Aisha K.
Mar 12, 2026
Clean layout and the results update instantly. Exactly what I needed for a quick planning check.
Statistics, Probability & Advanced Math
How to Calculate Confidence Interval
Instant math result
Confidence intervals communicate estimate uncertainty for a population mean. Enter sample statistics and a z critical value to compute the interval bounds.
Inputs
-100010000
0.011000
210000
13.5
Smart analysis
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Plain-English guide
Terms & how it works
Confused by a field? Read the short definitions here while you use the tool.
Sample Mean
The “Sample Mean” value used in this tool’s formula. Adjust it to see results update live.
Standard Deviation
The “Standard Deviation” value used in this tool’s formula. Adjust it to see results update live.
Sample Size
The “Sample Size” value used in this tool’s formula. Adjust it to see results update live.
Z-score (e.g. 1.96)
The “Z-score (e.g. 1.96)” value used in this tool’s formula. Adjust it to see results update live.
- z
Critical z
From confidence level.
When to use this Confidence Interval
Common use cases
- Check homework results with transparent formulas
- Estimate probability for common distributions
- Convert between related statistical measures quickly
Localized examples
- Classroom and exam-prep workflows
- Business analytics back-of-envelope checks
What you get
- Formula-backed outputs with clear labels
- Step-friendly defaults for learning
- Free online calculator — no sign up
How to Calculate Confidence Interval Step-by-Step
- 1Enter sample mean and standard deviation.
- 2Add sample size n.
- 3Set z (1.96 for ~95%) and review the interval.
Governing formula
CI = x̄ ± z·(σ/√n)
Normal-approximation confidence interval for a mean.
Example: set Sample Mean = 70, Standard Deviation = 12, Sample Size = 40, then read the result.
Variable definitions
- x̄
Sample mean
Observed average.
- z
Critical z
From confidence level.
- Assumes approximate normality / large n.
Frequently Asked Questions
Use t for smaller samples or when sigma is unknown—z is an approximation.
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4.8
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4 reviews
Daniel R.
Feb 28, 2026
Very usable on mobile. Would love a save/export option later, but the math feels solid.
Priya S.
Feb 3, 2026
The FAQ section answered my questions before I even had to search. Smooth dark mode too.
Marcus L.
Jan 19, 2026
Simple inputs, clear outputs. This replaced three bookmarks I used to juggle.
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