How this calculation works
More trials with zero observed events produce a lower upper bound at the same confidence level.
THE FORMULA
p upper = 1 − (1 − confidence)^(1/n)A worked example
For zero events in ten trials, the 95% upper bound is about 25.89%.
Good to know
The trials must be independent with a common event probability.
Reference: OpenStax Introductory Statistics (opens in a new tab) ↗
Read the result
Find the exact one-sided binomial upper bound after observing no events.
The primary result is labeled “Upper probability bound”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
The trials must be independent with a common event probability.
For a related exercise, try the statistics calculator.
A few questions, answered
How can I check the default inputs by hand?
For zero events in ten trials, the 95% upper bound is about 25.89%.
Which rule does this calculator apply?
p upper = 1 − (1 − confidence)^(1/n)