A weighted average is not the average of the prices
A position bought in more than one lot still has a single price, and that price is not the halfway point between the prices paid. Buying 100 units at 50 and then 400 units at 45 does not leave an average of 47.50. It leaves 46.00, because four times as many units sit behind the lower price. The weighted average multiplies each price by the units bought at it, adds those products together, and divides by the total units held. A price counts only in proportion to the units bought there.
That is why the weight of each lot is worth reading before the average itself. A lot holding 8% of the units barely moves the number whatever it was bought at; a lot holding 60% of them very nearly is the position. This page also runs the calculation the other way: name the price of a new purchase and the average you want to end at, and it returns the units that would get there — the exact figure, before any rounding to a whole unit.
The risk is measured from the average, not from the first entry
Once a position has been built in pieces, the price of the first purchase stops being a useful reference. There is one stop, one total size, and what that stop costs is the distance from the average to it multiplied by every unit held — not by the units of the opening lot. Reading the risk from the first entry understates it whenever the later lots were bought further from the stop, and understates it by more the larger those lots are.
That distance is the figure this page returns once a stop and a direction are filled in, and it is the same distance a sizing calculation begins from. Our position size calculator runs it in the other direction: from the account and the risk budget to the units a given stop allows. One measures the gap before the position exists; the other after it has already been added to.
Two ways to reach the same average
Two different actions produce identical arithmetic. In the first, the lots were decided before anything was bought: a size split into three, with the prices and the stop written down in advance, so each purchase is a step in a plan already made. In the second, the position was opened as a single lot, at a size chosen for that lot alone, the price moved, and the further purchases were decided afterwards.
The calculator cannot tell the two apart, and neither can the average it returns. What separates them is the stop. A scale-in planned in advance leaves the stop where the plan put it and the total risk inside the budget, because the size of every lot was chosen with that stop already in mind. Where the additions were decided afterwards, the stop is either left where the first lot put it while the units grow, or moved further away so the larger position fits — and either way the money at risk is no longer the figure it was at the opening.
Whether that number is still acceptable is not a question about one position on its own. It depends on what the rest of the account already has at stake at the same time, which is the sum our portfolio heat calculator adds up.
What happens to the size while the average moves
Every added lot does two things at once, and they point in opposite directions. It pulls the average toward the price paid, which brings the level where the position is flat closer to the market. It also raises the unit count and the capital committed, and with them what a stop would cost. The table above holds the stop still and adds equal lots at lower prices: the average falls from 50 to 40 while the risk to that same stop climbs from 2,200 to 6,000. Neither number moves without the other.
The level where the position is flat is not quite the average, either. Commission and spread are charged on each lot separately, so a position built in five pieces has paid five entry costs against the single exit still to come. Our break-even calculator adds those costs to the average this page returns.
How to read each number
The headline is the weighted average in the first mode and the units to add in the second. Units held and total cost describe the position as it stands: the cost is what has been paid in, not what the position is worth now. The weight of each lot is its share of the units, and so the share of the average it controls. With a stop filled in, money at risk is that distance across every unit, the share of the position turns it into a percentage of the capital committed, and the distance to the stop restates the same gap as a percentage of the average.
