I've made a similar circuit and omitted the base resistor prior to finding this schematic.

The circuit will operate an LED string around 14 watts, the power source is 2 amps and the transistor that requires the base resistor is a bc547, the voltage is 9 volts DC.

The output for the PIR is 3.2 volts.

I've searched for formulas and calculators but my calculations aren't matching up.

Can someone tell me the basic formula to nail down a base resistor for this project?

It works fine without the base resistor but I want to do it right.

Thanks.

Kevin.