# Calculate revenue from the margin and profit

Let's say I have a profit of $$50$$ and a margin of $$50\%$$.

Now I know that the revenue is $$150$$, despite not knowing the cost, because this is the only possibility for the $$50\%$$ margin i.e.

$$Cost * (1 + Margin) = Revenue$$

$$100 * (1 + 0.5) = 150$$

Now, what would the formula be to get the revenue by just knowing the $$50\%$$ margin and the $$50$$ profit?

• Does COGS mean Cost?
– lulu
Commented Jul 9, 2021 at 2:05
• Yes, Cost Of Goods Sold Commented Jul 9, 2021 at 2:08
• Ok. Well, letting C=Cost, R=Revenue. Then the Margin is $R-C$ so you'd have $R-C=50$ and $R-C=\frac C2$. Can you finish from there?
– lulu
Commented Jul 9, 2021 at 2:10
• I'm afraid I didn't get what you're aiming at... Commented Jul 9, 2021 at 2:19

Let ...

• $$c$$ represent Cost
• $$m$$ represent Margin
• $$r$$ represent Revenue
• $$p =r-c$$ represent Profit

Your formula is $$c(1+m)=r$$ you want to express this using $$p$$ instead of $$c$$

so substitute $$(r-p)$$ for $$c$$ $$(r-p)(1+m) = r$$

now isolate $$r$$ $$r(1+m)-r = p(1+m)$$ obtain the result $$r = p\bigg(\frac{1+m}m \bigg ) = p \left ( 1+\frac 1m \right )$$

in your case $$m=0.5$$ so $$\frac 1m = 2$$ and you get $$r = 50(1+2)=150$$

• Oh your formula is better than the one I posted. Thank you for the explanation. Commented Jul 9, 2021 at 2:37

I found an old calculation of mine. The formula is:

\begin{align} Revenue = \frac{Profit}{1 - \frac{1}{1 + Margin}}\end{align}

• That is the same formula that I got in a different form
– WW1
Commented Jul 9, 2021 at 2:37
• Yes, way cleaner than mine. Thank you. Commented Jul 9, 2021 at 2:38
• I strongly recommend that whenever you want to do algebra, name your variables as single letters rather than words, it makes it much easier to see the mathematical structure of a formula. I find it quite shocking how much more difficult it is to do algebra with words instead of letters, it feels almost like a right handed person trying to write with their left hand.
– WW1
Commented Jul 9, 2021 at 2:55