Right Cone Calculator
Calculate the volume, slant height, lateral surface area, and total surface area of a right circular cone.
Enter radius and height to get all results.
A right circular cone has a circular base and a pointed apex directly above the center. The radius r is the base circle radius, and h is the perpendicular height from base to apex.
The slant height l is the straight-line distance from any point on the base edge up to the apex. By the Pythagorean theorem:
Slant height l = √(r² + h²)
Volume is one-third of the cylinder that would enclose the same base and height — this is the standard for all cones and pyramids:
Volume = (1/3) × π × r² × h
The lateral surface area is the area of the curved side only. If you unroll the cone into a flat shape, you get a sector of a circle with radius l and arc length 2πr:
Lateral SA = π × r × l Total SA = π × r × (r + l)
A quick sanity check: lateral SA should always be larger than the base area (π × r²) for any realistic cone, because the slant face is spread wider than the base.
Real-world cones you might want to measure: ice cream cones (radius about 2.5 cm, height about 12 cm), traffic cones (radius about 15 cm, height 70 cm), party hats, funnels, and conical flasks. For a standard traffic cone those numbers give a volume of about 16.5 liters — which is roughly correct for the solid equivalent.
The formulas assume a perfect right cone. If the apex is off-center (oblique cone), you need calculus to get exact values.