Enter the base radius (or diameter) and the vertical height of a cone. The calculator returns the volume, the slant height, the lateral area and the total surface area, and draws the cone so you can see that the height is measured straight up, not along the slanted side.
24 solids in six groups. Enter the dimensions and the model updates instantly.
Prices are in whatever currency you use. The material price needs a material or density above.
Export the shape at your real size for 3D printing, or print a flat net you can cut out and fold into a paper model.
Use the straight vertical height, not the slanted edge. If you only know the slant height, find h with h = √(s² − r²) first. You can also print a flat net of the cone as a PDF from the buttons under the results.
This page is the cone view of the full 3D Shape Calculator, which covers 24 solids. Every shape button is still available, so you can compare solids without leaving the page.
In every formula, r is a radius, h is a height or depth, and all measurements must use the same unit. The result is in that unit cubed for volume and squared for area.
A funnel shaped like a cone has a radius of 4 cm and a height of 12 cm. The volume is (1/3) × π × 4² × 12 ≈ 201.1 cm³, about 0.201 litres. The slant height is √(4² + 12²) ≈ 12.65 cm, so the side surface is π × 4 × 12.65 ≈ 159.0 cm².
Cones describe traffic cones, funnels, ice-cream cones, party hats, piles of gravel or sand, silos with conical roofs and rocket nose cones. The volume tells you how much a pile contains, and the lateral area gives the material needed to make the cone from flat sheet.
Why is the volume of a cone one third of a cylinder? A cone fits inside a cylinder with the same base and height, and it fills exactly one third of it. This was known to the ancient Greeks and follows from calculus as well.
What is the difference between height and slant height? The height runs straight from the centre of the base to the tip. The slant height runs along the surface from the rim of the base to the tip, and is always longer.
How do I find the volume of a cone from its diameter? Halve the diameter to get the radius and use V = (1/3) × π × r² × h, or switch the input to Diameter in the calculator.
How much gravel or sand is in a conical pile? Measure the height and the diameter of the pile, enter them here and multiply the volume by the material’s density. Pick a material under More options to get the weight.