DIY Cost Tools
Conical Frustum Calculator
Find truncated cone volume, slant height, lateral area, and total area. Enter dimensions in one consistent unit for an immediate estimate.
Radii must be nonnegative, at least one radius positive, and vertical height positive. Use the same length unit throughout. Maximum input: 1 trillion.
How to use
Measure radius from the center to the edge, rather than across the entire circle. Convert measurements to a common unit, enter them above, and select Calculate. Default results appear on page load. Areas use squared input units; volumes use cubed input units. Results are rounded to ten significant digits.
Formula and explanation
V = πh(R² + Rr + r²)/3; s = √((R − r)² + h²); lateral area = π(R + r)s; total area = lateral area + πR² + πr². Height h is perpendicular to the parallel ends.
Worked example
Radii 5 and 3 with height 4 produce volume 196π/3 ≈ 205.2507 cubic units and slant height √20 ≈ 4.4721 units.
Important limitations
Assumes a right circular frustum with parallel ends and straight side profile. Not suitable for tilted, curved, irregular, or elliptical vessels. Use inside dimensions for capacity. Total area includes both ends, even for an open container. This does not certify structural or pressure-vessel safety. Measurement uncertainty and floating-point precision can affect results.
Frequently asked questions
Can the top be wider than the bottom?
Yes. Swapping radii leaves all results unchanged.
Can one radius be zero?
Yes, giving a cone. Both cannot be zero.
What if radii are equal?
The result is a cylinder, with volume πR²h.
Does lateral area include the ends?
No. Total area adds both circular ends.
Review notes
Reviewed October 1, 2026. Default outputs were independently checked against geometric formulas. Required fields, invalid dimensions, excessive values, and geometric boundary cases were tested. Educational and planning estimates only.