How far can a radio transmit? There are many factors that go into the answer. The advertised distance of a radio is usually theoretical distances; a distance achieved in optimal conditions. Very similar to the miles per gallon ratings of new cars. How much do you believe in those?
The distance a radio wave can travel depends highly on the frequency being used, the water vapor in the air, ionization in the upper atmosphere, and interference from other sources.
Propagation: VHF and higher frequencies
Light of sight is a common term used with VHF and higher frequency radios. This means that radio waves are not bent by the atmosphere. The radio waves cannot follow the curvature of the Earth. If the Earth’s surface was perfectly smooth (like if you were on water) and you were not standing on anything, you could see about 3 miles. Moving up to a height of 500 feet and you’ll see 27 miles. Granted, this is assuming perfect atmospheric conditions. If the thing you are looking for is elevated, then factor in their height too. Theoretically, a 6-foot person (with binoculars) should be able to see the head of another 6-foot tall person six miles away.
A handheld radio would follow this same theory. The good news is that most public safety antenna towers are tall. If the radio was held at 6 feet and was transmitting to a 500-foot high tower, then the maximum range would be about 30 miles. 27 miles for the tower + 3 miles for the person = maximum possible range.
Cell phones operate at frequencies higher then VHF, so they are all line of sight.
Propagation: Below VHF frequencies
These radio frequencies bounce off the upper atmosphere and are directed back to Earth. For most users, this is enough of a description to get a visual of what’s occurring. The actual process is that the ionosphere is refracting the radio waves similar to how a glass of water makes a straw look bent. When the sun is shining on the atmosphere, it changes the characteristics of the ionosphere to increase the radio wave’s signal loss. At night, the characteristics of the atmosphere become more favorable for radio waves. This is why you can hear more distance radio stations at night, and pick up shortwave (HF) radio stations from other countries more at night.
A radio wave that is bouncing off the atmosphere creates skip zones. A radio transmitting from Washington, DC to San Diego, CA successfully doesn’t mean that the radio waves will be heard in Kansas City, MO. The radio waves may be refracting in the upper atmosphere over Kansas and not near the ground where they can be received.
A lot of very smart people have posted other information about calculating exact radio distance based on power, antenna height, frequency, time of day, weather and so on. Here is just enough information to get your feet wet.
Understanding propagation: http://www.hamqsl.com/Understanding%20Propagation.pdf
US Navy propagation explanation: http://www.fas.org/man/dod-101/navy/docs/es310/propagat/Propagat.htm