# Calculating the position size knowing only the loss, buy and sale price.

Say I buy 1000 items of something (position size) at the price of 2500 and I then sell them again for 2000, I incur a loss of 200.

So, my calculation so far is:

1000/2500 = 0.4
0.4*2000 = 800

Loss: \$200


Now, the problem I am facing is ...I want to pre-define the loss, buy and sale price and I need to calculate the amount of items (position size). So basically the whole calculation in reverse, while NOT knowing the value of 1000.

How would I do that? Any help is greatly appreciated :)

I must say I don't understand your calculation in the first place. If you bought something ($$1000$$ items or whatever) for $$\2500$$ and sold them all for $$\2000$$, isn't the loss $$\500$$? Or if the price was per item, isn't the loss $$\500$$ per item, i.e. $$\500\times 1000=\500,000$$ altogether?

Your calculation only makes sense to interpret as "you spent $$\1000$$ to buy something that costs $$\2500$$ per item, and then sold it for $$\2000$$ per item, how much did you lose? With that interpretation, let $$P$$ be the position, $$B$$ be the buying price, $$S$$ be the selling price and $$L$$ the loss. Your calculation is, basically:

$$L=P-\frac{P}{B}S=P\left(1-\frac{S}{B}\right)=P\frac{B-S}{B}$$

which then yields:

$$P=L\frac{B}{B-S}$$

In our case:

$$\200\times\frac{\2500}{\2500-\2000}=\200\times\frac{\2500}{\500}=\200\times 5=\1000$$