This calculator computes the full geometry of a right circular cone from just its base radius and height. Enter those two values and it returns the volume, slant height, lateral (curved) surface area, base area and total surface area. It is useful for geometry homework, engineering, and practical jobs like sizing a funnel, hopper or party hat. Keep your units consistent and read all results instantly.
How it works
From the radius (r) and height (h), the tool first finds the slant height using the Pythagorean theorem, then applies the standard cone formulas:
| Quantity | Formula |
|---|---|
| Slant height (l) | √(r² + h²) |
| Volume | ⅓ · π · r² · h |
| Lateral surface area | π · r · l |
| Base area | π · r² |
| Total surface area | π · r · l + π · r² |
It uses full-precision π before rounding for display.
Example
A cone with radius 3 and height 4:
slant = √(3² + 4²) = √25 = 5 volume = ⅓ · π · 9 · 4 = 12π ≈ 37.699 lateral area = π · 3 · 5 = 15π ≈ 47.124 total area = 15π + 9π = 24π ≈ 75.398
So this cone has a volume of about 37.70 and a total surface area of about 75.40 cubic/square units. Everything updates instantly in your browser.