Calculators

Conical Frustum Calculator

Calculate volume, slant height, lateral area, and total surface area of a right circular conical frustum from two radii and vertical height.

Right circular conical frustum. Enter radii, not diameters, and use the same length unit for all inputs. Height is perpendicular to the bases.

Measure a truncated cone from its two radii and height.

For radii R and r and perpendicular height h, volume V = πh(R² + Rr + r²)/3, slant height s = √(h² + (R − r)²), lateral area L = π(R + r)s, and total surface area A = L + π(R² + r²). With radii 5 and 3 and height 4, volume is approximately 205.25072 cubic units. Both radii may be entered in either order. Equal radii describe a cylinder; one zero radius describes a cone. At least one radius and the height must be positive. Nonzero dimensions must be from 1e-50 to 1e50. Use consistent length units; areas use square units and volume uses cubic units. The total surface includes both circular bases. This assumes a solid right circular shape with parallel concentric bases, not an oblique frustum or a hollow vessel with wall thickness. Results use browser floating-point arithmetic rounded to 12 significant digits. All calculations stay in your browser.

Frequently Asked Questions

Everything you need to know about this tool, how it works, and privacy.

What is a conical frustum?

It is the portion of a cone between two parallel circular planes. This calculator assumes the centers of the bases lie on a perpendicular axis.

Should I enter radii or diameters?

Enter radii. Divide each diameter by two first. Use the perpendicular height, not the sloping side length.

Does total surface area include the bases?

Yes. Total surface area includes the curved lateral surface and both circular bases. Lateral area excludes the bases.

Can the radii be equal or zero?

Equal positive radii give a cylinder. One zero radius gives a cone. Both radii cannot be zero, and height must be positive.

Which units and number formats work?

Use one consistent length unit. Decimal and scientific notation are supported, with nonzero dimensions from 1e-50 to 1e50. Areas are in square units and volume in cubic units. Values stay in your browser.