WorkedMathGlossary

Surface Area Calculator

Pick a shape below to instantly get its surface area.

Surface Area
96

Surface Area Formulas by Shape

  • Cube: 6s²
  • Rectangular prism: 2(lw + lh + wh)
  • Sphere: 4πr²
  • Cylinder: 2πrh + 2πr²
  • Cone: πr(r + slant height)

Need step-by-step work for one specific shape? See the dedicated sphere, cylinder, or cone calculators.

A common mistake with the rectangular prism formula is dropping one of the three face pairs — it's easy to compute lw + lh but forget wh entirely. Double-check that all three pairs of opposite faces (top/bottom, front/back, left/right) are accounted for before multiplying by 2.

Worked examples

A cube with side 4.

Surface area = 6 × 4² = 6 × 16 = 96

A rectangular prism with length 5, width 3, and height 2.

Surface area = 2(5×3 + 5×2 + 3×2) = 2(15 + 10 + 6) = 2 × 31 = 62

Keep going

  • Surface area already covers five shapes including the sphere; the sphere calculator isolates that one shape and adds volume alongside its surface area. Sphere Calculator
  • Surface area covers a cylinder as one of five shapes; the cylinder calculator adds volume and isolates just that shape's numbers. Cylinder Calculator

Frequently Asked Questions

What is surface area?

Surface area is the total area covering the outside of a three-dimensional shape — the sum of the area of every face or curved surface. It's measured in square units, the same as any 2D area.

Why is surface area useful?

Surface area comes up anywhere you need to know how much material covers something — paint for a wall, wrapping paper for a box, or the sheet metal needed to build a tank.

What's the difference between surface area and volume?

Surface area measures the outer covering (square units); volume measures the space inside (cubic units). A shape can have a large volume but relatively small surface area, or the reverse, depending on its proportions.

Why is a cube's surface area 6 × side²?

A cube has 6 identical square faces, and each face has an area of side × side, or side². Add up all six of those identical faces and you get 6 × side² — no more, no fewer, since every face of a cube is congruent.

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