Rectangular Prism Volume Calculator - Length, Width, and Height

A rectangular prism volume calculator finds the inside space of any box-shaped solid from three perpendicular side lengths: length, width, and height. It applies the V = l * w * h rule used for fish tanks, raised beds, suitcases, and storage containers, and returns the volume in the same cubic unit the user typed, with the base area and surface area alongside it.

• • Fish tank and aquarium sizing: Check that a 30 x 12 x 12 inch tank holds the labeled water volume in gallons or liters, and see the glass surface area.
• • Raised bed and planter soil volume: Work out how many cubic feet of potting soil a 4 x 2 x 0.5 foot raised bed actually needs, so the garden store can fill the right number of bags.
• • Suitcase and shipping carton capacity: Compare a 30 x 19 x 11 inch suitcase with a 28 x 21 x 12 inch one, or check a moving carton against the dimensions on the booking page.

A rectangular prism is a three-dimensional solid bounded by six rectangles, with opposite faces equal and parallel. It has 8 vertices, 12 edges, and 6 faces. A cube is the special case where all three side lengths are equal, and the V = l * w * h rule reduces to V = s^3. The word cuboid is a synonym for a rectangular prism, which is why the calculator also returns the surface area for shipping label weight and paint coverage.

For the base area of the rectangular footprint the calculator uses, the Length Width Area Rectangle Calculator works in square units from the same two side lengths.

The calculator applies the universal rectangular prism volume formula, V = l * w * h, where l is the length, w is the width, and h is the height of the prism. The three side lengths are measured along perpendicular directions, so the same V = B * h rule from any right prism also works when the base area is taken as length times width.

• l, w: length and width of the rectangular base of the prism
• h: perpendicular height, the distance from the base plane to the opposite face
• B: base area, equal to l * w in square units
• V: resulting volume in cubic length units, equal to l * w * h
• SA: surface area in square length units, equal to 2 * (l * w + l * h + w * h)

The V = l * w * h rule works for any rectangular prism regardless of which face is the base, because multiplication is commutative. For a cube, the rule reduces to V = s^3 and the surface area becomes SA = 6 * s^2, a useful cross-check on the same calculator.

According to Wolfram MathWorld, a cuboid has volume equal to the product of its three edge lengths, V = a * b * c, and surface area equal to 2 * (a * b + a * c + b * c).

For other 3D shapes like cones, cylinders, spheres, and pyramids, the Volume Calculator keeps the matching V = B * h, pi * r^2 * h, (4/3) * pi * r^3, and (1/3) * B * h rules in one place.

These four terms decide whether the formula matches the box you are measuring.

A common error is to use the diagonal of a face in place of one of the side lengths. The face diagonal is the line across the front of the box, not the perpendicular height, and using it will overstate the volume.

For a pyramid that sits on the same rectangular base, the Pyramid Volume Calculator applies the same base area but multiplies by h and then divides by 3 to get V = (1/3) * B * h.

Type the three perpendicular side lengths of the box into the form, then read the volume, base area, and surface area from the result panel.

1. 1 Pick the linear unit first: Decide whether to type the three side lengths in inches, feet, centimeters, or meters. The calculator labels the result in cubic and square units of that unit.
2. 2 Enter the length of the rectangular base: Type the longest edge of the rectangular base into the Length box. For a 30 x 12 x 12 inch aquarium, length is 30.
3. 3 Enter the width of the rectangular base: Type the shorter edge of the rectangular base into the Width box. For the same aquarium, width is 12.
4. 4 Enter the perpendicular height: Type the third side into the Height box. For the same aquarium, height is 12.
5. 5 Read the base area and volume: Use the Base Area row to confirm the l * w footprint, and the Volume row for the cubic inside space.
6. 6 Read the surface area: Use the Surface Area row when you need paint, glass, fabric, or wrap coverage for the same box.

A 30 x 12 x 12 inch long aquarium has volume 4,320 cubic inches, base area 360 square inches, and surface area 1,728 square inches. After conversion the inside capacity is about 18.7 US gallons, the right ballpark for a labeled 20-gallon long tank.

Once the volume is in cubic inches, the Volume Converter moves the result into gallons, liters, or cubic feet for the fish store, the soil bag, or the shipping manifest.

A rectangular prism volume calculator that uses three simple side lengths and shows the base area, volume, and surface area together makes the result easier to read and to cross-check against the dimensions on a spec sheet.

• • Three inputs match the spec sheet: Length, width, and height are the three numbers printed on most box and tank labels, so the user does not have to derive a missing dimension first.
• • Base area shown alongside volume: The base area is displayed as a separate result row, so the user can confirm the calculator used the right footprint.
• • Surface area for material estimates: The same three side lengths return the outside surface area in square units, useful for paint, glass, fabric, wrap, or label coverage.

The calculator exposes both B = l * w and SA = 2 * (l * w + l * h + w * h) as separate result rows so the user can verify the formula step without re-typing the values. The same V = l * w * h result is reached from the base-area shortcut V = B * h, useful when the footprint is already measured.

For a separate surface-area calculation on a different 3D shape, the Surface Area Calculator handles cubes, prisms, cylinders, cones, pyramids, and spheres in one place.

A rectangular prism volume calculator is a simple product of three side lengths, but a few measurement choices decide whether the result matches the real box.

• • The calculator does not solve for a missing side length when only the volume is known, because the same volume can come from many different side-length combinations.
• • Real boxes are rarely perfect rectangular prisms: shipping cartons have rounded corners, plastic bins taper, and aquarium glass has thickness. The geometric volume is an estimate, not a survey-grade measurement.
• • Rounded display output can differ by a few hundredths from a hand calculation that rounds after each intermediate step. The internal computation keeps full precision before the display rounds.

For an irregular base that is not a rectangle, the V = l * w * h rule does not apply directly. The base area must be computed for the actual footprint, and the V = B * h rule from any right prism can then be used.

According to Wikipedia, the volume of a cuboid is the product of its three edge lengths, V = a * b * c, and the surface area is SA = 2 * (ab + ac + bc).

According to Wolfram MathWorld, a right prism has volume equal to base area times perpendicular height, V = B * h, and a rectangular prism is the right prism whose base is a rectangle of area l * w.

For a box that becomes a cylinder when the width and height are equal, the Cylinder Volume Calculator returns the V = pi * r^2 * h case on the same V = B * h template.