My well water pump comes on even when I'm not using water in the house. Is this normal?

No This is a sign of a leak. The reason the pump goes on is because your pressure is dropping to or below turn on pressure.

Check your toilets and outside faucets.

Chuck

Thank you! That's a big help, now I know I need to call a plumber.

The checks I have recommended are visual and can be done by u before calling a plumber.

It my be an easy fix.

Chuck

Chuck is right, a leaking toilet possibly. Put 10 drops of red or blue food coloring in the toilet tank, not the bowl, swish it around and wait awhile and look in the bowl. Is the water colored? If so, you need to replace the flapper and possibly the seat too. If this is a pump with a foot valve, you may have a leak there too. Hope for a toilet, $10 DIY job. If you are on a slab, look for wet ground around the edge and if you are on a crawl, look for drips there. Basements are fairly easy to see.

Yes, I will do that first. Thanks

Just be aware that the leak could be wellpipe or a checkvalve. Hopefully, it will be something in the house. Much easier to deal with.