Confidence Interval Calculator

Calculated using standard mathematical and industry formulas.

Free online Confidence Interval Calculator calculator and unit conversion tool for everyday, engineering, and home projects.

How to use this calculator?

1. Select whether you are estimating a mean or a proportion.
2. Choose the confidence level (95% is standard for most research).
3. Enter your sample statistics: mean and SD (or proportion) and sample size.
4. Read the confidence interval bounds and margin of error.

Formula & calculation method

Z-based confidence interval formula

CI = x̄ ± z* × (s/√n) · For proportions: CI = p̂ ± z* × √(p̂(1−p̂)/n)

z* critical values: 90%=1.645, 95%=1.96, 99%=2.576. SE = s/√n for means.

Step-by-step calculation example

x̄=100, s=15, n=50, 95% CI: SE=15/√50≈2.12, MOE=1.96×2.12≈4.16. CI=[95.84, 104.16].

Key insights to remember

• A 95% CI means: if you repeated the study 100 times, 95 of the CIs would contain the True parameter.
• Wider CIs = more uncertainty. Narrower CIs require larger samples.
• Margin of error (MOE) = z* × SE. Higher confidence levels require larger z* values.
• For proportions, SE = √(p(1−p)/n). Maximum SE occurs at p = 0.5 (most uncertainty).

How to interpret your results?

Reading the interval

CI [A, B] means the True population parameter is estimated to lie between A and B with the stated confidence level.

Confidence vs probability

The True mean is fixed (not random). The CI is random (it depends on your sample). The confidence level refers to the procedure, not the specific interval.

Frequently asked questions

How do I use the Confidence Interval Calculator calculator?

Enter your numerical input and select desired units to get instant accurate results.

How accurate are the conversions?

Conversions use official ISO conversion factors for maximum precision.

Does it convert metric and imperial units?

Yes, seamless conversions between metric (meters, kg) and imperial (feet, lbs) are supported.

Is my data stored?

No, all calculations execute 100% locally in your browser with zero data logging.

Can I use this for DIY or engineering projects?

Yes, it provides reliable estimates for construction, crafting, science, and everyday math.

What if I enter invalid inputs?

The calculator will display a friendly error prompt if non-numeric values are entered.

Related calculators

• Z-score Calculator — Convert a raw score to a Z-score (standard score), find its percentile, and compute cumulative probability under the normal distribution.
• Sample Size Calculator — Determine the minimum sample size needed for a survey or study based on margin of error, confidence level, and population size.
• P-value Calculator — Calculate the P-value from a Z-statistic for one-tailed or two-tailed hypothesis tests and determine statistical significance.

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