There is a service for that called Tweriod. You can use their free service to gather various information.
Tweriod the free twitter tool that helps you make the most of Twitter by letting you know the best time to tweet. It also includes:
This free service works great with Buffer - so you can time your tweets perfectly and beware that timing may change during different seasons.
Check out the Tweriod today and see how your tweets can be timed for your followers and your tweets - You just sign in with your Twitter username and off your go, they will analyze your account and send you an email with the results.
Remember don't leave all your social media to social media science, you do need to be social on the social networks. After all isn't that what social networking is all about - being social?