How to use this calculator
- Enter or choose base given as.
- Enter or choose base radius or diameter.
- Enter or choose i also know the.
- Enter or choose length unit.
- The total surface area (with base) updates as you type. Use Copy result or Share to keep it.
Method
l = √(r² + h²); Lateral = πrl; Base = πr²; Total = πr(r + l)
- r
- base radius
- h
- vertical height
- l
- slant height
Worked example
- l = √(3² + 4²) = 5 cm.
- Lateral = π × 3 × 5 = 15π ≈ 47.12389 cm².
- Total = 15π + 9π = 24π ≈ 75.398224 cm².
A cone with base radius 3 cm and height 4 cm has a total surface area of about 75.40 cm².
What the result means
Use the lateral area for an open cone such as a funnel, party hat or conical roof, and the total for a closed solid cone.
Assumptions and limits
- A right circular cone: the tip is directly above the centre of the base.
- Seams, overlaps and material thickness are not included.
- A truncated cone (frustum) needs a different formula.
Questions
Why does the curved area use slant height, not height?
Unrolled, the side is a sector of a circle whose radius is the slant height l, and its area works out to πrl.
How do I get the slant height?
By Pythagoras: l = √(r² + h²), because the radius, height and slant form a right triangle.