Rectangular Prism Surface Area
Also known as surface area of a box · cardboard needed · box surface area
Worked example: 3 m cube as a prism → 54 m^2 (= 6 s^2) — press Try an example to run it live, then adjust anything.
Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Try different units for next level excitement!
Wrapping the box →
Grade 10Grade 10 Math
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Rectangular Prism Surface Area explained
A box has six faces in three matching pairs, so the total area is — top and bottom, front and back, two ends. It is the formula behind every cardboard-cost estimate, every quote for cladding a duct, and every calculation of how much paint a shipping crate will drink. A carton 40 cm × 30 cm × 20 cm needs cm² of board, before you add a single glue flap.
The sanity check to keep in your pocket: set and the expression collapses to , the cube. If a general box formula does not reduce to six squares when you feed it a cube, it is wrong.
Solving backwards for one edge stays easy, which surprises people who expect a quadratic. Peel off the two faces that do not involve the unknown edge and what remains is linear: . The catch is physical rather than algebraic. If the area you were given is less than those two fixed faces already account for, no box exists, and the solver says so rather than handing back a negative length.
Rectangular Prism Surface Area formula
- = Surface area (m²)
- = Length (m)
- = Width (m)
- = Height (m)
Missing one of these? Work it out first, then come back
- Surface area — Cone Total Surface Area, Torus Surface Area
- Length — Rectangle Perimeter, Rectangle Diagonal
- Width — Rectangle Perimeter, Rectangle Diagonal
- Height — Area of a Triangle, Cone Frustum Volume (Truncated Cone)