The math is fairly simple. There are two cases: viral and non-viral.<p>The viral case is when the value you can offer to paying customers actually increases as more free users join the system. In this case, the free users are the resource and as long as the revenue you can extract from their added value exceeds the cost to support them, you can do freemium profitably.<p>The second case is non-viral and is where most people are. Here, the basic premise is that the free users may A) become paying customers or B) attract paying customers through word-of-mouth/scale halo effect.<p>In both cases, you need to estimate the lifetime cost of a free user. Even if it's only $0.25 per year, it will be <i>something</i> and is important. You will also need to estimate the lifetime profit of a customer (lifetime value minus lifetime cost). Don't forget user/customer support costs and overhead.<p>For case 2A, you then calculate the conversion rate for free users. If the lifetime profit of a customer exceeds the lifetime cost of a free user divided by the conversion rate, you win. If not, free users are a drag on profitability and not worth it.<p>For case 2B, you again calculate the lifetime profit of a customer and compare vs the lifetime cost of free users divided by the expected referral rate free users generate. If the profit exceeds the referral cost, you win. Otherwise, again, free users are not worth it.<p>Obviously, the above is very rough overview, and in real life there are many additional complexities. There are various ways these cases may mix, the functions may not be linear, etc. But in the end, it's just math and you can guestimate if freemium is economical for your business.