What the Cone Volume Calculator Does
This free online tool calculates the volume of a right circular cone from just two measurements: the radius of its circular base and its vertical height. Beyond the volume, it also computes several related geometric properties in one go — the slant height, the base area, the lateral (side) surface area and the total surface area — so you get a complete picture of the cone's dimensions in a single calculation.
The Inputs You Provide
- Radius: the distance from the centre of the circular base to its edge.
- Height: the perpendicular (vertical) distance from the base to the apex (tip) of the cone.
Both values should be in the same unit (e.g. centimetres). The volume result will be in those units cubed, and areas in units squared.
The Formula Explained
The calculator uses the standard cone volume formula:
Volume = (1/3) × π × r² × Height
A cone holds exactly one third the volume of a cylinder with the same base and height — that is the source of the 1/3 factor. The tool also derives the slant height using the Pythagorean theorem, s = √(h² + r²), then uses it for the surface areas:
- Base area: B = πr²
- Lateral surface area: L = πr·s
- Total surface area: A = πr(r + s)
Worked Example
Suppose a cone has a radius of 3 and a height of 4.
- Volume = (1/3) × π × 3² × 4 = (1/3) × π × 36 = 37.70
- Slant height = √(4² + 3²) = √25 = 5
- Base area = π × 3² = 28.27
- Lateral surface area = π × 3 × 5 = 47.12
- Total surface area = π × 3 × (3 + 5) = 75.40
Enter 3 for radius and 4 for height and the calculator returns these figures instantly.
Frequently Asked Questions
Do I need to enter the slant height? No. You only enter the radius and vertical height. The calculator derives the slant height automatically for its surface-area outputs.
What units does the result use? The tool is unit-agnostic. Whatever unit you use for the inputs, volume is returned in that unit cubed and areas in that unit squared.
Does this work for any cone? The formula applies to a right circular cone (apex directly above the centre of the base). It is not designed for oblique or elliptical cones.
