Math

Instant, private, and free

Truncated Cone Calculator.

Calculate a conical frustum's slant height, areas, and volume.

On-device calculationNo signup
01

Set your values

Results update as you type.

Slant height: 4.472136

Slant height

0.000000
Volume: 205.25072

Volume

0.000000
Lateral area: 112.397036

Lateral area

0.000000
Surface area: 219.211186

Surface area

0.000000

Results update automatically as you type.

Use Cases

Engineering and Manufacturing

Determine the material needed for a frustum-shaped part or container, such as a bucket or a funnel, by calculating its volume and surface area.

Example: A bucket with larger radius 15 cm, smaller radius 10 cm, and height 20 cm.

Construction and Architecture

Estimate concrete or paint quantities for truncated cone structures like pillars, planters, or decorative elements.

Example: A planter with larger radius 0.5 m, smaller radius 0.3 m, and height 0.4 m.

Frequently Asked Questions

What is a truncated cone?
A truncated cone is a cone with its top cut off by a plane parallel to the base. It has a larger circular base and a smaller circular top, connected by a slanted side. This calculator uses the larger radius, smaller radius, and height to compute its volume and surface area.
How is the volume of a truncated cone calculated?
The volume is calculated using the formula V = (1/3) * π * height * (R^2 + R*r + r^2), where R is the larger radius, r is the smaller radius, and height is the perpendicular distance between the two bases. This calculator applies this formula instantly.
What units should I use for the inputs?
You can use any consistent unit for all three inputs (larger radius, smaller radius, height). The result will be in cubic units for volume and square units for surface area. For example, if you use centimeters, volume will be in cubic centimeters.

Tips & Common Mistakes

Tips

  • Ensure all inputs are in the same unit (e.g., all in meters or all in inches) to get correct results.
  • The larger radius must be greater than or equal to the smaller radius; if they are equal, the shape becomes a cylinder.
  • For a quick estimate, you can round the radii and height to the nearest whole number, but for precise work, use exact measurements.
  • Use the surface area result to estimate the amount of material needed for coating or wrapping the truncated cone.

Common Mistakes to Avoid

  • Using different units for the radii and height, which leads to incorrect volume and surface area calculations.
  • Confusing the larger and smaller radii, which can produce a negative or incorrect result if the larger radius is smaller than the smaller radius.
  • Forgetting that the height is the perpendicular distance between the two bases, not the slant height.

Last updated: August 13, 2026