Using the Vertical Dome Calculator

A vertical ellipsoid dome has a circular base and an elliptical cross-section. This shape can create unusual buildings ranging from tall multi-story to wide UFO-like structures. Unlike the Ellipsoid Dome Calculator, which is only for half-ellipsoid domes, the Vertical Ellipsoid Dome Calculator precisely inputs the ellipsoid shape with the base set at any distance above or below the equator.

Typically the calculator is for three common designs. The first is for oblate ellipsoids — also known as spheroids — that extend below the equator. These wide domes sort of “tuck in” and create a more rounded shape — sort of like an M&M. Second are tall prolate ellipsoids that also extend below the equator. These tall shapes allow for narrow multi-story structures where land is limited, or height is desired. And third is for prolate ellipsoids cut off above the equator. These prolate “tops” are unusual shapes with a more pointed look. A fourth option is the top portion of an oblate ellipsoid which is rarely used because it offers no real advantages over a low-profile spherical dome.

All parameters are stored in the page URL which may be bookmarked, saved, and shared. Use “Copy to Clipboard” to copy-and-paste results into your notes or emails. Print page or save as PDF for a professional copy of the drawing and results. Be aware that just because the calculator can draw a structure, it does NOT mean the structure can be built. This calculator is just a tool. Always consult with qualified professionals before proceeding with a project.

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Default vertical ellipsoid dome calculator design

The default design for the Vertical Ellipsoid Calculator is a 50-foot maximum diameter by 20-foot tall dome where the floor is below the equator. This is in contrast to a similar half-ellipsoid dome design with a stem wall. It often comes down to personal preferences or the aesthetic the dome builder is trying to achieve when deciding to build an over-center dome or a half-dome with a stem wall. Click for the live version of this design.

Inputs

Horizontal. The horizontal radius is the distance measured horizontally from the ellipsoid center to the dome side.

Vertical. The vertical radius is the distance measured vertically from the ellipsoid center to the dome apex.

Height. Overall height is the distance measured vertically from the floor to the dome apex.

Level. The optional horizontal level above the floor — forming a subsection of the structure. It calculates an imaginary circle at that level plus the upper portion of the structure from that level to the apex. The level is useful for calculating the second floor.

Overlay. A scaled, graphical overlay to assist in visually representing the building size and purpose.

Units. The selectable unit will label the calculator outputs and properly scale the overlay. Note that all numerical inputs must be given in the same selected unit.

Floor

Diameter. The calculated floor diameter is a circle representing the floor, stem wall, and dome base diameter.

Radius. The floor radius is half the floor diameter and is a useful number for various calculations.

Circumference. The floor circumference is the distance around the circle-shaped floor, stem wall, and dome base.

Area. The floor area is the area of the circle inscribed by the floor diameter.

Dome

Horizontal / Vertical Radius. Reference output of the ellipse cross-section radii.

Height. The dome height is the distance from the floor of the dome to the apex.

Ellipticity Ratio. The ratio between the equatorial radius and vertical radius describing the cross-section ellipse. A ratio greater than one is an oblate ellipsoid, and less than one is a prolate ellipsoid. The maximum recommended oblate ellipsoid ratio is 1.45 — the Airform membrane begins to wrinkle at ratios higher than 1.45.

Surface Distance. The dome surface distance is the length from the apex, following the dome curve down to the dome base.

Surface Area. The dome surface area is technically the dome’s lateral surface area from the base to the apex.

Volume. The dome volume is the cubic measure of the volume encompassed by the structure’s dome portion.

Tall, four story prolate ellipsoid dome home design

The three-story Palapa Pineapple Dome Home is a tall prolate ellipsoid with a height greater than the vertical radius. The homeowner wanted a tall home overlooking the ocean from their lot in Belize. There is a fourth-story deck atop the dome. Click for the live version of this design.

Level @

Height Above Floor. The level height is the distance from the floor to a horizontal “slice” at the level specified above the floor. It effectively creates a subsection of the overall building.

Diameter. The level diameter is the calculated diameter at the specified level above the floor.

Radius. The level radius is the calculated radius — half the level diameter — at the specified level above the floor.

Circumference. The level circumference is the perimeter around the imaginary slice at the level specified above the floor.

Area. The level area is the area of the circle described by the imaginary slice at the level specified above the floor. A common use is to set the level at 10-feet (3 m) to calculate the second floor’s diameter and area.

Portion Above Level

Remaining Height. The imaginary slice through the structure at the specified level essentially creates a second portion of the overall structure. The remaining height is calculated as the height from the specified level to the apex of the dome.

Surface Distance. The level surface distance is the overall surface distance from the dome apex to the imaginary slice at the specified level. It will correctly follow the dome and even down the stem wall.

Surface Area. The level surface area is the remaining structure’s overall surface area above the imaginary slice at the specified level. It’s a surprisingly useful measure when calculating material needs for a dome.

Volume. The level volume is the total cubic volume encompassed by the remaining structure above the specified level.

Top portion of prolate ellipsoid dome

This unusual shape is the top portion of a highly elliptical prolate ellipsoid. Input a small horizontal radius, large vertical radius, and a height less than the vertical radius. Click for the live version of this design.

Overlays

An overlay is a scaled illustration to help convey the size, purpose, and scope of the calculated structure. They are for convenience only. No attempt is made to “fit” them inside the building or to determine their appropriate use for a structure. They are merely a visual aid.

None. The none option deletes the overlay.

Person. The person overlay is the default overlay. It is a person rendered at 6-feet (1.8 m) tall.

Car. The car overlay is a mid-sized sedan with a 6-foot (1.8 m) person standing beside it.

BBall. The bball overlay is the side silhouette of a standard American competition basketball court on a six-inch floor. We recommend setting the level parameter to 20.5 feet to show the standard clearance height required for a competition floor.

Loader. The loader overlay is a small front-end loader — 6,000 pounds (2800 kg) operating capacity with bucket — approximately 8 feet (2.5 m) tall next to a 6-foot (1.8 m) tall person.

Heavy. The heavy overlay is a large front-end loader — 66,000 pounds (30,000 kg) operating weight — approximately 12.5 feet (3.8 m) tall next to a 6-foot (1.8 m) tall person.

Highly-elliptical oblate ellipsoid

A highly-elliptical oblate ellipsoid with a tall height creates a wide ufo-like structure. The high ellipticity ratio — horizontal to vertical radius — of 2.00 can cause the Airform membrane to wrinkle a little at the equator. Click for the live version of this design.