Confidence Level & Interval Calculator
Calculate the margin of error and confidence intervals for survey results or experiments.
80%
85%
90%
95%
99%
99.9%
Calculation Results
Sample Proportion (p̂):
0
Z-Score:
0
Standard Error:
0
Margin of Error:
0
Confidence Interval:
0
How to Calculate Confidence Level and Intervals
In statistics, a confidence level represents how frequently the percentage of the population that matches a specific response would fall within a specific range. For example, a 95% confidence level means that if you repeat the experiment 100 times, 95 of those times the results would stay within your calculated interval.
The Formula for Confidence Intervals
To calculate the confidence interval for a proportion, we use the following formula:
CI = p̂ ± Z * √[p̂(1 – p̂) / n]
- p̂ (Sample Proportion): The number of successes divided by the total sample size.
- Z (Z-Score): A constant value based on the chosen confidence level (e.g., 1.96 for 95%).
- n (Sample Size): The total number of observations in your study.
- Standard Error: The square root part of the formula, representing the deviation.
Common Z-Scores for Confidence Levels
When calculating, statisticians use standard normal distribution values:
- 90% Confidence: Z = 1.645
- 95% Confidence: Z = 1.96
- 99% Confidence: Z = 2.576
Real-World Example
Imagine you survey 1,000 people (n = 1000) and find that 500 (x = 500) prefer coffee over tea. Your sample proportion (p̂) is 0.50. At a 95% confidence level (Z = 1.96), your margin of error would be approximately 3.1%. This means you can be 95% confident that between 46.9% and 53.1% of the entire population prefers coffee.