The math behind it

Three formulas draw the whole chart. Here they are in full, so you can check them against your own numbers rather than taking the tool on trust.

How the line is built

1 · Contribution margin

What's left of one order after the product, the shipping, the gateway fee and the returns:

CM = (1 − refund%) × (AOV − COGS)
     − shipping − gateway fee

Returned orders give the product back but you still ate the shipping and the processing fee.

2 · The break-even line

Revenue × margin must cover the ad spend and every fixed cost:

ROAS = (spend × (1+fee) + fixed)
       ÷ (spend × CM%)

Every point on that line is a spend/ROAS pair that lands exactly on zero. CPP = AOV ÷ ROAS, so the same line is a CPP ceiling too.

3 · Why it curves

Rewrite it and the shape is obvious:

ROAS = (1+fee)/CM% × (1 + fixed/spend)

Double the spend and you halve the fixed-cost penalty. The line decays toward the floor but never touches it. Scale makes the target easier, never free.

Assumptions: ROAS is measured on gross revenue before returns, the way ad platforms report it. Fixed costs are treated as truly fixed across the spend range. If hiring or warehousing steps up at higher volume, raise the fixed-cost input in step 3 for that scenario. Everything is calculated in your browser; no numbers are sent anywhere.