Bought a new battery, do I need to calibrate it?

No

Calibration of batteries (Li Ion or Li Po, used in almost all mobile devices) is a myth

You can start using it straight away and charge as you normally did with earlier batteries

This post will help you understand more:

Looking for a consistent answer about battery calibration

Using calibration apps doesn't really help as the battery files in system (to which these apps write) are renewed and previous data erased when you charge / reboot

As explained in this article

It [Batterystats.bin file which stores calibration information] has no impact on the current battery level shown to you.
It has no impact on your battery life.......it is reset every time you unplug from power with a relatively full charge (thus why the battery usage UI data resets at that point)...

Explanation in Italics mine from the same article

Related Myth : Charging a new battery for X hours

Charging a new battery for x hours before use is a "legacy hangover" from the days when Nickel Cadmium batteries were used. Those batteries had a "memory effect". As a result, over a period of time, they "remembered" lesser battery capacity than rated capacity. To prevent this, it was advised to always fully charge these batteries

• This is not the case with Lithium Ion or Lithium polymer batteries. There is no logic to charge fully or x hours before use. Just use the battery normally, as suggested by others in comments




• Table 1 corroborates with additional information