The cheaper single tube dosimeters will max out and saturate at radiation levels far below those that are immediately harmful to human health. (This was the source of the famous "3.6 roentgen per hour, not great, not terrible" meme-- he was looking at a meter that was reading off-scale high at 0.001 R/s)
If you're buying a dosimeter with the threat in nuclear war in mind, check the specs for maximum readings.