Surface Area Calculator

What Surface Area Means

Surface area is the total area of the outside of a solid. Imagine unfolding it and laying every face flat, then adding up those areas. (Volume, by contrast, is the space inside.)

That “add up the faces” idea is the whole thing:

• A box has 6 rectangles - add their areas and it tidies up to $2(lw + lh + wh)$.
• A cylinder is two circular ends plus the curved side that wraps around them.
• A cone is its circular base plus one slanted side.
• A sphere is the one shape that cannot be unfolded flat, but its area still works out neatly to $4\pi r^2$.

Pick a shape above and the bar under the figure splits the total into those parts, so you can see what adds up to what.

Surface Area Formulas

$$\begin{aligned} \text{box} &= 2(lw + lh + wh) \\ \text{cube} &= 6 \times \text{side}^2 \\ \text{sphere} &= 4\pi r^2 \\ \text{cylinder} &= 2\pi r(r + h) \\ \text{cone} &= \pi r(r + \ell), \quad \ell = \sqrt{r^2 + h^2} \end{aligned}$$

How to Use It

1. Choose the shape.
2. Enter its measurements.
3. Read the surface area and the steps.

Worked Examples

Shape	Measurements	Surface area
Box	4 × 3 × 2	52
Cube	side 4	96
Sphere	radius 3	≈ 113.1
Cylinder	radius 3, height 4	≈ 131.9
Cone	radius 3, height 4	≈ 75.4

FAQ

How do you find the surface area of a box?

Add the areas of all six faces: $2(lw + lh + wh)$. For 4 × 3 × 2: $2(12 + 8 + 6) = 52$.

What is the surface area of a sphere?

Use $4 \times \pi \times r^2$. For a radius of 3: $4 \times \pi \times 9 \approx 113.1$.

How do you find a cone’s surface area?

Add the circular base ($\pi r^2$) and the curved side ($\pi r \times \text{slant}$), where the slant height is $\sqrt{r^2 + h^2}$.

What is the difference between surface area and volume?

Surface area is the total area of the outside, in square units; volume is the space inside, in cubic units. The volume calculator handles the latter.