Dome template generator: printable gores for a dome or a hemisphere in paper, EVA foam or sheet metal

A dome cannot be cut from one flat sheet: a sphere does not unroll. It is built from gores, the long pointed panels of a globe or a beach ball, each one running from the top to the base. This page draws the gore for any dome, from a shallow cap to a full hemisphere, in any number of gores, and prints it at full size on A4 or Letter: for a paper or cardboard model, an EVA foam helmet or armour piece, a lamp shade, or a sheet metal dome.

It is the same layout as the spherical head in gores, which adds the crown plate, the plate thickness on both faces and the DXF for the cutting table. Everything here runs in your browser: nothing to install and no account.

Dome template generator

Type the diameter of the dome at its base and its height: half the diameter for a hemisphere, less for a shallower dome. Pick the number of gores and, for foam or sheet, the thickness. Print gives one gore at 1:1; cut as many as there are gores.

Embed this calculator on your site

Free, and it works on any site: paste the code where you want the calculator. It links back to this guide.

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How to use the template

1. Print at actual size, 100 %, with no fit-to-page, and measure the check bar on the sheet: it must read 100 mm or 4 in. Glue the sheets on the repeated strip when the gore took more than one.
2. Cut out the gore and trace it as many times as there are gores. Mark the centre line on each: it is the true length from the top to the base.
3. Join the gores edge to edge, from the base up: glue for paper and foam, tape or tabs for card, tack welds for sheet. The tips meet at the top.
4. The edges come out slightly longer than the centre line (3.84 % with 8 gores on a hemisphere, 1.71 % with 12): ease them as you go, and the dome closes. More gores give a rounder dome and less to ease.
5. For a whole ball, make two hemispheres and join them at the equator.

The formula

Take D as the diameter of the dome at the base and h as its height. The sphere radius, and the angle from the top to the base, are

Sphere radius and angle

R = (D²/4 + h²) / (2h) ; θ0 = arccos((R − h) / R) For a hemisphere h = D/2, R = D/2 and θ0 = 90°. With a thickness t, the gore is worked on the middle of the material: R − t/2.

The gore at each station

length along the centre line = R × θ ; half width = π × R × sin θ / n θ runs from 0 at the top to θ0 at the base, and n is the number of gores. The half width is measured along the station, which is an arc of radius R × tan θ centred on the centre line, on the side of the tip: the parallel of the sphere unrolled on the cone that touches it there.

That is the layout the boilermaking books give for a spherical head, and it puts the base of each gore on the base circle of the dome. The area comes out a little over the sphere's and the edges a little longer than the centre line; the material takes it up as it is joined.

Worked example

A 600 mm hemisphere (D = 600, h = 300) in paper, in 8 gores:

1. R = (600²/4 + 300²) / 600 = 300 mm, and θ0 = 90°.
2. The gore is π × 300 / 2 = 471.2 mm long, from the tip to the base.
3. At the base it is 2 × π × 300 / 8 = 235.6 mm wide, and the edge is 489.3 mm long, 3.84 % over the centre line.

How many gores

More gores make a rounder dome, narrower panels and less to ease at the edges. For a 600 mm hemisphere:

A shallow dome eases less: a 1000 mm dome 250 mm high in 1 mm sheet, in 12 gores, has gores 579.1 mm long and 260.5 mm wide at the base, with the edge 0.82 % over the centre line.

For EVA foam, measure the dome on the outside and type the foam thickness: a 400 mm hemisphere in 10 mm foam, in 6 gores, works on a 195 mm radius, with gores 306.3 mm long and 204.2 mm wide.

Frequently asked questions

How do you make a dome template?

Work out one gore: its length along the centre line is the sphere's arc from the top to the base, and its width at each height is the circle at that height divided by the number of gores. The generator above does it from the diameter and the height, and prints the gore at full size.

How many gores does a hemisphere need?

Six is the fewest that look round; 8 to 12 is usual. On a 600 mm hemisphere, 8 gores are 235.6 mm wide at the base and 12 gores 157.1 mm, with the edges 3.84 % and 1.71 % longer than the centre line.

How do I make a dome out of EVA foam?

Type the outside diameter and height of the dome and the foam thickness, print the gore, cut it as many times as there are gores and glue the edges with contact cement, from the base up. Heat the foam lightly so the gores take the curve.

Can I make a full ball?

Make two hemispheres with the same diameter and gores and join them at the equator: each gore of one meets a gore of the other.

Does the template work for sheet metal?

Yes: type the plate thickness and the gore is worked on the middle of the plate. For a head on a tank, with a crown plate and the DXF, use the spherical head in gores.