About the Cone Calculator
A cone narrows smoothly from a circular base to a single point. Ice cream cones, traffic cones, funnels and party hats are all cones. This calculator uses the radius of the base and the vertical height to find the volume, the slant height along the side, the area of the base, the curved side area and the total surface area. A second mode runs the volume formula backwards: give it a radius and a volume, and it returns the height. It handles right circular cones, where the tip sits directly above the centre of the base.
Updated October 2026
How to use the Cone Calculator
- 1Choose volume and surface area, or height from volume.
- 2Enter the radius of the circular base.
- 3Enter the height, or the volume if you are solving for height.
- 4Read the volume and the slant height first.
- 5Use the lateral and total area lines for paint, fabric or paper estimates.
Example: filling a funnel
A funnel has a top radius of 6 cm and a depth of 10 cm. Its volume is ⅓ × π × 36 × 10, about 377 cubic centimetres, or 0.377 litres. The slant height is the square root of 136, about 11.66 cm, which tells you how long a strip of metal is needed to roll one.
Handy relationships
- A cone's volume is one third of a cylinder with the same base and height.
- Halving the height halves the volume, but halving the radius cuts it to a quarter.
- The unrolled curved surface is a sector of a circle with radius equal to the slant height.
- The angle at the tip can be found with trigonometry from the radius and height.
Where to go next
Compare shapes with the Cylinder Calculator and Sphere Calculator, use the Pythagorean Theorem Calculator for the slant height by itself, or the Volume Calculator for boxes and prisms. The Trigonometry Calculator handles the cone's angles.
Features
- Volume, slant height and four area figures
- Reverse mode: height from volume and radius
- Works with any consistent length unit
- Clear errors for zero and negative values
- Full-precision pi
- Nothing leaves your browser
Frequently asked questions
What is the formula for the volume of a cone?
One third times pi times the radius squared times the height. With a 4 cm radius and a 9 cm height, the volume is ⅓ × π × 16 × 9, about 150.8 cubic centimetres. It is exactly a third of the cylinder with the same base and height.
What is the slant height?
It is the distance from the tip down the side to the edge of the base. It forms the hypotenuse of a right triangle with the radius and the vertical height, so slant height equals the square root of radius squared plus height squared.
How do I find the surface area of a cone?
Add the base area, π r², and the curved lateral area, π r times the slant height. The sum is the total surface area. The lateral part alone is what you need to cover the outside of a party hat.
How do I find the height from the volume?
Multiply the volume by 3 and divide by π times the radius squared. A 150 unit volume with a 4 unit radius gives a height of about 8.95. Choose the height mode and the calculator does the arithmetic.
Does it work for slanted cones?
Volume works the same for an oblique cone as long as you use the vertical height, not the slant. The surface area formulas here assume a right cone, so they will not be exact for a leaning one.
What about a cone with the top cut off?
That shape is a frustum. You can find its volume by subtracting the small cone that was removed from the big complete cone, using this calculator twice.