Cone Frustum Calculator (Volume & Surface Area)
Cone Frustum Calculator (Volume & Surface Area)
A cone frustum (or truncated cone) is what remains when the pointed top of a cone is sliced off with a cut parallel to the base - lampshades, buckets, and drinking cups are everyday examples. Enter the top radius, bottom radius, and height (in whatever unit you like), and this calculator finds the slant height, volume, and surface area, along with a diagram and the full step-by-step working.
- V = ⅓πh(r₁² + r₂² + r₁r₂), so a frustum with top radius 2, bottom radius 5, and height 6 has a volume of ⅓ × π × 6 × (4+25+10) ≈ 245.04 cubic units.
- The slant height is l = √(h² + (r₂ - r₁)²) - it accounts for both the vertical height and the difference between the two radii, giving √(36+9) ≈ 6.71 for this example.
- Setting r₁ = 0 turns the formulas back into a full cone's - the frustum formulas are the general case, and a regular cone is just the special case where the top radius shrinks to a point.
How do I find the volume of a cone frustum?
Use V = ⅓πh(r₁² + r₂² + r₁r₂), where r₁ and r₂ are the two radii and h is the height. For radii 2 and 5, height 6: V = ⅓ × π × 6 × (4+25+10) ≈ 245.04.
What is a cone frustum used for?
Frustum-shaped objects are everywhere - lampshades, plant pots, buckets, and traffic cone bases are all cone frustums, since a full pointed cone is often impractical to use.
Cone Frustum Calculator (Volume & Surface Area)
A cone frustum (or truncated cone) is what remains when the pointed top of a cone is sliced off with a cut parallel to the base - lampshades, buckets, and drinking cups are everyday examples. Enter the top radius, bottom radius, and height (in whatever unit you like), and this calculator finds the slant height, volume, and surface area, along with a diagram and the full step-by-step working.
- V = ⅓πh(r₁² + r₂² + r₁r₂), so a frustum with top radius 2, bottom radius 5, and height 6 has a volume of ⅓ × π × 6 × (4+25+10) ≈ 245.04 cubic units.
- The slant height is l = √(h² + (r₂ - r₁)²) - it accounts for both the vertical height and the difference between the two radii, giving √(36+9) ≈ 6.71 for this example.
- Setting r₁ = 0 turns the formulas back into a full cone's - the frustum formulas are the general case, and a regular cone is just the special case where the top radius shrinks to a point.
How do I find the volume of a cone frustum?
Use V = ⅓πh(r₁² + r₂² + r₁r₂), where r₁ and r₂ are the two radii and h is the height. For radii 2 and 5, height 6: V = ⅓ × π × 6 × (4+25+10) ≈ 245.04.
What is a cone frustum used for?
Frustum-shaped objects are everywhere - lampshades, plant pots, buckets, and traffic cone bases are all cone frustums, since a full pointed cone is often impractical to use.