If your vehicle is showing radiator cooling fan runs constantly at maximum speed, here are the most likely causes and the parts you'll need to fix each one.
If the engine computer loses the signal from the coolant temperature sensor, it enters a fail-safe mode and runs the fan at maximum speed to prevent potential overheating. This is highly common if the sensor is accidentally left unplugged after recent engine work.
The electrical relay that switches power to the fan can have its internal contacts weld together from electrical arcing over time. This causes the fan to receive constant power, sometimes even when the vehicle is turned off.
Many modern vehicles use a solid-state control module to vary fan speed rather than a simple relay. When this module shorts out internally, it typically defaults to running the fan at full blast continuously.
The engine computer monitors A/C system pressure and turns the fan on high to cool the condenser when pressure rises. A faulty switch that falsely reports extreme high pressure will force the fan to run constantly.
The fan may simply be doing its job because the engine is actually running too hot. This can be caused by low coolant, a stuck thermostat, or poor coolant circulation.