They aren't. They're circles (or they would be, if rain were falling throughout your field of view).

A rainbow appears in a circle of a particular size (the size has to do with the refractive index of water, so it's the same for all rainbows) centered around a point opposite the Sun in the sky (the "antisolar point"). But since the Sun has to be up for a rainbow to appear, the antisolar point is necessarily below the horizon, so less than half the rainbow is visible if you're on a flat surface.

If you're in a position where there can be rain "below" the horizon in your sky (as if, for example, you're in a plane or on top of a high mountain), you can sometimes see the full circle of the rainbow. But most people live on approximately flat surfaces or at the bottom of valleys, not near the tops of steep hills, and it's hard to get the geometry right to have the Sun above you and the rain below, so rainbows are normally just small portions of a circle.

They are actually circular.

The thing is they appear as a circle with the center being in the exact opposite side of your head from where the sun is.

If you look at a rainbow the sun is behind you and the center of the rainbow is exactly on the opposite side of where you head is.

There is a line from the sun, though your skull to the apparent center of the rainbow.

Obviously since the sun tends to be in the sky, the center of the rainbow tends to be below the horizon.

If you are high up in an airplane or similar you may be able to see the full circular rainbow if the sun is low enough.

The sun shines at the water droplets in the air and due to the way light going from air to water and back works part of it ends up back where it came from. Sort of like a mirror.

So if you just had a single color of light shining at water droplet in the air from behind you, you would see a single thin ring of that color.

Since different wavelengths of light get thrown back at slightly different angles you don't see just one white ring but a spectrum of visible light drawn out across the rainbow

It works light a prism splitting up light into a rainbow of colors when the light goes from air to glass and back to air and the surfaces where the glass to air interface are, are at an angle.

The raindrops are made of water not glass and they are spherical not prism shaped, but it is the same general principle.

The spherical shape also means that the light acts the same way in any direction all raindrops that are at a certain angle from the line from the sun through you will send the light back at you.

That angle is about 42°.

There are additional fainter rainbows at different angles that you don't really see easily with your eyes, but that can appear on photographs.

I saw full rainbow circles while flying a little Cessna around 5000’ above the ground. It was a memorable experience.

Rainbows happen when light from the sun behind you hits water droplets in front of you, and gets bent back towards you. The places where the light of each wavelength gets bent by the right amount to reach your eyes are in a circle around the line from the sun through your head. So what you see is however much of a circle as the landscape around you allows - usually about half a circle. And different colours get bent by different lines amounts, so the colours get smeared out into circles of different widths.

It's possible to see a full circular rainbow under the right conditions (say, from a plane or high-enough ground); there are photos out there. Google it.

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Others are saying that they're circular, which they kind of are, but only in 2D. Rainbows are cones, with you at the point (and the centre of the cone lining up with your eyes and the Sun).

When you look at a rainbow, you're seeing light being reflected through water droplets that are somewhere in that cone. So it could be that two parts of the rainbow you see that are right next to each other are from water droplets miles apart, if some are much closer and some much further away.

The reason why they are cones involves a bit of physics and a bunch of geometry. Essentially the light from the Sun hits the raindrops and gets scattered out in all directions at an angle of about 40 degrees (that is just a 2D slice, imagine it being rotated around). So the scattered light comes out in a cone from each raindrop, and by geometry and symmetry, the light from a bunch of different raindrops that hits any given point (i.e. your eyes) forms a cone of itself.

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