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输入长宽高,立即计算长方体的底面积、侧面积、表面积、体积和棱长总和。
Formulas
Surface Area: S = 2(ab + ah + bh)
Volume: V = abh
Total Edge Length: L = 4(a + b + h)
Space Diagonal: d = √(a² + b² + h²)
All dimensions (length, width, height) must be positive numbers.

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If you have a shipping box that is 40 cm long, 30 cm wide, and 20 cm high, our rectangular prism calculator can instantly determine its base area (1,200 cm²), lateral area (2,800 cm²), surface area (5,200 cm²), volume (24 liters), and total edge length (360 cm). Let's explore when to use this tool, how it works, and how to interpret the results.
Home Renovation: Measure the length, width, and height of a room to calculate the wall area (lateral area) or floor area (base area) for estimating paint or tile requirements. For example, a bedroom that is 5 meters long, 4 meters wide, and 2.8 meters high has a lateral area of about 50.4 square meters and a base area of 20 square meters.
Packaging and Shipping: Shipping boxes and luggage usually provide length, width, and height. Use the calculator to find out how much the box can hold (volume) and its total surface area (useful for estimating printing, lamination, or wrapping paper costs).
Aquarium/Tank Capacity: A fish tank measuring 100 cm long, 40 cm wide, and 50 cm high has a volume of 200 liters (mind the unit conversions), which helps you quickly determine how many fish it can accommodate.
Student Homework: Quickly verify your manual geometry calculations, or work backward from a target volume to find dimensions.
Let's use a solid wooden block as an example: Length = 12 cm, Width = 8 cm, Height = 5 cm.
How does the calculator work behind the scenes? It uses the following formulas:
Interpreting the results: The lateral area of this wooden block is 200 cm², which is the total area of the four sides (excluding the top and bottom). The surface area of 392 cm² is the total area you would need to paint. The volume of 480 cm³ is roughly equal to 0.48 liters. The total edge length of 100 cm means a 1-meter-long piece of wire could perfectly form its 12 edges.
Comparison Example 1: Cube (Length = Width = Height) For a perfect cube, let's say the length, width, and height are all 10 cm. Enter 10, 10, 10:
You can see the surface area of the cube is 600 cm², whereas a rectangular prism with the same dimensions (but unequal sides) often has a larger or smaller surface area, allowing for intuitive comparisons.
Comparison Example 2: Extremely Flat Rectangular Prism Length = 100 cm, Width = 1 cm, Height = 1 cm. We enter 100, 1, 1:
This example shows that for the same volume, the flatter the shape, the larger the surface area. If you are designing packaging boxes and want to save cardboard, try to keep the length, width, and height as close as possible.
| Result | Meaning | Common Scenarios |
|---|---|---|
| Base Area | Area of the bottom face (Length × Width) | Floor tiling, cardboard needed for the bottom of a box |
| Lateral Area | Total area of the four side faces (excluding top and bottom) | Wall painting, wallpaper usage |
| Surface Area | Total area of all six faces | Packaging materials, heat dissipation area, coating costs |
| Volume | Internal space size | Load capacity, volume capacity (note unit conversion: 1 liter = 1,000 cm³) |
| Total Edge Length | Total length of all 12 edges | Frame materials, wire length, decorative trim |
Value Reference: For typical household items, volumes range from a few liters to several hundred liters; surface areas range from a few hundred to tens of thousands of square centimeters. If the result is negative, it means you entered a negative number. If the result is extremely large (e.g., millions), check if you accidentally used millimeters instead of centimeters, as cubic millimeters and cubic centimeters differ by a factor of 1,000.