How much is a battery for a iPhone 13

“If your battery has an issue that's covered by the Apple Limited Warranty, AppleCare+, or consumer law, we'll service your iPhone at no additional cost. Our warranty doesn’t cover batteries that wear down from normal use. If your battery wears down, we offer out-of-warranty battery service for a fee. If you have AppleCare+, it covers your iPhone for no additional charge if your product's battery holds less than 80 percent of its original capacity. We might need to test your product to find the cause of your battery issue.”

iPhone Repair - Official

Hi,

Pricing for battery service can vary, and is based on a few different factors. 

I would recommend contacting Apple Support to start a service request for your iPhone, determine the best service options for you, and confirm if battery service is needed to resolve your issue. 

To answer your question based on what information you have provided:

• iPhone 13 and iPhone 11 Out of Warranty pricing for battery service is 69 USD.
• If iPhone is covered by Limited Warranty or AppleCare+, and the battery issue has been confirmed, the battery service is free of charge. 

Resources

• Batteries - Maximizing Performance
• If you see 'Your iPhone battery may need to be serviced'
• iPhone Battery and Performance
• About genuine iPhone batteries
• iPhone Battery Replacement
• Get your iPhone, iPad, or iPod touch ready for service
• Apple Repair and Repair Status Check
• Repair Provider Verification
• Legal - Repair Terms and Conditions
• Legal - Hardware Warranties - Apple

Hope this helps!

Apple does not sell parts. You should allow them to service your battery.

iPhone Battery Replacement - Official Apple Support