Formula Used
Failures: failures = sample size − successes
Observed success rate: p̂ = successes ÷ sample size
Observed failure rate: q̂ = failures ÷ sample size
Expected successes: n × p
Expected failures: n × (1 − p)
Success failure condition: expected successes ≥ minimum successes and expected failures ≥ minimum failures
Z score: z = (p̂ − p) ÷ √((p × (1 − p)) ÷ n)
Margin of error: z critical × √((p̂ × (1 − p̂)) ÷ n)
Confidence interval: p̂ ± margin of error
How to Use This Calculator
Enter the total sample size. Add the number of successful outcomes. Enter the expected success percent. Set the minimum expected successes and failures. Choose the confidence level. Select a decision rule. Add the rule limit. Press calculate. The result appears above the form.
Example Data Table
| Case |
Sample Size |
Successes |
Expected Rate |
Rule |
Likely Result |
| Campaign test |
200 |
126 |
50% |
Success rate at least 55% |
Pass |
| Small pilot |
12 |
9 |
50% |
Success rate at least 70% |
Review |
| Quality audit |
500 |
470 |
90% |
Failure rate at most 8% |
Pass |
| Training check |
80 |
58 |
65% |
Success count at least 60 |
Review |
What this calculator does
A success failure condition check helps you judge a set of outcomes before making a decision. It is useful for tests, surveys, audits, campaigns, trials, and quality checks. The tool compares observed results with practical limits. It also tests the normal approximation rule used for proportions. That rule needs enough expected successes and failures.
Why the condition matters
Many reports use a success rate as one simple number. That number can be misleading when the sample is small. A rate from ten trials is not as stable as a rate from ten thousand trials. The expected success count is n times p. The expected failure count is n times one minus p. When both values meet your chosen minimum, the sample has stronger balance.
Decision checks
The calculator separates two ideas. First, it checks whether the statistical condition is satisfied. Second, it checks your business or project rule. Your rule can be a minimum success rate, maximum failure rate, minimum success count, or maximum failure count. This makes the result easier to explain. A campaign may pass the sample condition, yet fail the target. A small pilot may beat the target, yet still need more data.
Confidence range
The confidence range estimates where the true success rate may fall. It uses the observed rate and a selected z value. A finite population correction can reduce the margin when the sample covers a large share of a known population. The range is still an estimate, not a guarantee. Use it with judgment and context.
Best use cases
Use this calculator when you need a quick pass or fail review. It fits conversion tests, inspection batches, eligibility rules, production checks, learning goals, medical screening summaries, and user acceptance testing. You can export the result for records. The example table shows how different sample sizes change the final decision.
Practical notes
Choose thresholds before viewing the outcome. This prevents biased decisions. Use a higher minimum expected count when mistakes are costly. Check raw counts as well as percentages. A neat rate can hide too few trials. Keep notes about data source, dates, and exclusions. Clear notes make future comparisons safer and easier. Review unusual results before any final action.
FAQs
What is a success failure condition?
It checks whether expected successes and expected failures are large enough for a proportion-based normal approximation. Many basic rules use at least 10 expected successes and 10 expected failures.
What does expected success percent mean?
It is the assumed or target success probability. The calculator multiplies it by sample size to estimate expected successes. It uses the remaining probability to estimate expected failures.
Why can my result pass the rule but fail the condition?
Your observed result may meet the business rule, but the sample may be too small or unbalanced for strong statistical support. More data may be needed.
What should I enter for the decision rule limit?
Use a percent when choosing a rate rule. Use a count when choosing a count rule. For example, enter 60 for 60 percent or 60 successes.
What is the confidence interval?
It is an estimated range for the true success rate. A wider interval means more uncertainty. Larger samples usually create narrower intervals.
What is finite population correction?
It adjusts the margin of error when the sample is a large part of a known population. Leave population size as zero when it is unknown.
Can this calculator be used for quality control?
Yes. It can check inspection batches, defect limits, pass rates, and failure limits. Always match the rule to your quality policy.
Does a pass guarantee future success?
No. A pass only means the entered data meets the selected checks. Future results can change because of process shifts, bias, or random variation.