Calculators
Coupon Collector Calculator
Calculate expected draws, repeat draws, and standard deviation for collecting every equally likely outcome, privately in your browser.
Estimate how many independent draws with replacement it takes to collect every equally likely outcome at least once. Enter 1–1000000 outcomes. For example, collecting all six die faces takes 14.7 rolls on average. All processing stays in your browser.
How coupon collection works
For n equally likely outcomes, independent sampling with replacement takes E[T] = n × Hₙ draws on average to see every outcome, where Hₙ = Σ(1/k) for k from 1 to n. Each newly collected outcome leaves fewer unseen outcomes, making the final few harder to find. For six die faces, the expected total is 14.7 rolls, including 8.7 repeat rolls. Variance is Σ[n(n−k)/k²] and standard deviation is its square root. For one outcome, exactly one draw is needed and variance is zero. Expected repeats equal E[T] − n. The mean is not a guaranteed completion time, and standard deviation does not define a completion probability or confidence interval. The model assumes every outcome is equally likely, draws are independent, and duplicates are possible. It does not apply to unequal rarity, sampling without replacement, or collecting several copies of each outcome. Enter a whole number from 1 to 1000000; leading zeros and surrounding whitespace are accepted, while decimals, signs, scientific notation and separators are rejected. Compensated summation limits rounding error; results display up to 12 significant digits. Inputs are not uploaded or stored.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
How many rolls collect all six die faces on average?
For a fair six-sided die, the expected total is 6 × (1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6) = 14.7 rolls.
Is the expected draw count a guarantee?
No. It is an average over repeated collections. An individual collection can take fewer or many more draws. Standard deviation describes variability, not a completion deadline.
Can I use this for outcomes with unequal rarity?
No. This formula requires independent draws with replacement and equally likely outcomes. Unequal rarity needs a different model.
What are expected repeat draws?
They are expected total draws minus the number of distinct outcomes. For six outcomes, this is 14.7 − 6 = 8.7 repeats.
What happens with just one outcome?
Exactly one draw collects everything; expected repeats, variance and standard deviation are all zero.
Does this upload or save my inputs?
No. Calculation and copying run locally in your browser.