How does increasing sample size affect confidence intervals?

Larger sample sizes reduce standard error, making the confidence interval narrower and the estimate more precise.

What is margin of error?

The margin of error represents the maximum expected difference between the sample estimate and the actual population value at the chosen confidence level.

When is a 99% confidence level preferred?

99% confidence is used in medical, legal, and high-consequence safety studies where higher certainty is critical.

Mathematics Tools• Confidence Limits

Confidence Interval & Margin of Error Calculator

Estimate population parameters with statistical confidence. Calculate lower and upper confidence limits and margin of error across 90%, 95%, and 99% confidence levels.

Calculations run client-side. Zero data sent to servers.

Sample Parameters

Sample Mean

Sample Std Dev (s)

Sample Size (n)

Confidence Level

95% Confidence Interval

[95.84, 104.16]

Margin of Error: ±4.158 (SE = 2.121)

There is a 95% probability that the true population mean lies between 95.84 and 104.16.

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How to Use Confidence Interval Calculator

Input Sample Metrics

Enter sample mean, sample standard deviation, and sample size (n).

Select Confidence Level

Choose 90% (z=1.645), 95% (z=1.96), or 99% (z=2.576).

Inspect Interval Bounds

Review lower bound, upper bound, standard error, and margin of error.

About Confidence Interval Calculator

Applies formula CI = Mean +- (Critical Value * (s / sqrt(n))), defining the range within which the true population mean is expected to fall with the specified confidence probability.

Supported Formats

Summary StatsRaw Numbers

Operational Limits

•Uses normal distribution (Z) for large samples (n >= 30) and Student's t for smaller samples.

Key Features

Computes 90%, 95%, and 99% confidence intervals automatically
Calculates standard error SE = s / sqrt(n)
Computes exact margin of error MOE = z * SE (or t-distribution for small n)
Supports raw dataset entry or summary statistics input
Visual interval range bar showing point estimate and limits

Frequently Asked Questions

It means that if the same sampling study was repeated 100 times, approximately 95 of the calculated intervals would contain the true population mean.

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