Geometry
Face-by-face workingSurface Area Calculator
Pick a solid, enter its measurements and see the surface area built up face by face — no magic formula, just the pieces added together in front of you.
Your numbers
Worked solution
Surface area of the box
108 u²
6 × 4 × 3 — three pairs of faces
SA = 2(lw + lh + wh) = 2(24 + 18 + 12) = 108 square units.
The working
2 stepsWork out each pair of faces
A box has three pairs of identical opposite faces: top/bottom, front/back, left/right.
- Top & bottom (2 × 6 × 4)
- 48 u²
- Front & back (2 × 6 × 3)
- 36 u²
- Left & right (2 × 4 × 3)
- 24 u²
Add the three pairs
SA = 2(24 + 18 + 12) = 108
Works instantly in your browser — nothing is uploaded, and the URL keeps your numbers so you can share the exact worked example.
Why the formulas look the way they do
Every surface-area formula is just an inventory: list the faces, compute each one with flat geometry, add them up. A box is six rectangles. A cylinder is two circles plus a rectangle that has been rolled up. A cone is a circle plus a rolled-up sector. Once you see the inventory, there is nothing to memorise.
Frequently asked questions
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