Mapbox does not currently provide the ability to cap your monthly billing. For now, the best way to create predictable monthly API usage is by monitoring your account statistics and your invoices.
Once your account statistics and/or invoices reach a level where you'd like to be capped, you can:
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Delete your access tokens from your tokens page (deactivating any mapping implementations that were authenticated by that access token). Or,
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Remove your access tokens from your code. Where you see our map initialization code block occurs depends on your implementation. You can temporarily remove your access tokens so that no traffic authenticates.
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When you're ready to accrue map traffic again, you can add the access token back into your map code will reactivate the maps.
For more information about your account statistics or invoices, check out our Accounts Documentation.