Confidence Interval Calculator

Calculate confidence interval bounds and margin of error at 90%, 95%, or 99% confidence.

Lower Bound

48.040

Upper Bound

51.960

Margin of Error

±1.960

Details

CI (95%)[48.040, 51.960]
Standard Error1.0000
Z-value1.960
Margin of Error1.960

Use the Confidence Interval Calculator above to calculate your results. Enter your values and see instant results — all calculations run in your browser.

Disclaimer: This calculator is for informational purposes only and does not constitute tax, financial, or legal advice. Results are estimates based on the information you provide and current rates. Always consult a qualified tax professional or financial advisor for advice specific to your situation.

How It Works

This calculator determines a range of values, known as a confidence interval, within which the true population parameter (like a mean or proportion) is likely to fall. It's crucial for understanding the reliability and precision of estimates derived from sample data, especially when it's impractical to measure an entire population.

The calculator typically uses the formula: Estimate ± (Critical Value * Standard Error). The 'Estimate' is from your sample (e.g., sample mean), the 'Critical Value' comes from a t-distribution or z-distribution table based on your desired confidence level, and the 'Standard Error' quantifies the variability of the sample estimate.

A common mistake is misinterpreting the confidence level; a 95% confidence interval means that if you repeated your sampling many times, 95% of those intervals would contain the true population parameter, not that there's a 95% chance the true parameter is within your *specific* interval. Also, ensure your sample is random and representative to avoid biased results.

Example: Estimating Average Customer Spend

  1. 1 A coffee shop wants to estimate the average amount customers spend. They randomly sample 50 customers and find the average spend to be $5.25 with a standard deviation of $1.50. They want a 95% confidence interval.
  2. 2 Inputting these values: Sample Mean = $5.25, Sample Standard Deviation = $1.50, Sample Size = 50, Confidence Level = 95%. The calculator will determine the standard error and the appropriate critical t-value (since the population standard deviation is unknown and sample size is relatively small).
  3. 3 The calculator outputs a 95% confidence interval of [$4.83, $5.67].
  4. 4 Based on this sample, we are 95% confident that the true average spending of all customers at the coffee shop is between $4.83 and $5.67. This interval provides a more informative estimate than just the sample mean of $5.25.

Source: Khan Academy · Last updated: April 2026

Frequently Asked Questions

What does a 95% confidence interval mean?
A 95% confidence interval means that if you repeated the study many times, 95% of the calculated intervals would contain the true population parameter. It does not mean there is a 95% probability the true value is in this specific interval.
How do you calculate a confidence interval?
CI = sample mean ± (z-score x standard error). The z-score is 1.96 for 95% confidence, 1.645 for 90%, and 2.576 for 99%. Standard error = standard deviation / sqrt(sample size).
When should I use 90% vs 95% vs 99% confidence?
95% is the standard in most research. Use 90% for exploratory work or when a wider margin is acceptable. Use 99% for high-stakes decisions like medical trials or engineering tolerances where being wrong is costly.

You might also need

Percentage Calculator

Calculate percentages three ways: what is X% of Y, X is what % of Y, and percentage change from X to Y.

Fraction Calculator

Add, subtract, multiply, and divide fractions. Results shown as fraction, mixed number, and decimal.

Standard Deviation Calculator

Calculate mean, variance, and standard deviation (population and sample) from a data set.