Cone Volume Calculator

Radius

Height

Enter radius and height values to calculate the cone volume

Formula: Volume = (1/3) × π × r² × h
Where π ≈ 3.14159, r is the radius, and h is the height of the cone.

Cone Volume Formula, How to Use, and Features of the Calculator

Cones are fascinating three-dimensional shapes found throughout nature and human-made objects. From ice cream cones to traffic cones, and from volcanic mountains to party hats, understanding how to calculate their volume is essential in various fields. This comprehensive guide explains the cone volume formula, its practical applications, and introduces our interactive calculator tool.

What is a Cone?

A cone is a solid geometric shape that tapers smoothly from a flat circular base to a point called the apex or vertex. When we refer to a “cone” in mathematical contexts, we typically mean a right circular cone, where the axis from the center of the base to the apex is perpendicular to the base.

Key Properties of a Cone:

Radius (r): The distance from the center to the edge of the circular base
Height (h): The perpendicular distance from the base to the apex
Slant Height (l): The distance from the apex to any point on the edge of the base
Base Area: The area of the circular base, calculated as πr²

The Cone Volume Formula

The volume of a cone represents the amount of three-dimensional space it occupies. The formula for calculating cone volume is:

V = (1/3) × π × r² × h

Where:

V = Volume
π = Pi (approximately 3.1416)
r = Radius of the circular base
h = Height of the cone

Understanding the Formula

The cone volume formula derives from the fact that a cone occupies exactly one-third the volume of a cylinder with the same base and height. This relationship makes sense when you consider that a cone could be filled with liquid and poured into a cylinder of the same dimensions exactly three times.

Key Features of the Cone Volume Calculator:

Dual Unit Support(centimetres, meters, or inches)
Automatic Unit Conversion
Explanation of Formula
PDF Export

How to Use the Cone Volume Calculator

Step 1: Enter the Radius

Input the radius value in the first field
Select the appropriate unit (cm, m, or in) from the dropdown

Step 2: Enter the Height

Input the height value in the second field
Select the corresponding unit

Step 3: Calculate

Click the “Calculate” button to see the volume result
The tool will display the volume in the original units plus conversions

Step 4: Reset or Download (Optional)

Use “Reset” to clear all fields and start over
Use “Download PDF” to save your calculation

Example Calculation

Let’s calculate the volume of a cone with:

Radius = 4 cm
Height = 9 cm

Using the formula:
V = (1/3) × π × r² × h
V = (1/3) × 3.1416 × (4)² × 9
V = (1/3) × 3.1416 × 16 × 9
V = (1/3) × 3.1416 × 144
V = (1/3) × 452.3904
V = 150.7968 cm³

Our calculator would display this result and also provide conversions to m³ and in³.

Try Our Calculator Now!

The interactive calculator below is ready to use. Input your cone’s dimensions and discover its volume instantly!