Using the Legacy Prolate Dome Calculator

The legacy prolate dome calculator is technically a horizontal ellipsoid calculator. The most common design is a prolate ellipsoid on its side — like a watermelon cut lengthwise and set on a table. But the calculator can be used for shorter, oblate ellipsoids set horizontally, too. The important thing to remember is that the side and top views are elliptical and the end view is circular.

The horizontal ellipsoid is the least used design in the Monolithic Dome industry, but it is still important and calculating the measurements is extremely difficult without help. This is a legacy port of the original advanced calculator created in the early 2000s. There will be a modern version developed similar to the spherical, half-ellipsoid, and vertical ellipsoid calculators. Two other calculators are the priority before returning to modernize this one.

This calculator is subject to our Terms of Service.

Sketch of prolate ellipsoid

A sketch of a horizontal prolate ellipsoid that can be input in this calculator to find the floor radii and overall surface area.

Dave South

Inputs

Major radius. The horizontal distance from the ellipsoid center to the furthest apex of the dome.

Minor radius. The vertical distance from the ellipsoid center to top of dome defining a circular cross-section bisecting the dome.

Height. The overall height from the floor to top of the dome.

Level. A distance above the floor to calculate the horizontal ellipse at that level.

Outputs

Floor major radius. The calculated major radius or semi-major axis of the elliptical floor.

Floor minor radius. The calculated minor radius or semi-minor axis of the elliptical floor.

Floor perimeter. The distance around the elliptical base of the dome. This is an iterative calculation with about four significant digits of precision.

Floor area. The floor area of the elliptical base of the dome.

Prolate Surface Area. The surface area of the dome shell. It is an iterative calculation with about four or five significant digits of precision.

Level

Major radius @ level. The major radius or semi-major axis of the horizontal elliptical cross-section at the specified level.

Minor radius @ level. The minor radius or semi-minor axis of the horizontal elliptical cross-section at the specified level.

Floor perimeter @ level. The distance around the horizontal elliptical cross-section at the specified level. This is an iterative calculation with about four significant digits of precision.

Floor area @ level. The floor area of the horizontal elliptical cross-section at the specified level.

Notes

Always click “calculate” after changing input values. This calculator cannot save values for future reference so take a screenshot or write down the outputs. This calculator is subject to our Terms of Service.