3D Shape Master Calculator

An ellipsoid with three unequal semi-axes has no elementary closed-form surface area formula — it genuinely requires an elliptic integral to compute exactly. This calculator uses Knud Thomsen's widely used approximation, which stays within roughly 1% of the true value across realistic axis ratios, while the ellipsoid's volume figure remains mathematically exact.

Surface area is the shape's entire outer skin, including any flat top and bottom. Lateral area strips those flat caps out and reports only the curved or slanted side — the relevant number if you're wrapping, painting, or cladding just the barrel of a cylinder or the sloped face of a cone rather than its ends.

Yes, as long as the object closely matches one of the twelve idealized shapes and you measure its dimensions accurately. The formulas assume perfectly flat faces, uniform curvature, and zero wall thickness, so a tank with rounded corners, a domed lid, or thick walls will have a real volume that differs somewhat from the idealized number shown here.

The major radius is the distance from the torus's center hole to the middle of its tube, and the minor radius is the tube's own thickness. If the tube radius were equal to or larger than that distance, the tube would overlap itself through the center rather than forming a real donut shape, so the geometry only makes physical sense when the minor radius stays smaller.

The unit system selector tells the calculator whether your typed dimensions are inches or centimeters, and every output — volume in cubic feet, cubic meters, liters, and gallons, plus surface area in square feet and square meters — is derived from that single interpretation. Switching the toggle changes how your existing numbers are read, not what you've entered.