Cone Calculator
Right circular cone. Volume is one third π r squared h. Slant height is the hypotenuse of r and h. Lateral and total surface follow from that slant. Units are whatever you typed.
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How to compute cone volume and surface
- Enter a radius greater than 0. The default is 3.
- Enter a height greater than 0. The default is 4, so slant height is 5.
- Read volume, slant height, lateral area, and total surface area.
- Keep radius and height in the same unit. Volume is then that unit cubed.
Right circular cone
Volume and surface from radius and perpendicular height
| Volume | V = (1/3) π r² h |
|---|---|
| Slant height | l = hypot(r, h) |
| Lateral area | π r l |
| Total surface | π r (r + l), base included |
| Default example | r = 3, h = 4, l = 5, V = 12π |
| π | JavaScript Math.PI |
What this cone page computes
A right circular cone has a circular base and an apex above the center. You type radius and perpendicular height. Volume is (1/3) π r² h. The slant is the generator from the base rim to the apex. The page includes the base in total surface area. An oblique cone or a frustum is not modeled.
How volume and surface are computed
Volume = (1/3) π r² h. Slant l = hypot(r, h). Lateral area = π r l. Total surface = π r (r + l). The default 3-4-5 triple is a Pythagorean check on slant. A right circular cylinder with the same r and h is three times this volume on the cylinder page.
Cone, cylinder, and sphere
A sphere uses a single radius on the sphere page. Ice-cream-cone composites are two solids you add yourself. Construction pile takeoffs that are not right cones need another sketch. Math.PI is a floating-point value, not a hand-typed 22/7.
Use cases
A geometry homework 3-4-5 cone, a party-hat net check, or a grain-hopper sketch that you already treat as a right cone. Funnel truncation is a frustum, not this form.
Limits
Radius and height must be greater than 0. No frustum. No slant as an input. No units conversion. IEEE floating point applies. CZNull does not receive the numbers.