calc.engineer / General & Math / Confidence Interval

Confidence Interval v1.0.0

Calculate the confidence interval for a sample mean. Given a sample mean, sample size, standard deviation, and confidence level, computes the margin of error, lower and upper bounds, critical z-score, and standard error. Supports finite population correction (FPC) when a population size is provided, which narrows the interval for samples that are a large fraction of the population. Uses the Abramowitz & Stegun rational approximation for the inverse normal CDF to derive the critical z-value. Common in survey analysis, A/B testing, and quality control.

← from p_value
The observed sample mean (x-bar) around which the confidence interval is centered.
The number of observations in the sample (n). Must be a positive integer.
The standard deviation of the sample or population. Must be a positive number.
Confidence level as a decimal between 0 and 1 (e.g. 0.95 for 95%). Default is 0.95.
Total population size for finite population correction (FPC). Omit for infinite population assumption.
Fill in the inputs and Compute to see the structured result.

From an agent (MCP) or the API

curl -X POST https://calc.engineer/api/confidence_interval \
  -H "Content-Type: application/json" \
  -d '{"sample_mean": …, "sample_size": …, "standard_deviation": …}'

MCP: connect to https://calc.engineer/mcp and call confidence_interval.

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