Perhaps the safest way to determine that, and increase your likelihood of significance outcomes, is to do a power calculation based upon your principle outcome measurement, and your expected magnitude of effect (based upon previous literature).
To determine that, you can use some power calculation software. For using this software like (G*power), as Dr. Hackney mentioned, you need to know expected magnitude of effect (based upon previous studies). this kind of software can be handy to calculate your power and sample size of your sample. Anthony C. Hackney Raja Ili Airina Raja Khalif
Using 'power of test' as a search term in google, I found at least one online calculator for sample size: https://www.stat.ubc.ca/~rollin/stats/ssize/n2.html.
The calculator requests the input values it needs and provides input areas for the values. More info can be found in statistics books such as the one by Steel and Torrie and the one by Snedecor and Cochran (I think my spelling right)