Confidence Interval Calculator
Build the interval around a proportion or a mean — the range the truth plausibly occupies.
Free · No signup · By the analysts at Blackridge Research · Updated 2026-07-18
Inputs
Results
What this means
Adjust the inputs to calculate.
About the Confidence Interval Calculator
A confidence interval gives you a range where the true population value is likely to fall.
It's the range the truth plausibly occupies, not a fixed point estimate.
Formula
CI = Mean ± (z × σ/√n)
- CI
- — Confidence Interval
- z
- — Z-score for confidence level
- σ
- — Standard deviation
- n
- — Sample size
How to use this calculator
- 1
Enter sample mean
The average value from your sample.
- 2
Enter standard deviation
The standard deviation of your sample.
- 3
Enter sample size
The number of observations in your sample.
- 4
Choose confidence level
Common choices: 90%, 95%, or 99%.
Example calculations
Average project cost estimation
Your sample of 100 projects has an average cost of $50,000 with a standard deviation of $10,000.
CI = $50,000 ± 1.96 × ($10,000/√100) = $50,000 ± $1,960
- Confidence interval:
- $48,040 — $51,960
- Margin of error:
- $1,960
- Lower bound:
- $48,040
- Upper bound:
- $51,960
The true average project cost is between $48,040 and $51,960 with 95% confidence.
Interpreting your results
A narrower confidence interval means more precise estimates. Use larger sample sizes for narrower intervals.
The confidence level tells you how often the interval would contain the true value across repeated samples.
Need the market data behind this calculator?
The Confidence Interval Calculator is only as good as its inputs. Blackridge Research publishes syndicated market reports with vetted market sizes, growth rates, and competitive landscapes across 40+ industries — and builds custom studies when the shelf report doesn't exist.
Industry applications
Business
- Financial forecasting: project ranges around revenue and cost estimates.
- Market research: build confidence intervals around willingness-to-pay data.
- Investment cases: show the range of possible outcomes.
Construction
- Cost estimation: confidence intervals around construction costs.
- Schedule estimation: ranges around project duration estimates.
Research
- Research reporting: present all estimates with confidence intervals.
- Data interpretation: assess the precision of measurements.
Common mistakes to avoid
-
✗ Treating the mean as the true value
The mean is an estimate — the confidence interval shows the uncertainty.
-
✗ Using the wrong distribution
For small samples (n<30), use the t-distribution instead of z-scores.
Frequently asked questions
›What is a confidence interval?
A range of values that likely contains the true population value.
›95% vs 99% confidence: which should I use?
95% is standard. Use 99% when the cost of being wrong is high.
Glossary
- Confidence interval:
- The range of values that likely contains the true population value.
- Standard error:
- The standard deviation of the sampling distribution.
- T-distribution:
- Used for small samples instead of the normal distribution.
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