Calculadora de Margem de Erro
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
E = z · σ / √n
About this calculator
The Margin of Error Calculator determines the confidence interval of a statistical sample. It calculates the value E (margin of error) using the formula E = z · σ / √n, where z is the z-score corresponding to the desired confidence level, σ is the population standard deviation, and n is the sample size. The result indicates how much the sample estimate may vary from the true population value.
To use the calculator, enter the confidence level (90%, 95%, or 99%), the population standard deviation, and the sample size. The tool automatically applies the appropriate z-score (1.645, 1.96, or 2.576) and calculates the margin of error. For example, with 95% confidence, σ=10, and n=100, the margin of error is approximately 1.96.
This calculator is useful in opinion polls, market research, and scientific experiments. It helps size samples and interpret results, showing the precision of estimates. A smaller margin of error indicates greater confidence in the collected data.
Cautions: the formula assumes a random sample and known population standard deviation. If σ is unknown, use the sample standard deviation and the t-distribution. Also, the margin of error does not eliminate sample biases; it only measures random variation.
Frequently asked questions
What does a margin of error of 3% mean?
It means the true population value is likely within 3% above or below the sample result, at the chosen confidence level.
Can I use the calculator if I don't know the population standard deviation?
Not directly. If σ is unknown, use the sample standard deviation and the t-distribution, which is more appropriate for small samples.
Which confidence level should I choose?
95% is most common in surveys. Use 90% for less precision or 99% for more certainty, but this increases the margin of error.
Does the margin of error eliminate sample bias?
No. The margin of error only measures random variation. Selection or response biases are not corrected.
How do I increase the margin of error?
Increase the confidence level or use a smaller sample. To decrease it, increase the sample size or reduce the confidence level.