What is the mileage radius that a rainbow can be seen?

Rainbows are a “prism effect” in the raindrops, so the rainbow will move with where the person is observing the rainbow. That is why you can never get to the end of the rainbow for the “Gold”.

The distance is usually only a couple of miles, but will appear in different places for multiple observers.

For an observer on the ground with eye level at h = 5 ft 7 in (1.70 m), the horizon is at a distance of 2.9 miles (4.7 km). For an observer standing on a hill or tower 100 feet (30 m) in height, the horizon is at a distance of 12.2 miles (19.6 km). (from Wikipedia)

Since the rainbow is simply a prismatic view of water vapor, it must end at the horizon since we cannot see around the curvature of the earth.

So for a person on the ground at sea level, around 3 miles.

There is no “same” rainbow for everyone. Each observer has their own rainbow. Nor is the rainbow you see necessarily located at a specific distance from you. Some of the refracting droplets may be yards away, some miles away, but they all contribute to build “your” rainbow.

It’s a matter of angle, not distance. If the sun is unobstructed, low to the horizon and at your back, and if there is some mist-producing phenomenon somewhere out in front of you (whether it be a weather system or a waterfall or a sprinkler), you stand a good chance of seeing a rainbow provided that you are directly in the line between the sun and the mist. If you were a little out of line, the rainbow would disappear.

So whether someone at a distance would also be seeing a rainbow at the same time as you would depend entirely on how big the mist-producing phenomenon is. A rainstorm is big, so someone far to your right or left could still be in a direct line between the sun and the storm.

It cannot be a radius, since only people with the sun behind them can see it. People with the sun in front of them will not see a rainbow but only rain.