How to use this calculator
- Enter or choose shape.
- The total surface area updates as you type. Use Copy result or Share to keep it.
Method
Sphere 4πr²; hemisphere 3πr²; cube 6a²; box 2(lw + lh + wh); cylinder 2πr(r + h); cone πr(r + s), s = √(r² + h²); square pyramid a² + 2a√(h² + (a/2)²)
- r
- radius
- h
- perpendicular height
- a
- edge length
- l, w
- length and width
- s
- slant height
Worked example
- Curved side: 2π × 3 × 10 = 60π ≈ 188.4956.
- Two ends: 2 × π × 3² = 18π ≈ 56.5487.
- Total: 78π ≈ 245.0442.
A closed cylinder of radius 3 and height 10 has a surface area of about 245.04 square units.
What the result means
Use the lateral area for open shapes, such as a pipe or a tube without ends, and the total for closed containers. Units are the square of the length unit you entered.
Assumptions and limits
- Ideal solids with straight sides; the cone and pyramid are right (apex above the centre of the base).
- Heights are perpendicular heights, not slant heights.
- Material estimates need extra for seams, overlaps and waste.
Questions
What is the difference between lateral and total surface area?
Lateral area excludes the base or bases; total area includes them. For a can, the label covers the lateral area.
I only know the slant height of a cone. What now?
Perpendicular height h = √(s² − r²). Enter that value as the height.