Cuboid Calculator - Volume, Surface Area & Diagonal

A cuboid calculator is a box-shaped geometry tool that takes the three edge lengths of a rectangular solid and returns volume, total surface area, lateral surface area, base area, and the longest interior diagonal in one pass.

• • Packaging and shipping: Estimate the cardboard area and the inside capacity of a custom box, mailer, or storage bin before you order material.
• • Furniture, cabinetry, and storage: Size a chest of drawers, wardrobe, kitchen cabinet, or open shelf in liters, square feet, and diagonal reach before you buy materials.
• • Concrete, soil, and insulation: Compute the volume of a rectangular footing, raised garden bed, or attic cavity, then size the panel area that wraps the same space.
• • Classroom and homework support: Verify a worked L*W*H or 2(LW+LH+WH) problem, demo the formulas, and switch units in a single tool.

The cuboid is the most general box-shaped solid in elementary geometry: six rectangular faces, twelve edges, and eight vertices, with three independent edge lengths. Real-world examples include moving boxes, freezers, shipping cartons, raised garden beds, concrete footings, and most cardboard mailers.

When all three edges are equal, the same formulas collapse to the cube case and the cube volume calculator returns a^3, 6a^2, and a*sqrt(3) for the same single-edge input.

The tool converts the three edges to meters, evaluates the standard cuboid formulas, and re-expresses the results in the chosen volume and area units so the page returns a complete profile of the box in one pass.

• L: Longest edge of the cuboid, in the chosen length unit.
• W: Second edge of the cuboid, perpendicular to L, in the same length unit.
• H: Third edge of the cuboid, perpendicular to both L and W, in the same length unit.

Each product L*W, L*H, W*H represents a pair of opposite faces, so multiplying the sum by 2 covers the entire outside. The lateral and base splits separate the four side faces from the top and bottom. The space diagonal is the Pythagorean distance from one corner to the opposite corner through the interior of the box.

According to Wolfram MathWorld, a cuboid has three pairs of congruent rectangular faces, the volume equals the product of the three edge lengths, and the space diagonal equals sqrt(L^2 + W^2 + H^2).

According to Math Open Reference, the surface area of a cuboid with edges L, W, and H is 2(LW + LH + WH), while the volume is L*W*H, and these are the formulas used by every standard cuboid calculator.

Each face of a cuboid is just a rectangle, so a single-face sanity check with the length width area rectangle calculator confirms the matching L*W product used in the total and base areas.

Four small ideas explain every result this page returns and the small differences between volume, surface area, and the space diagonal.

Each concept above also travels with a peer calculator that focuses on the same idea for a different shape or unit, so the four ideas do not stay trapped inside a single page.

These four ideas explain why the result panel returns five numbers from the same three inputs, and the same three-face-pair reasoning extends to spheres, cylinders, and cones in the surface area calculator.

Use this page in five short steps, switching length, area, and volume units at any time without re-entering the dimensions.

1. 1 Enter the length: Type the longest edge of the box into the Length field.
2. 2 Enter the width and height: Add the second and third edges, each perpendicular to the others.
3. 3 Pick the length unit: Select mm, cm, m, in, ft, or yd. The same unit is shared by length, width, and height.
4. 4 Choose the volume unit: Pick m^3, cm^3, ft^3, in^3, liters, or US gallons for the volume result.
5. 5 Choose the area unit: Pick m^2, cm^2, ft^2, or in^2 for the total, lateral, and base surface area results.

If you are sizing a 60 cm x 40 cm x 30 cm storage bin, set the length unit to centimeters, type 60, 40, 30, choose liters for the volume, and choose square centimeters for the area. The calculator returns 72 L of capacity, 10,800 cm^2 of total surface, 6,000 cm^2 of lateral, 4,800 cm^2 of top plus bottom, and a space diagonal of about 78.10 cm.

A dedicated cuboid tool removes the algebra from five tightly related numbers and keeps the units consistent for both metric and imperial work.

• • Volume and surface area in one pass: Enter the three edges once and get L*W*H, total area, lateral area, and base area side by side.
• • Space diagonal included: The interior diagonal comes back automatically, which is useful for shelf reach, container clearance, and stairwell checks.
• • Metric and imperial in one tool: Lengths can be mm, cm, m, in, ft, or yd; areas can be m^2, cm^2, ft^2, or in^2; volumes can be m^3, cm^3, ft^3, in^3, L, or US gal.
• • Eliminates six-face counting errors: The 2(L*W + L*H + W*H) formula is applied automatically, so there is no need to add up six rectangles by hand.
• • Hands off to cube and prism peers: When L = W = H the same inputs flow into the cube case, and a separate cuboid volume or surface area tool can be opened in one click for a deeper focus.

These benefits make this page useful for quick planning and for routine geometry work where several related measurements of the same box are needed at once.

For a deeper focus on the volume result alone, the cuboid volume calculator returns the same L*W*H number in m^3, cm^3, ft^3, in^3, L, or US gal with a simpler one-property interface.

Three measurable factors control the precision of every result on this page, and two practical limits apply to any real-world box-shaped solid.

• • The cuboid tool assumes a perfect rectangular box. Real cardboard, plastic, or wood objects have rounded edges, corner bevels, label cutouts, or material thickness, so the true surface area is usually a little below the 2(L*W + L*H + W*H) result.
• • The tool does not subtract openings such as windows, doors, vents, or handle cutouts. For a crate with a 30 cm x 20 cm cutout, manually subtract 600 cm^2 from the total face area on the affected side before ordering sheet material.

These factors and limits are the only practical concerns for a pure geometric cuboid. The tool is for planning, homework, and quick estimates; cross-check against a project drawing when the result drives a purchase order.

As published by Encyclopaedia Britannica, a cuboid is a box-shaped solid whose total surface area equals twice the sum of the products of its three edge lengths taken two at a time, written 2(LW + LH + WH).

If you need the same cubic result re-expressed in a unit this page does not expose, the volume converter handles the cubic meter, liter, US gallon, US cup, and imperial gallon conversions in one place.