Gaming calculators

Drop Chance Calculator

Updated Aug 18, 2026 By Jehan Wadia
Rate Formulas

Forward Calculator — Chance of At Least One Drop

Drop parameters
Chance of the item dropping on a single attempt (0.01–100).
How many kills, runs, rolls or pulls (1–100,000).
Pity system (guaranteed drop after N failures)
Guarantees a drop once you reach the pity attempt without one.
Attempt number at which a drop is guaranteed.
Pity Inactive

Your Drop Odds

Chance of at least one drop Pity Inactive
98.24%

With a 33% drop chance over 100 attempts, you have a 98.24% chance of getting at least one drop.

Rounding note: at extreme combinations (very low drop chance with a very large attempt count) floating-point arithmetic can display exactly 100%. True probability approaches but never reaches 100% with any finite number of attempts.

Expected attempts per drop
3.03
On average, you would expect 1 drop every 3.03 attempts.
Expected number of drops
33.00
Over 100 attempts, you can expect about 33.00 drops on average.
Step-by-Step Solution

Reverse Calculator — How Many Runs Do I Need?

Target odds
Capped at 99.99% — a true 100% is unattainable in any finite number of attempts.
Attempts required 6

You need at least 6 attempts for a 90% chance at a 33% drop rate.

Actual probability at that count
90.98%
Attempts are rounded up, so real odds slightly exceed the target.
Attempts for 99% certainty
12
A useful benchmark at this drop rate.

Probability Milestone Breakdown

Cumulative chance of at least one drop at a 33% drop rate across common attempt milestones. The row matching your current attempt count is highlighted.
Attempts Cumulative Probability Chance of Still Having Nothing Rating

Probability Growth Curve

Reference lines are drawn at 50% and 90%. The milestone table above provides the same data in text form.

Multiple Desired Drops (Binomial)

Binomial parameters
Calculation Mode
Probability of at least 2 drops 100.00%

Expected drops (n × p)
33.00
Mean of the binomial distribution.
Most likely outcome (mode)
33 drops
Probability of that exact count: 8.36%

Introduction

Ever farmed a boss 50 times and still got nothing? This Drop Chance Calculator tells you the real odds. Type in the item's drop rate and how many runs you plan to make. The tool shows your chance of getting at least one drop.

It works for any RPG or loot game — boss kills, chest opens, gacha pulls, dungeon runs, or rare mob farming. You can also turn on a pity system if your game gives a guaranteed drop after a set number of tries, the same way our Genshin Pity Calculator tracks banner counters.

The calculator gives you more than one number:

  • Drop odds: your chance of at least one drop over your runs.
  • Runs needed: how many tries to hit 90%, 99%, or any target you pick.
  • Average tries: how many attempts one drop usually takes.
  • Multiple drops: the odds of getting 2, 3, or more copies of the same item.
  • Charts and a table: see how your odds grow run after run.

One thing to know: your odds never truly reach 100%. A 1% drop can dodge you for 500 runs, and that is just bad luck, not a broken game. This tool shows you what to expect so you can plan your farming time instead of guessing. If you want the general math behind any random event, our Probability Calculator covers the basics.

How to use our Drop Chance Calculator

Enter your item's drop rate and how many runs you plan to do. The calculator shows your chance of getting at least one drop, how many attempts you need for a target chance, and your odds of getting several drops.

Drop Chance (%): Type the drop rate for one attempt, like 33 for a 1-in-3 item. You can use decimals, such as 0.05 for very rare loot. If your game lists the rate as a fraction like 1/128, convert it first with the Fraction to Percentage Calculator.

Number of Attempts: Type how many kills, runs, rolls, or pulls you will do. The calculator gives your total chance of at least one drop over all of them.

Enable Pity System: Turn this on if your game gives a guaranteed drop after a set number of misses. Leave it off for normal random drops.

Pity Threshold (attempts): Type the attempt number where the drop is promised, like 50. This box only works when the pity switch is on.

Reverse — Drop Chance (%): Type the same drop rate again to work out how many runs you need.

Desired Probability (%): Type the odds you want to reach, like 90. The tool tells you how many attempts that takes. You cannot pick 100%, since no amount of runs makes a drop certain.

Multiple Drops — Drop Chance (%): Type the drop rate for the item you want more than once.

Number of Attempts: Type how many runs you will make for this multi-drop check.

Number of Drops Desired: Type how many copies you want, like 2 for a second weapon or armor piece.

Calculation Mode: Pick "At least N drops" for that many or more. Pick "Exactly N drops" for that exact number and no other. Both modes use the same math as our Binomial Distribution Calculator.

Calculate and Reset: Press Calculate to update all results, charts, and the step-by-step math. Press Reset to put every box back to its starting value.

What Is a Drop Chance?

A drop chance (also called a drop rate) is how likely a game is to give you an item after one try. That try can be one boss kill, one dungeon run, one chest, or one gacha pull. A 5% drop rate means the game rolls a hidden number each time, and about 1 out of every 20 rolls gives you the item. It is the same style of hidden roll behind a shiny encounter or a Poké Ball catch check.

Why 20 Runs at 5% Does Not Mean You Get It

Each try is independent. The game does not remember your bad luck. Past failures do not make the next roll better. So the odds never add up to 100%. Instead, they stack like this: you find the chance of failing every single time, then flip it around.

The math is 1 − (1 − p)n, where p is the drop rate and n is the number of tries. If you want to see how that exponent behaves on its own, try it there. At a 5% rate over 20 runs, you have about a 64% chance of at least one drop — not a guarantee. About 36 out of 100 players still walk away empty-handed. That is normal, not a bug. RuneScape players can see the same effect measured in real logs with the OSRS Dry Calculator.

Expected Attempts and Expected Drops

The average number of tries per drop is 1 ÷ p. A 5% rate means about 20 tries on average. But "average" hides a lot. Some players get it on run 2, and some grind past run 60. The expected number of drops is tries × rate, so 100 runs at a 5% rate should give about 5 items. This is the same expected-value idea used in the EV Calculator, and it pairs well with a DPS Calculator when you are timing how long each run takes.

Pity Systems

Many modern games use a pity system to protect unlucky players. Once you hit a set number of failed tries, the item is handed to you for free. Games like Genshin Impact, Honkai: Star Rail, and Fire Emblem Heroes use this idea. With pity turned on, your odds climb to a true 100% once you reach the pity count. Without pity, you can grind forever and still get nothing. For banner planning and primogem budgeting, pair this page with the Genshin Wish Calculator and the Genshin Resin Calculator.

When You Need More Than One Copy

Some gear needs several copies to upgrade, craft, or fuse. That changes the math to a binomial problem: the chance of getting at least N drops, or exactly N drops, in a set number of runs. Needing 3 copies takes far more grinding than needing 1, so plan your farming time around the higher number. Card gamers face the same problem when drawing from a finite deck — for that, use the Hypergeometric Calculator, the Card Draw Calculator, or the MTG Probability Calculator.

Quick Tips for Grinding

  • Aim for the 90% or 99% mark, not 100%. True 100% never happens without pity.
  • Stack drop rate buffs, luck stats, or double-drop events before a long grind. A small rate boost saves many hours — check the gain with the Percentage Increase Calculator.
  • Pick the fastest run, not the highest rate. Ten quick 3% runs often beat one slow 10% run; a Time Duration Calculator helps you compare total farm time.
  • Bad streaks are expected. Rare items feel unfair because the odds are truly harsh, not because the game hates you.

Related Gaming and Probability Calculators

Formulas used

Chance of at least one drop in n attempts
P = 1 - (1-p)^{n}, \quad p = \frac{c}{100}
Pity-adjusted chance of at least one drop
P_{\text{pity}} = \begin{cases} 1 & \left\lfloor \frac{n}{t} \right\rfloor \ge 1 \\ 1 - (1-p)^{\,n \bmod t} & \text{otherwise} \end{cases}
Expected attempts per drop and expected number of drops
E[\text{attempts}] = \frac{1}{p}, \qquad E[\text{drops}] = n \cdot p
Attempts needed to reach a target probability
n = \left\lceil \frac{\ln(1 - P_{\text{target}})}{\ln(1 - p)} \right\rceil
Probability of exactly k drops (binomial PMF)
P(X = k) = \binom{n}{k} p^{k} (1-p)^{n-k}
Probability of at least k drops
P(X \ge k) = 1 - \sum_{i=0}^{k-1} \binom{n}{i} p^{i} (1-p)^{n-i}
Most likely number of drops (binomial mode)
k_{\text{mode}} = \left\lfloor (n+1)\,p \right\rfloor
Standard deviation of drop count
\sigma = \sqrt{n\,p\,(1-p)}

Frequently asked questions

How do I enter a drop rate like 1 in 128?

Divide 1 by the number, then multiply by 100. For 1 in 128: 1 ÷ 128 = 0.0078, and 0.0078 × 100 = 0.78%. Type 0.78 in the Drop Chance box. Some common ones:

  • 1 in 50 = 2%
  • 1 in 100 = 1%
  • 1 in 512 = 0.2%
  • 1 in 5000 = 0.02%

Can I count the runs I already did?

Yes. Just add them to your total. If you already killed a boss 80 times and plan 40 more, type 120 in Number of Attempts. The result is your chance of at least one drop across all 120 kills.

But past runs do not help your next roll. Each attempt starts fresh at the same rate.

Why does the tool block 100% in the Desired Probability box?

Because 100% is impossible with random drops. Every extra run pushes your odds closer to 100% but never lands on it. The highest you can pick is 99.99%. Only a pity system can give a real guarantee.

What does "Chance of Still Having Nothing" mean?

It is the chance you finish that many runs with no drop at all. It is the leftover from the cumulative odds. If your chance of a drop is 90%, then the chance of nothing is 10%.

Use it to check your dry streak. If the number is still 20%, then 1 in 5 players would be as dry as you. That is normal bad luck.

What is the difference between "At least N drops" and "Exactly N drops"?

At least N counts N or more. Pick this when you need 3 copies and extras are fine.

Exactly N counts only that number, no more and no less. Pick this if you are curious about one exact outcome. "At least" is almost always the number you want for farming.

Does this work for gacha pulls and banners?

Yes. Treat one pull as one attempt. Type the banner rate (like 0.6%) and how many pulls you plan. Turn on the pity switch and type the pity count if the game has one.

Note: this tool uses hard pity only. It does not model soft pity, where the rate slowly climbs before the guarantee.

Why does my answer jump to 100% when I turn pity on?

Because you entered enough attempts to reach the pity count. Once you hit that attempt number, the game hands you the item, so the chance is a true 100%.

If your attempts are below the pity number, the tool goes back to normal random math.

How do I add a drop rate buff or luck bonus?

Work out the boosted rate first, then type that number. If your item drops at 4% and a buff gives +50%, the new rate is 4 × 1.5 = 6%. If an event doubles drops, just double the rate.

Run the numbers both ways to see how many hours the buff saves you.

Why does the result show "<0.01%"?

Your odds are real but tiny — smaller than one hundredth of a percent. The tool shows this instead of rounding down to 0.00%, so you know the chance is not zero.

What do the Low, Moderate, High, and Very High ratings mean?

They are quick labels for your odds in the milestone table:

  • Low: under 25% — expect to keep grinding.
  • Moderate: 25% to 75% — a coin flip zone.
  • High: 75% to 95% — most players have it by now.
  • Very High: 95% and up — going dry here is rare.

Why are two lines on the chart?

The second line only shows when pity is on. The purple line is normal random odds. The green line is your pity-adjusted odds, which shoot to 100% at the pity attempt. Comparing them shows how much the safety net helps.

What does "Most likely outcome (mode)" mean?

It is the drop count you are most likely to end up with after all your runs. At a 33% rate over 100 runs, the most common result is 33 drops. It is the tallest bar on the chart.

Even so, that exact number is far from certain. Results spread out on both sides of it.

My expected drops say 5, so why is my chance not 100%?

Expected drops is an average, not a promise. Drops clump together. Some players get 8 in the same run count, and some get 0. At a 5% rate over 100 runs you average 5 drops, but there is still about a 0.6% chance of getting none.

The boss drops several items. What rate do I type?

Type the rate for the one item you want. Loot tables list each item on its own, so a 2% sword stays 2% no matter what else is on the table.

If you want any one of several items, add their rates together and use that total.

How many attempts can I enter?

Up to 100,000 in the main calculator and up to 10,000 in the multiple drops section. If you type a bigger number, the tool trims it to the limit and shows a note.

Do I have to press Calculate every time?

No. Results update as you type. The Calculate button is there if you want to force a refresh, and Reset puts every box back to its starting value.

Is it better to farm a 10% drop or a 3% drop?

Compare total time, not just rate. A 3% drop needs about 33 runs on average, and a 10% drop needs about 10. If the 3% run takes 30 seconds and the 10% run takes 5 minutes, the 3% farm wins: about 17 minutes versus 50.

Use the Expected attempts per drop number, then multiply by your run time.

I am 300 runs dry on a 1% drop. Is the game broken?

Probably not. Type 1% and 300 attempts. Your chance of a drop is about 95%, so about 5 in 100 players are still dry at that point. Rare, but it happens. The game does not track your bad luck unless it has a pity system.

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