📦 Rectangular Prism Surface Area Calculator
Calculate Surface Area of Boxes & Cuboids
Perfect for boxes, rooms, tanks & packaging
Rectangular Prism Surface Area Calculator
📦 Enter Dimensions (Length × Width × Height)
📊 All 6 Faces
📊 Calculation Breakdown
Rectangular Prism Surface Area Formulas
Total Surface Area
Where l = length, w = width, h = height
Lateral Surface Area
Perimeter of base × height
Volume
Space Diagonal
Cube (Special Case)
When all sides are equal (l = w = h = a)
Understanding the 6 Faces
| Face Pair | Dimensions | Area Formula | Count |
|---|---|---|---|
| Top & Bottom | Length × Width | 2 × l × w | 2 faces |
| Front & Back | Length × Height | 2 × l × h | 2 faces |
| Left & Right | Width × Height | 2 × w × h | 2 faces |
Real-World Applications
| Application | Example | Why Surface Area Matters |
|---|---|---|
| Packaging | Shipping boxes | Amount of cardboard needed |
| Painting | Room walls | Paint quantity calculation |
| Wrapping | Gift boxes | Wrapping paper required |
| Construction | Tanks, containers | Material cost estimation |
| Manufacturing | Product casings | Sheet metal requirements |
How to Calculate Rectangular Prism Surface Area
- Measure length, width, and height — Identify all three dimensions of the prism.
- Calculate each face pair — Find areas: l×w (top/bottom), l×h (front/back), w×h (sides).
- Double each pair — Multiply each area by 2 (since faces come in pairs).
- Add all together — Sum the three doubled areas: 2(lw + lh + wh).
- Verify units — Ensure your answer is in square units (cm², m², etc.).
Educational Resources
Frequently Asked Questions
A rectangular prism (also called a cuboid or rectangular parallelepiped) is a 3D solid with 6 rectangular faces. Think of a box, brick, or cereal box — any shape where all angles are 90° and opposite faces are identical rectangles.
The formula is SA = 2(lw + lh + wh) or SA = 2lw + 2lh + 2wh, where l = length, w = width, and h = height. This accounts for all 6 faces in 3 pairs.
A cube is a special rectangular prism where all edges are equal (l = w = h). A cube has 6 square faces, while a general rectangular prism has rectangular faces that may differ in size.
Lateral surface area includes only the side faces (front, back, left, right), excluding the top and bottom. Formula: LSA = 2h(l + w) = perimeter × height.
For an open box (no top), use: SA = lw + 2lh + 2wh. This includes the bottom (lw) plus all 4 sides, but excludes the top face.
A rectangular prism has exactly 6 faces (all rectangles), 12 edges, and 8 vertices (corners). The faces come in 3 pairs of identical opposite faces.
The space diagonal is the longest line inside the prism, connecting two opposite corners through the interior. Formula: d = √(l² + w² + h²).
By convention: length is typically the longest horizontal side, width is the shorter horizontal side, and height is the vertical dimension. However, the formula works regardless of which dimension you assign to each variable.
Surface area measures the total area of all outer faces (in square units) — how much material covers the outside. Volume measures the space inside (in cubic units) — how much it can hold.
100% free! No sign-up required. Calculate rectangular prism surface areas unlimited times.
Created by OmniCalculator.space — Your trusted source for free online tools.
Last Updated: January 2026