Quick answer
A cone's volume is V = ⅓πr²h, its slant height is √(r² + h²) and its total surface area is πr(r + slant). With r = 3 and h = 4: volume 37.6991, slant height 5 and surface area 75.3982.
Enter the radius and height. The calculator returns volume, slant height and surface area.
Related tools: Cylinder Volume Calculator: Volume of a cylinder. Sphere Volume Calculator: Volume and surface area of a sphere. Volume of a Hemisphere Calculator: Volume and surface area of a hemisphere.
How to use the Cone Volume Calculator
- Enter radius (above 0).
- Enter height (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Radius | A number | > 0 |
| Height | A number | > 0 |
Formula and method
Formula
V = (1/3)πr²h; slant = √(r² + h²); A = πr(r + slant)
IEEE-754 double precision; shown to at most 6 decimal places.
Standard cone formulas.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Radius = 3; Height = 4.
| Result | Value |
|---|---|
| Volume | 37.699112 |
| Slant height | 5 |
| Surface area | 75.398224 |
Example 2
Inputs: Radius = 1; Height = 3.
| Result | Value |
|---|---|
| Volume | 3.141593 |
| Slant height | 3.162278 |
| Surface area | 13.076181 |
The first line is the headline result (volume). Below it the cone Volume Calculator lists slant height and surface area, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
A third of a cylinder
A cone has exactly one-third the volume of the cylinder with the same base and height: the cylinder would be π × 9 × 4 = 113.1, and a third is 37.7. The 3-4-5 right triangle gives the slant height.
Surface area
Total area = base πr² (28.27) + lateral surface πr × slant (47.12) = 75.40. For an ice-cream cone or funnel, only the lateral area matters. Units are cubic for volume and square for area.
How the result changes with radius
Holding every other input at the first worked example, this table changes only radius. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Radius | Volume | Slant height | Surface area |
|---|---|---|---|
| 1.5 | 9.424778 | 4.272002 | 27.199918 |
| 3 | 37.699112 | 5 | 75.398224 |
| 6 | 150.796447 | 7.211103 | 249.023416 |
| 12 | 603.185789 | 12.649111 | 929.249579 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Height: entering "0" shows "Height must be greater than 0." beside that field and no result.
Choosing between the Cone Volume Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Cylinder Volume Calculator](/math/cylinder-volume-calculator/) | radius and height | Volume |
| [Sphere Volume Calculator](/math/sphere-volume-calculator/) | radius | Volume |
| [Volume of a Hemisphere Calculator](/math/volume-of-hemisphere/) | radius | Volume |
| [Pyramid Volume Calculator](/math/pyramid-volume-calculator/) | base length, base width and height | Volume |
| [Cube Volume Calculator](/math/cube-volume-calculator/) | side | Volume |
Background: geometry measurements
Geometry results carry units that depend on the quantity: a perimeter or length is in linear units such as cm, an area or surface area is in square units (cm²) and a volume is in cubic units (cm³). Use one length unit for every input, because the calculator multiplies the numbers as given.
Flat (2D) shapes have an area and a perimeter; solids (3D) have a surface area and a volume. Two familiar checks: a circle of radius r has area πr² and circumference 2πr, and a sphere has volume (4/3)πr³ and surface area 4πr².
Assumptions and limitations
- Positive dimensions
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for height to confirm this.
Frequently asked questions
What is the slant height?
The distance from the apex to the edge of the base.
How do I find the volume of a cone with diameter 6?
Halve the diameter first: a 6 diameter means radius 3, so V = ⅓π × 9 × h.
What is a frustum?
A cone with the top cut off.
What does the Cone Volume Calculator calculate?
Volume, slant height and surface area of a cone. It returns Volume, Slant height and Surface area.
What formula does the Cone Volume Calculator use?
V = (1/3)πr²h; slant = √(r² + h²); A = πr(r + slant). Standard cone formulas.
What do I need to enter in the cone Volume Calculator?
You enter Radius and Height.
What is an example of a cone Volume result?
With radius 3 and height 4, the volume is 37.699112.
Related calculators
- Cylinder Volume Calculator — Volume of a cylinder.
- Sphere Volume Calculator — Volume and surface area of a sphere.
- Volume of a Hemisphere Calculator — Volume and surface area of a hemisphere.
- Pyramid Volume Calculator — Volume of a pyramid from its base area and height (rectangular base).
- Cube Volume Calculator — Volume, surface area and diagonal of a cube.
- Prism Volume Calculator — Volume of any prism from base area and height.
- Hollow Cylinder Volume Calculator — Volume of material in a pipe or tube.
- Triangular Pyramid Volume Calculator — Volume of a pyramid with a triangular base.
- Torus Volume Calculator — Volume and surface area of a torus.
Sources
- OpenStax, Prealgebra 2e (Rice University): perimeter, area, volume, circumference and the Pythagorean theorem
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.