Cone Volume Calculator

Advanced cone calculator with 3D visualization. Supports right circular cones, elliptical cones, and oblique cones. Calculate volume, surface area, and dimensions.

Cone Volume Formula: V = (1/3) × π × r² × h
Where: r = radius, h = height, π ≈ 3.14159
Find Volume
Find Radius
Find Height
Find Slant Height
Units:
cm
Distance from center to edge of base
cm
Vertical distance from base to apex
Ice Cream Cone
Traffic Cone
Party Hat
Volcano Model
Funnel
Click to load example dimensions
Calculating...

Understanding Cones

A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (usually circular) to a point called the apex or vertex. It is one of the basic shapes in geometry with many practical applications.

Key Cone Formulas:

  • Volume: V = (1/3) × π × r² × h
  • Slant Height: s = √(r² + h²)
  • Lateral Surface Area: A_lateral = π × r × s
  • Base Area: A_base = π × r²
  • Total Surface Area: A_total = π × r × (r + s)

Cone Properties

1

Right vs. Oblique Cones: A right cone has its apex directly above the center of its base. An oblique cone has its apex not aligned above the center. Our calculator assumes right circular cones.

2

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

3

Slant Height: The distance from the apex to any point on the circumference of the base, measured along the surface.

Real-World Applications

  • Architecture: Cone-shaped roofs, spires, and decorative elements
  • Engineering: Funnels, nozzles, traffic cones, and hoppers
  • Food Industry: Ice cream cones, party hats, and measuring cups
  • Nature: Volcanoes, pine cones, and certain sea shells
  • Manufacturing: Conical springs, drill bits, and tapered rollers

Calculator Features:

  • Calculate volume, surface area, slant height, and other dimensions
  • Solve for any parameter given the others (radius, height, volume, slant height)
  • Visualize cone with accurate dimensions and labels
  • Compare cone volume to cylinder and pyramid with same base and height
  • Switch between metric and imperial units

Frequently Asked Questions

This relationship can be demonstrated through calculus (integration) or geometrically by comparing the volumes. A cone can be thought of as a pyramid with a circular base. Since any pyramid's volume is one-third of the corresponding prism (base area × height), the same applies to cones as a special case of pyramids.

The height (or altitude) is the perpendicular distance from the base to the apex. The slant height is the distance from the apex to any point on the circumference of the base, measured along the lateral surface. They are related by the Pythagorean theorem: slant height = √(radius² + height²).

This calculator is designed for complete cones. For a truncated cone (frustum), you would need both the top and bottom radii along with the height. The volume formula for a frustum is V = (1/3)πh(R² + Rr + r²), where R and r are the radii of the two bases and h is the height.

Calculations use double-precision floating-point arithmetic with π accurate to 15 decimal places (3.141592653589793). Results are typically accurate to at least 10 decimal places, which is more than sufficient for most practical applications.

No, with only the volume, there are infinitely many cones that could have that volume (different combinations of radius and height). You need at least one additional dimension (radius, height, or slant height) to determine a unique cone.