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.
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This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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