Chance of a Hit by Pull Count (At Least 1)
| Pulls | At least 1 | Zero | Expected |
|---|---|---|---|
| 1 | 3.00% | 97.0% | 0.03 |
| 10 | 26.3% | 73.7% | 0.30 |
| 30 | 59.9% | 40.1% | 0.90 |
| 50 | 78.2% | 21.8% | 1.50 |
| 100 | 95.2% | 4.76% | 3.00 |
| 150 | 99.0% | 1.04% | 4.50 |
| 200 | 99.8% | 0.23% | 6.00 |
| 300 | >99.9% | 0.01% | 9.00 |
| 500 | >99.9% | <0.01% | 15.00 |
What the Gacha Probability Calculator Does
Enter a drop rate and a number of pulls, and this calculator gives you the theoretical chance of landing what you want. Unlike a simulator that rolls random pulls, it shows the exact value from the formula.
A common misreading is "3% rate, so 100 pulls gives me 3 copies." Three is the average; about 5% of players get nothing at all. This tool shows the expected count next to the probability of at least one hit, so you can see the realistic line before you spend.
Gacha Probability Formula: Chance of a Hit in n Pulls
Assuming each pull is independent, the chance of zero hits in n pulls is (1−p)^n. One minus that is the probability of at least one hit. At a 0.7% rate over 100 pulls: 1 − 0.993^100 ≈ 50.4%.
The k-or-more probability uses the binomial distribution: sum the chance of exactly i hits for i = 0 through k−1, then subtract from 1. "Pulls for 50% of players" is the smallest n where the failure rate (1−p)^n drops below 0.5, i.e. ceil(ln(0.5) / ln(1−p)).
Pulls Needed by Drop Rate: Quick Reference (0.5% to 5%)
For common drop rates, here are the pulls at which 50%, 90% and 99% of players have at least one hit, plus the chance of zero hits in 100 pulls. Find the row closest to your rate for a quick no-pity estimate.
| Rate | 50% | 90% | 99% | Zero in 100 |
|---|---|---|---|---|
| 0.5% | 139 | 460 | 919 | 60.6% |
| 0.7% | 99 | 328 | 656 | 49.5% |
| 1% | 69 | 230 | 459 | 36.6% |
| 2% | 35 | 114 | 228 | 13.3% |
| 3% | 23 | 76 | 152 | 4.8% |
| 5% | 14 | 45 | 90 | 0.6% |
Theoretical values with no pity and a 100% rate-up share.
Calculating with Pity, Rate-Up Share, and Cost
Chance of hitting before pity and pity-capped pulls needed
Enter a pity count and the probability becomes 100% at that many pulls; the pulls-needed figures are capped there too. The tool also shows the chance of hitting before pity, which helps you decide whether to save up for a guaranteed pull.
Effective drop rate from the rate-up share
This is the share of top-rarity drops that go to your target unit. A 3% top-rarity rate with a 50% share is calculated as an effective 1.5%. If your game publishes an explicit rate for the featured unit, enter that as the rate and leave the share at 100.
Cost per pull: gems or money needed
Enter a gem count or currency amount and cost appears alongside the pull-count table and pulls-needed figures. Any unit works — gems per pull, or a 10-pull price divided by ten.
Gacha Calculator vs. Gacha Simulator
Use this calculator to learn how many pulls you need for a given confidence; use the Gacha Simulator to feel how streaky real luck is. Get the target number here first, then check the variance in the simulator.