How is the expected number of attempts calculated?

Each attempt is an independent trial with a fixed success chance p. The expected number of attempts to get one success follows a geometric distribution with mean 1/p. For 25 percent odds that averages four attempts per level.

Why does the cost grow so fast at low success rates?

Expected cost is attempts multiplied by per-attempt cost. Because expected attempts scale as 1/p, halving the success rate doubles both the average attempts and the average spend, which is why rare enchants are so expensive.

What does the within-budget probability mean?

It is the chance of landing at least one success within the number of attempts your budget buys. It uses the cumulative geometric formula 1 minus (1 minus p) to the power of N, so you can see how likely a fixed budget is to pay off.

Are these the exact in-game numbers?

Path of Exile enchant odds vary by league, item, and method, so you supply the per-attempt success rate yourself. The maths is exact for whatever probability you enter, which makes it accurate for any source you trust.

Does this account for multiple enchant levels?

Yes. For independent levels the expected attempts is simply your target levels divided by the per-attempt success chance, and the tool sums the expected cost across all of them.

Path of Exile Enchant & Gear Score Calculator

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Path of Exile’s enchanting and crafting are governed by probability, not guaranteed progress. This calculator turns a per-attempt success rate into the numbers that actually matter: how many tries you should expect, what that will cost in currency, and how likely a fixed budget is to get you there.

How it works

Each enchant attempt is an independent Bernoulli trial with success chance p. The maths follows the geometric distribution:

expected attempts per success = 1 / p
expected total attempts       = target levels / p
expected total cost           = expected total attempts × cost per attempt
chance within N attempts       = 1 − (1 − p)^N

Because expected attempts scale with 1 / p, low-probability enchants cost dramatically more on average than their nominal odds suggest.

Example and tips

At a 20 percent success rate, one enchant level averages five attempts. To gain three levels you should budget for about fifteen attempts on average — but variance is high, so set the “budget attempts” field to see your real odds of finishing within a cap. If the within-budget chance is below 50 percent, plan to buy more currency before you start.