Take length x width x 1.5 divided by the wattage of the fixtures you want to use.

You can have too many recessed lights and end up creating an overly bright kitchen, which is definitely not what you want! It's good that you have some other sources of light, too, so you can have layers.

We have some guidelines for spacing recessed lights correctly that you can use in tandem with the advice provided by sooz001!

@Merry Recessed lights vary greatly in their output, so be sure you understand HOW much light YOUR particular ones put out. Even hook one up as a trial run (like in your basement) just to SEE for yourself HOW bright it is. Be sure to place them in the correct position in relation to your work area and not too far out into the room so that YOU cause yourself to cast a shadow over the very space you were trying to illuminate! Online guides CAN be very helpful! :)

@ Lights online.... well done! :)

@Cabinets 4U I believe many of us find it supremely irritating to see someone post in every dilemma the same cut-and-paste sentence and link. Grossly obvious self-promotion isn't always the best path to go, IMHO.