Cone Calculator

What is a Cone Calculator?

A cone calculator is a mathematical tool that helps you calculate various properties of a cone, including volume, surface area, slant height, lateral surface area, and base area. A cone is a three-dimensional geometric shape with a circular base that tapers smoothly to a point called the apex.

How to Use This Calculator

1. Choose calculation mode: Select what you want to calculate
2. Enter known values: Input the radius and height (or other known values)
3. View results: Instantly see all calculated properties

Cone Formulas

Basic Measurements

• 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

Slant Height Formula

l = √(r² + h²)

The slant height is found using the Pythagorean theorem, as the radius, height, and slant height form a right triangle.

Volume Formula

V = (1/3) × π × r² × h

The volume of a cone is one-third of the volume of a cylinder with the same base and height.

Surface Area Formulas

• Base Area: A = π × r²
• Lateral Surface Area (LSA): LSA = π × r × l
• Total Surface Area (TSA): TSA = π × r × (r + l)

Real-World Applications

Architecture & Construction

• Designing conical roofs and towers
• Calculating materials for cone-shaped structures
• Planning traffic cones and markers

Manufacturing

• Ice cream cone production
• Funnel design
• Speaker cone specifications

Science & Engineering

• Volcano shape analysis
• Rocket nose cone design
• Particle accelerator components

Frequently Asked Questions

What's the difference between slant height and height?

The height (h) is the vertical distance from the base to the apex, measured perpendicular to the base. The slant height (l) is the distance along the surface of the cone from the apex to the edge of the base.

How accurate is this calculator?

This calculator uses standard mathematical formulas and provides results accurate to several decimal places. For practical applications, round to the appropriate precision for your needs.

Can I calculate radius from volume?

Yes! Our calculator supports reverse calculations. Enter the volume and height to find the radius, or enter volume and radius to find the height.

What units should I use?

Use consistent units throughout. If you enter measurements in centimeters, your results will be in centimeters (linear), square centimeters (area), and cubic centimeters (volume).

Tip: The slant height is always longer than the height because it represents the hypotenuse of a right triangle formed by the radius and height.