Target range, the distance at which radar can clock a vehicle, depends upon radar model, target-vehicle cross section (frontal area), terrain, weather and a slew of lesser factors. For this reason there's a big disparity between theoretical target range and what's seen in the real world.
For example, when I first tested the Stalker Dual SL police radar, on a trip from Dallas to Denver, driving at night on Highway 287 in west Texas, target speeds appeared magically—with no vehicles in sight. Nothing. At length, headlights would pop into view far in the distance. A minute or so later, I would meet an 18-wheeler. Finally it was clear that the radar had targeted the trailer while the tractor headlights remained obscured by tiny hills between us.
The range was so extreme that, overcome by curiosity, when the next target speed appeared, I punched the trip odometer reset button. As the 18-wheeler and I met, I noted the mileage and repeated this half a dozen times to get an average. Target range on a conventional-cab Peterbilt 379-style tractor pulling a box trailer: 2.1 miles.
Practical radar range is far less, often no more than a quarter-mile and sometimes less than 700 feet, at least if the officer is following the rules.
That's because before using any type of speed-measuring hardware to check speeds, radar case law dictates that the officer must first witness the violation—speed in this case—identify the vehicle and visually estimate the target's speed. Only then should he activate his radar to confirm the estimated speed.
Most police officers believe that radar detectors are ineffective. And in a confrontation with instant-on radar, they're right—the cops usually win.