If it's an activity that you scheduled or approved, and you had time to notice that traffic might cause the delay, you should pay. If it's just the park or library, and it's because she's not getting in the car faster, suggest that she set an alarm on her phone.

I would be annoyed because if it happens frequently then it’s getting in the way of my plans for the kid. Even if it’s just dinner and family time, it would bother me.

I wouldn’t pay for the inconvenience.

Do talk to her and ask that she be on time. After that, stop paying.

I'm a nanny and don't expect to get paid under that circumstance. I once took the kids on a special outing very far away and underestimated the timing and how long we'd spend there and texted the parents to see if it was OK to be an hour late. I said I wouldn't charge for the hour since it was my poor planning that caused it and they said it was fine and insisted on paying me for that time. So,..not expected, but it does build good will.

No, you should not pay her. She should be on time.

And I'm a nanny

Ok. Thank you both!

I do not expect to be paid if I am running late. If it’s a scheduled activity or a trip to someplace farther, then I expect to be paid.

No

I have three children. The older two are in school, and I work during the school day two days a week while my sitter watches my youngest child. Every now and again, my babysitter is late getting my son back home by the end of her shift. I guess they are out at the playground or whatever and having a good time, and she gets home late.
Am I supposed to pay her for this time? It isn’t that much money, maybe $30/month. But it’s more the principle of it.