How do you calculate the volume of a rectangular prism?

Volume = length x width x height. Multiply all three dimensions together. For example, a box that is 10 cm long, 5 cm wide, and 3 cm tall has a volume of 10 x 5 x 3 = 150 cubic centimeters (cm cubed). Volume tells you how much space is inside the prism or how much it can hold.

How do you calculate the surface area of a rectangular prism?

Surface Area = 2(lw + lh + wh). This formula adds the areas of all 6 faces. A rectangular prism has 3 pairs of identical faces: top/bottom (l x w), front/back (l x h), and left/right (w x h). For a 10 x 5 x 3 box: SA = 2(50 + 30 + 15) = 2(95) = 190 square centimeters.

What is the space diagonal of a rectangular prism?

The space diagonal is the longest straight line you can draw inside a rectangular prism, connecting two opposite corners through the interior. It is calculated as d = sqrt(l squared + w squared + h squared). For a 10 x 5 x 3 box: d = sqrt(100 + 25 + 9) = sqrt(134) = approximately 11.58 units.

What is the difference between surface area and lateral surface area?

Surface area includes all 6 faces of the prism. Lateral surface area only includes the 4 side faces, excluding the top and bottom. LSA = 2h(l + w). Lateral surface area is useful when you need to wrap or paint the sides of a box but not the top and bottom, such as wrapping a gift without covering the openings.

What units does this calculator support?

The calculator supports millimeters, centimeters, meters, kilometers, inches, feet, and yards. Select your preferred unit before entering dimensions. Volume results are in cubic units (e.g., cm cubed) and surface area results are in square units (e.g., cm squared). All calculations use the same unit throughout.

Can I use this for real-world measurements?

Yes. Common uses include calculating how much material you need to build or wrap a box, finding the volume of a room for HVAC sizing, determining shipping box dimensions, calculating storage capacity, and figuring out how much paint is needed for walls. Enter your real measurements and the calculator gives you exact results.

How do I find the volume of an irregular box?

If your box has slightly different dimensions on each side (not a perfect rectangular prism), measure the longest length, widest width, and tallest height. The calculator gives an approximate volume. For precise results with irregular shapes, you would need to break the shape into multiple rectangular prisms and add their volumes together.

Free Rectangular Prism Calculator

Rectangular Prism Calculator

Q: What is a rectangular prism?

A rectangular prism (also called a cuboid or rectangular box) is a 3D shape with 6 rectangular faces, 12 edges, and 8 vertices. Every face meets at a right angle. Common real-world examples include shoeboxes, bricks, rooms, shipping containers, and refrigerators. It is defined by three measurements: length, width, and height.

Calculate the volume, surface area, space diagonal, and more for any rectangular prism. Enter length, width, and height in your preferred unit to get instant results with a 3D visualization.

Unit of Measurement

Length (cm)

Width (cm)

Height (cm)

Enter length, width, and height to calculate.

Rectangular Prism Formulas

Every formula you need for rectangular prism calculations, all in one place.

PropertyFormulaWhat It Measures

VolumeV = l x w x hTotal space inside the prism

Surface AreaSA = 2(lw + lh + wh)Total area of all 6 faces

Lateral Surface AreaLSA = 2h(l + w)Area of the 4 side faces (no top/bottom)

Space Diagonald = sqrt(l^2 + w^2 + h^2)Longest line inside the prism (corner to corner)

Face Diagonald = sqrt(a^2 + b^2)Diagonal across any face of the prism

Edge PerimeterP = 4(l + w + h)Total length of all 12 edges

How to Use the Rectangular Prism Calculator

Get all measurements in three simple steps.

Select Your Unit

Choose from millimeters, centimeters, meters, kilometers, inches, feet, or yards. The calculator uses this unit for all inputs and outputs. Volume appears in cubic units and surface area in square units of your selection.

Enter the Dimensions

Type the length, width, and height of your rectangular prism. You can also click an example preset like Shoebox, Brick, or Room to quickly load common dimensions and see how the calculator works.

Read the Results

The results panel instantly shows volume, surface area, lateral surface area, space diagonal, face diagonals, and edge perimeter. A 3D wireframe diagram displays the shape with labeled dimensions for visual reference.

Why Use Our Rectangular Prism Calculator

Instant Calculations

All six properties update in real time as you type. No buttons to click, no page reloads. Change a dimension and see every result update immediately.

All Properties at Once

Volume, surface area, lateral surface area, space diagonal, three face diagonals, and edge perimeter. Every measurement you could need from a single input.

7 Unit Options

Work in millimeters, centimeters, meters, kilometers, inches, feet, or yards. The calculator labels all results with the correct square and cubic unit notation.

3D Visualization

A labeled wireframe diagram shows your rectangular prism with dimensions. Helps verify you entered the right values and understand the spatial relationships.

Real-World Presets

Load common objects like shoeboxes, bricks, rooms, and shipping containers with one click. Great for quick estimates or learning how the formulas work.

Free and Private

No signup, no account, no data collection. Everything runs in your browser. Use it for homework, construction projects, or professional estimates without limits.

Complete Guide to Rectangular Prism Calculations

What Is a Rectangular Prism?

A rectangular prism is one of the most common three-dimensional shapes in everyday life. It has six faces, all of which are rectangles. Opposite faces are identical in size and shape. The shape has 12 edges and 8 corners (vertices). Every corner angle is exactly 90 degrees, which is what makes it rectangular.

You encounter rectangular prisms constantly: rooms, boxes, books, phones, monitors, cabinets, containers, and most buildings are rectangular prisms or close approximations. This makes knowing how to calculate their properties practically useful. Whether you are shipping a package, painting a room, filling a pool, or sizing furniture, you are working with rectangular prism geometry.

Understanding Volume

Volume measures the three-dimensional space inside the prism. The formula is straightforward: length times width times height. The result is always in cubic units because you are multiplying three linear measurements together. Cubic centimeters (cm3), cubic meters (m3), and cubic feet (ft3) are the most common volume units.

Volume has many practical applications. When you want to know how much water a fish tank holds, you calculate the volume in cubic centimeters and then convert to liters (1 liter = 1,000 cm3). When an HVAC contractor sizes an air conditioner for a room, they calculate the room volume in cubic feet. Shipping companies charge by volume (or weight, whichever is greater) when pricing freight.

One common confusion is between volume and capacity. Volume is the space the prism occupies or encloses, measured in cubic units. Capacity is how much a container can hold, typically measured in liters or gallons. They are related: 1 cubic meter = 1,000 liters. The rectangular prism calculator gives you volume in cubic units, which you can convert to capacity units as needed.

Understanding Surface Area

Surface area is the total area of all six faces combined. Think of it as the amount of wrapping paper you would need to cover every side of a box with no overlap. The formula SA = 2(lw + lh + wh) works by calculating the area of three different face pairs and doubling the sum.

Surface area comes up whenever you need to cover or coat the outside of a rectangular object. Painting a room means calculating the surface area of the walls (lateral surface area) and potentially the ceiling. Wrapping a gift requires the full surface area. Estimating material for a box means knowing the surface area to determine how much cardboard is needed.

Lateral surface area is a variation that only counts the four side faces, excluding the top and bottom. This is useful for open-top containers, walls of a room (not the floor and ceiling), and similar situations where only the sides matter. The formula is LSA = 2h(l + w), which simplifies the calculation by only considering height combined with length and width.

The Space Diagonal Explained

The space diagonal is the longest possible straight line inside a rectangular prism. It runs from one corner to the diagonally opposite corner, passing through the interior of the shape. The formula d = sqrt(l2 + w2 + h2) extends the Pythagorean theorem from two dimensions to three.

The space diagonal has practical uses. If you want to fit a pole, rod, or piece of lumber inside a box, the maximum length that fits is the space diagonal. When moving furniture, the space diagonal of a room determines the longest single object that can fit inside. It is also used in 3D graphics and physics for distance calculations between opposite corners of bounding boxes.

Real-World Applications

Construction workers calculate volumes for concrete pours. If a foundation is a rectangular prism 20 feet long, 15 feet wide, and 6 inches (0.5 feet) deep, the volume is 20 x 15 x 0.5 = 150 cubic feet. Convert to cubic yards (divide by 27) and you need about 5.6 cubic yards of concrete.

Interior designers use surface area to estimate paint quantities. A gallon of paint covers approximately 350 to 400 square feet. A room that is 15 x 12 x 9 feet has a lateral surface area of 2 x 9 x (15 + 12) = 486 square feet. Subtracting about 40 square feet for doors and windows leaves 446 square feet, requiring about 1.2 gallons per coat.

Aquarium enthusiasts calculate volume to determine water quantity. A 60 cm x 30 cm x 36 cm tank holds 60 x 30 x 36 = 64,800 cm3, which equals 64.8 liters or about 17.1 US gallons. This determines the right filter size, heater wattage, and number of fish the tank can safely support.

Rectangular Prism vs Cube vs Cuboid

These terms are related but have specific meanings. A rectangular prism (or cuboid) has all rectangular faces with potentially different length, width, and height values. A cube is a special case where all three dimensions are equal and all six faces are identical squares. Every cube is a rectangular prism, but not every rectangular prism is a cube.

In some textbooks, cuboid and rectangular prism are used interchangeably. In others, cuboid specifically refers to a right rectangular prism where all angles are 90 degrees, while a general rectangular prism could theoretically be oblique (slanted). For practical purposes and for this calculator, we use the standard right rectangular prism where all faces meet at right angles.