Cone Calculator
Calculate volume, surface area, and other properties of a cone
Calculation Results
Enter cone measurements to calculate all properties.
Radius (r): units
Height (h): units
Slant Height (l): units
Volume (V): cubic units
Base Area (B): square units
Lateral Area (L): square units
Total Surface Area (S): square units
Cone Diagram
Cone Formulas
Key Properties
- Radius (r): Radius of the circular base
- Height (h): Perpendicular distance from base to apex
- Slant Height (l): Distance along the side from base to apex
- Volume (V): Space contained within the cone
- Base Area (B): Area of the circular base
- Lateral Area (L): Area of the side surface
- Total Surface Area (S): Base + Lateral area
Calculation Formulas
- Volume (V): V = (1/3)πr²h
- Base Area (B): B = πr²
- Lateral Area (L): L = πrl
- Total Surface Area (S): S = πr(r + l)
- Slant Height (l): l = √(r² + h²)
Where: r = radius, h = height, l = slant height, π ≈ 3.14159
Example Calculation
For a cone with:
Radius (r) = 3 units, Height (h) = 4 units.Calculations:
- Slant Height = √(3² + 4²) = 5 units
- Volume ≈ (1/3) × π × 3² × 4 ≈ 37.7 units³
- Base Area ≈ π × 3² ≈ 28.27 units²
- Lateral Area ≈ π × 3 × 5 ≈ 47.12 units²
- Total Surface Area ≈ π × 3 × (3 + 5) ≈ 75.4 units²
About Cones
A cone is a three-dimensional geometric shape that tapers smoothly from a flat circular base to a point called the apex or vertex. It has one curved surface and one circular base.
Real-World Applications
- Everyday Objects: Ice cream cones, traffic cones, party hats
- Engineering: Funnels, megaphones, conical springs
- Nature: Volcanic cones, pine cones (approximate)
- Architecture: Spires, conical roofs
Special Cases
- Right Circular Cone: The apex is directly above the center of the base
- Oblique Cone: The apex is not aligned above the center
- Cone Frustum: A truncated cone with the top cut off parallel to the base
Cone Components
Radius (r)
Base circle radius
Height (h)
Perpendicular distance
Slant Height (l)
l = √(r² + h²)
Volume (V)
V = (1/3)πr²h
Surface Area (S)
S = πr(r + l)
How to Use the Cone Calculator
The Cone Calculator helps compute various properties based on input values. Here's how to use it:
1. Select Calculation Method
Choose what measurements you know:
- Radius & Height - Enter radius and height
- Diameter & Height - Enter diameter and height
- Volume & Height - To find the radius
- Slant Height & Radius - To find the height
2. Enter Your Values
Input positive numbers in the appropriate fields:
Example 1: Radius = 3, Height = 4
Example 2: Volume = 37.7, Height = 4
3. Get Results
The calculator will compute all properties:
- Radius (r)
- Height (h)
- Slant Height (l)
- Volume (V)
- Base Area (B)
- Lateral Area (L)
- Total Surface Area (S)
Practical Applications
- Calculate material needed for conical structures
- Determine paint required for conical objects
- Find storage capacity of conical containers
- Solve geometry problems involving cones
Frequently Asked Questions
A cone has a circular base and one continuous curved surface, while a pyramid has a polygonal base and triangular faces meeting at the apex.
Use the formula: h = √(l² - r²) where l is slant height and r is radius.
Yes, but it would degenerate into a flat circle (height = 0).