Here's from the National Health Service website (United Kingdom) on the topic:
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Metformin will not affect the combined pill or emergency contraception.
But you might need a small adjustment in your metformin dose after starting contraceptive pills.
That's because contraceptive pills change how your body handles sugar.
However, if metformin makes you vomit or have severe diarrhoea for more than 24 hours, your contraceptive pills may not protect you from pregnancy. Check the pill packet to find out what to do.
Find out more about what to do if you're on the pill and you're being sick or have diarrhoea.
Your pharmacist should know the answer.