how does a new credit card impact my credit score?

It will likely lower by a small amount. It's tough to know by how much without knowing more about you than you should post here. However, you can get a good feel for how much by searching online for "credit score estimator" and trying out a before/after calculation on your credit score.

Adding a card gives you a hard inquiry as you know. It also reduces your average account life, which is best when over 9 years. Both will impact your score a bit.

Last, while not really a function of the score, it becomes part of your available credit. This may seem obvious, but a bank that's about to lend you money, for a mortgage, for example, will look at the total credit you can tap, and take it into account, regardless if you are actually using the cards.

Applying for a new credit card can hurt your credit score a little. According to FICO, when a card issuer pulls your credit after you apply for a new credit card - it can lower your credit score by 5 points or less.

However, the impact is temporary. Hard pulls stay on your credit report for two years, but their credit score effects wear off after one year. Though the credit score impact of a single card application can be small, too many of them in a short amount of time can add up to a significant loss.

This should help you solve your query.