Confidence Interval Calculator

The Confidence interval calculator is used to determine the range of values where a population parameter is likely to fall. It is helpful in statistics for research, surveys, experiments, and data analysis. This free MathCalc confidence interval calculator helps you make the process easier.

Confidence Interval Calculator

Calculate confidence intervals for sample means

How to Use
  1. Fill in the Required Values
  2. Click "Calculate" Button
  3. View Step-By-Step Solution

What is a confidence interval?

A confidence interval is a range of values, derived from sample data, that likely contains the actual value of a population parameter. It is expressed with a confidence level, which tells you how confident you can be that the range limits the exact value.

How to use the Confidence interval calculator?

This free MathCalc confidence interval calculator helps you easily calculate the lower or upper bounds of the interval for a population mean.

Example: Calculate 95% Confidence Level

  1. Step 1: Confidence interval calculation
  2. Step 2: Sample mean (x̄) = 50
  3. Step 3: Sample size (n) = 100
  4. Step 4: Standard deviation (σ) = 8
  5. Step 5: Confidence level = 95%
  6. Step 6: Z-score for 95% confidence = 1.96
  7. Step 7: Standard error = σ/√n = 8/√100 = 0.8
  8. Step 8: Margin of error = Z × SE = 1.96 × 0.8 = 1.568
  9. Step 9: Lower bound = x̄ - ME = 50 - 1.568 = 48.432
  10. Step 10: Upper bound = x̄ + ME = 50 + 1.568 = 51.568
  11. Step 11: 95% Confidence Interval: (48.432, 51.568)
  12. Step 12: Interpretation: We are 95% confident that the true population mean lies between 48.432 and 51.568
Result:
  • Confidence interval: (48.432, 51.568)
  • Lower bound: 48.432
  • Upper bound: 51.568
  • Margin of error: 1.568
  • Standard error: 0.8

Example: Calculate 90% Confidence Level

  1. Step 1: Confidence interval calculation
  2. Step 2: Sample mean (x̄) = 50
  3. Step 3: Sample size (n) = 100
  4. Step 4: Standard deviation (σ) = 8
  5. Step 5: Confidence level = 90%
  6. Step 6: Z-score for 90% confidence = 1.645
  7. Step 7: Standard error = σ/√n = 8/√100 = 0.8
  8. Step 8: Margin of error = Z × SE = 1.645 × 0.8 = 1.316
  9. Step 9: Lower bound = x̄ - ME = 50 - 1.316 = 48.684
  10. Step 10: Upper bound = x̄ + ME = 50 + 1.316 = 51.316
  11. Step 11: 90% Confidence Interval: (48.684, 51.316)
  12. Step 12: Interpretation: We are 90% confident that the true population mean lies between 48.684 and 51.316
Result:
  • Confidence interval: (48.684, 51.316)
  • Lower bound: 48.684
  • Upper bound: 51.316
  • Margin of error: 1.316
  • Standard error: 0.8

Example: Calculate 99% Confidence Level

  1. Step 1: Confidence interval calculation
  2. Step 2: Sample mean (x̄) = 50
  3. Step 3: Sample size (n) = 100
  4. Step 4: Standard deviation (σ) = 8
  5. Step 5: Confidence level = 99%
  6. Step 6: Z-score for 99% confidence = 2.576
  7. Step 7: Standard error = σ/√n = 8/√100 = 0.8
  8. Step 8: Margin of error = Z × SE = 2.576 × 0.8 = 2.0608
  9. Step 9: Lower bound = x̄ - ME = 50 - 2.0608 = 47.9392
  10. Step 10: Upper bound = x̄ + ME = 50 + 2.0608 = 52.0608
  11. Step 11: 99% Confidence Interval: (47.9392, 52.0608)
  12. Step 12: Interpretation: We are 99% confident that the true population mean lies between 47.9392 and 52.0608
Result:
  • Confidence interval: (47.9392, 52.0608)
  • Lower bound: 47.9392
  • Upper bound: 52.0608
  • Margin of error: 2.0608
  • Standard error: 0.8

How does the confidence interval calculator work?

The confidence interval calculator uses standard statistical formulas. It uses the Z-score and standard error. It automatically computes the margin of error and displays the result. It also works for 90%, 95%, or 99% confidence levels.

Why use the MathCalc confidence interval calculator?

Get Quick Results

Finding a confidence interval by hand can take time, especially when dealing with large numbers. This free MathCalc confidence interval calculator gives accurate results in seconds. Example: If you are calculating the confidence interval of the (sample mean (50), sample size (100), or standard deviation (8)) by hand, it takes a long time and effort. But a calculator gives accurate results in seconds.

Reduce Human Error

Manual math can lead to minor mistakes that cost you money or points. This tool provides proven formulas to reduce errors, and your results are always right. To avoid miscalculations, use the MathCalc confidence interval calculator.

User-Friendly

This free MathCalc Z-score calculator has a simple interface. It works perfectly on every device. It is user-friendly and valuable for students and teachers.

Tips for the Best Result:

Example:

  • Double-check your input.
  • Always select the right confidence level for your purpose.
  • Always interpret the confidence interval in the context of your study.

FAQs

What does a 95% confidence interval mean?

It means that if you repeated the same study many times, 95% of the calculated intervals would contain the actual population parameter.

Can I use this calculator for both mean and proportion?

This calculator only works for the sample mean, not for the proportion.

Does a higher confidence level mean more accuracy?

It means more certainly, but it also makes the interval wider.