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Cone Surface Area Calculator — result sheet
Calculate the slant height, base area, lateral area, and total surface area of a right circular cone.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: l = √(r²+h²); base area = πr²; lateral area = πrl; total area = πr² + πrl.
For a right circular cone, the slant height and radius form a right triangle with the vertical height. The total surface includes one circular base and the curved lateral surface.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Base radius — units; minimum 1.0E-6; maximum 1000000000
- Vertical height — units; minimum 1.0E-6; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Base radius | 3 |
| Vertical height | 4 |
Slant height: 5 units; total surface area: about 75.40 square units.
Assumptions and limits
- The shape is a right circular cone with a circular base and a straight axis perpendicular to that base.
- The base is included in total surface area; lateral area excludes it.
- All dimensions use one unit and the reported areas use squared units; thickness and openings are ignored.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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