of rows describe identical volumes in different units, and they are the best proof the tool is internally consistent. A 12-inch cube and a 1-foot cube are the same object; a 100 cm cube and a 1 m cube are the same object; a 36-inch cube and a 3-foot cube are the same object.

The gallons column disagrees with itself in the second decimal place across those pairs — 7.48 in inches against 7.5 in feet, 201.97 in inches against 202 in feet — because the two branches round to a different number of places. The volumes are identical; only the display differs.

Cubic Units to Gallons and Liters

The factors behind the conversions line. NIST Special Publication 811 gives the cubic foot as 2.831 685 E-02 m³, the cubic inch as 1.638 706 E-05 m³, the cubic yard as 7.645 549 E-01 m³ and the US gallon as 3.785 412 E-03 m³; everything below follows from those four numbers.

Two of these are definitions rather than measurements, which is why they come out exact. NIST names the liter as a special name for the cubic decimeter, so 1,000 cm³ is one liter with no rounding involved at all, and NIST Handbook 44 fixes the US gallon at 231 cubic inches.

The US and imperial gallons are different sizes and this calculator reports the US one throughout. An imperial gallon is roughly a fifth larger, so a UK reader should treat every gallons figure on this page as about 20 percent more gallons than their own.

What the Volume Weighs When It Is Water

Volume becomes weight the moment you plan to move, support or lift what you have measured, and for fresh water the conversion is unusually clean: a liter weighs almost exactly one kilogram, an accident of history from the days when the kilogram was defined against water. That makes one cubic meter of water about 1,000 kg, one US gallon about 8.34 lb, and one cubic foot about 62.4 lb. All three drift by a fraction of a percent with temperature, since water is at its densest near 4 °C.

Run those against results from the table above and the reason aquarium stands and floor joists get discussed becomes clear. The 48 × 13 × 21 in tank at 56.73 gallons is roughly 473 lb of water before the glass, the gravel or the stand. The 18 ft round pool at 7,614.2 gallons is on the order of 63,500 lb — close to 32 tons sitting on the ground.

Anything denser than water scales straight up from there. Concrete runs about two and a half times water's weight, so the 2.667 yd³ slab is a multi-ton pour, and wet soil in a raised bed is heavier than most people expect for 32 ft³.

How to Read Your Result

The panel returns four lines in a fixed order. There are no bands or categories to interpret, so reading the result is mostly a matter of knowing what each line is for and where the display quietly rounds.

The Four Lines the Panel Returns

Running a box of 4 × 3 × 5 in feet produces these, in this order:

The second line is the one to check when an answer surprises you, because it is the only place the calculator shows what it actually read. A sphere prints its working as "4⁄3 × π × 3³ (a = radius)", which is also the clearest reminder available that the number you typed was treated as a radius.

• The volume itself, with your chosen unit attached: 60 ft³. This is the headline figure and it is rounded to two decimal places.
• The shape name and the substituted working: "Rectangular box: 4 × 3 × 5". The five names are Rectangular box, Cube, Sphere, Cylinder and Cone, and the working shows the exact numbers the tool read from the fields.
• The conversions line, which changes with the unit: "= 448.8 US gallons = 2.222 yd³" in feet, gallons and cubic feet in inches, liters and cubic feet in meters, liters and milliliters in centimeters.
• A fixed footnote about unused dimensions. It mentions the sphere by name whatever shape you ran, so seeing sphere in the note on a box calculation is not a sign that anything went wrong.

The third line is often the real answer rather than a footnote. For anything that gets filled, gallons or liters is the useful figure and the cubic number is only how the tool got there.

Where the Rounding Bites

The headline is cut to two decimal places, and each conversion is rounded on its own schedule: gallons to one place in feet mode and two in inches mode, cubic yards to three, liters to none in meters mode and three in centimeters mode. That is why the lines can appear to disagree slightly with each other.

• Small results can vanish. Anything under 0.005 in your chosen unit displays as 0: a cube of side 0.17 in feet reads 0 ft³, while 0.171 reads 0.01 ft³.
• Whole answers print clean. A cube of side 3 in feet reads 27 ft³ rather than 27.00, and its cubic-yard line reads exactly 1.000.
• Enormous results switch notation. A sphere of radius 6,371,000 in meters reports its cubic-feet conversion as 3.825312730633274e+22, which is scientific notation rather than a number you can read at a glance.
• Very large customary results lose their commas in the second conversion: a 1,000 ft cube prints 37037037.037 yd³ where the gallons figure on the same line keeps its separators.

The clearest case is a half-meter cube. Enter a cube of side 0.5 in meters and the headline reads 0.13 m³ while the same line reports 125 liters — which is 0.125 m³. The liters figure is the more precise of the two, and nothing has gone wrong; the headline simply has fewer places to work with.

None of this touches the arithmetic. The value the calculator computes is full precision throughout, and only the printing is trimmed — so if you need a figure to more places than the headline shows, read it off the conversions line instead.

The Three Messages That Replace an Answer

The calculator refuses rather than guesses when a dimension it needs is missing, and there are exactly three ways to see that.

Zero and negative numbers are treated as missing rather than as values, which is the right call for a physical measurement: a solid with a zero dimension has no volume, and a negative length is not a length. A cube entered with side 0 or side −3 returns the first-dimension message rather than 0 ft³ or a negative volume.

• "Enter the first dimension" — the Length / Radius / Side field is empty, zero, negative or not a number. Every shape needs it.
• "Enter the second dimension" — a box, cylinder or cone is missing its Width / Height field. Cubes and spheres never produce this message.
• "Enter the third dimension" — only a box can produce this one, and only when Height (box only) is empty.

There is no message for the mistakes that produce a wrong answer rather than no answer. Mixed units, a diameter typed where a radius belongs, and slant height on a cone all return confident, well-formatted, incorrect figures — which is why the second line of the readout deserves a glance every time.

Why Volume Scales With the Cube of Size

Volume grows with the cube of linear size, and that is the single fact behind most bad estimates. Doubling every dimension does not double the contents — it multiplies them by eight.

The Cube Ladder, Run for Real

One shape, one unit, one field changed. Each row is the Cube shape in feet.

Ten percent more in each direction is a third more volume; twenty percent more in each direction is nearly three quarters more. Those two rows are the ones that catch people out, because a 10 percent bigger box does not look 33 percent bigger from across the room.

Spheres behave identically. A sphere of radius 1 in meters returns 4.19 m³ and radius 2 returns 33.51 m³ — precisely eight times, on a shape where only one number changed.

When Only One Dimension Grows

The cube-law only applies when everything scales together, and confusing the two cases is its own source of error. Take a plant pot as a cylinder of radius 6 and height 8 in inches: it returns 904.78 in³.

Widening alone squares the change, because radius appears twice in the cylinder formula: 1.2 × 1.2 is 1.44. Growing in all three directions cubes it: 1.2 × 1.2 × 1.2 is 1.728. Height alone is linear — it appears once, so 20 percent taller is 20 percent more soil and nothing more.

This is exactly why a diameter typed where a radius belongs is so expensive. It is a doubling of one dimension that gets squared on a cylinder and cubed on a sphere: 62.83 ft³ becomes 251.33 ft³ for the cylinder, and 4.19 ft³ becomes 33.51 ft³ for the sphere.

Limits: When This Calculator Does Not Apply

The tool computes the geometric volume of five idealized solids from dimensions you supply in a single unit. Being precise about the edge of that job is more useful than a longer list of things it does not attempt.

• It does not convert units. Choosing Feet does not turn inches into feet — it only labels the answer and selects the conversions line. Every dimension must already be in the chosen unit, and a slab entered as 12 × 12 × 6 in feet returns 864 ft³ instead of the correct 72 ft³.
• It cannot know whether you typed a radius or a diameter. Both are legal positive numbers, so a cylinder given 4 instead of 2 returns 251.33 ft³ against the true 62.83 ft³ without complaint.
• It assumes straight, untapered sides. A bucket, a plant pot and a laundry basket all narrow toward the base, so the straight-cylinder answer overshoots: the 11.5 in bucket reads 6.52 gallons against a 5-gallon rating.
• It gives geometric volume, not usable capacity. Wall thickness, headspace, fittings and the fill line all subtract, which is why the 22.5 in drum reads 57.66 gallons and is sold as 55.
• There is no partial-fill mode. A horizontal cylinder half full, a tank with dished ends or a pool with a sloping floor are all different problems, and averaging depths by hand before entering is the workaround for the last of them.
• Only these five shapes exist here. Pyramids, prisms with non-rectangular ends, tori and ellipsoids have their own formulas and none of them is in the Shape menu.
• Irregular objects need decomposing or displacing. Break the object into these solids and add the results, as with the silo's 1,570.8 ft³ barrel plus 157.08 ft³ roof; for something small and awkward, submerge it and measure the water it displaces instead.
• Zero and negative dimensions are rejected rather than computed, so a shape that has genuinely collapsed in one direction returns a prompt rather than a volume of 0.

Two apparent limits are not limits. Very small and very large numbers are handled correctly even when the display strains — a 1,000 ft cube returns a true 1,000,000,000 ft³ — and leftover values in fields the current shape ignores cannot affect the answer, so there is no need to clear them between calculations.