# MARGIN OF ERROR CALCULATOR

## Calculate your margin of error

Find out how representative your survey responses are of a population by calculating margin of error.

HOW TO USE THE MARGIN OF ERROR CALCULATOR

## What you need…

You’ll need to know the approximate size of the population you’ll be surveying, your confidence level for how representative responses will be, and also the sample size you’ll be sharing your survey with.

## Margin of error calculator FAQs

Everything you need to know about calculating margin of error for target population.

### What is margin of error?

The margin of error is a measure of the precision or uncertainty associated with the results obtained from a sample when estimating a population parameter.

It represents the maximum amount by which the sample result may differ from the true value of the population parameter.

Margin of error is typically expressed as a percentage and is influenced by factors such as sample size, variability within the population, and the chosen confidence level. A smaller margin of error indicates higher precision and confidence in the sample estimate.

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### Margin of error formula

There are a few formulas out there for calculating margin of error, but we’ve found this one the most useful:

Margin of error = Z * √ ((sample proportion * (1-sample proportion)) / sample size) * √ ((population size – sample size)/(population size-1))

To calculate your sample proportion, you’ll need to divide your “number of successes” by your sample size.

As you may not have shared your survey yet, we’ve used a sample proportion of 0.5 in our calculator. This is the standard value when you don’t have access to a sample proportion.

### How do you calculate margin of error?

Here are the steps for calculating the margin of error using the above formula:

**Determine the z-score**: Decide on the desired confidence level for your estimate and find the corresponding z-score. For example, for a 95% confidence level, the z-score is typically 1.96.

**Calculate the standard error of the proportion**: Use the formula √ ((sample proportion * (1-sample proportion)) / sample size) for this.

**Calculate the adjustment factor for finite populations**: Use the formula √ ((population size – sample size)/(population size-1)) for this.

**Multiply the z-score by the standard error and adjustment factor**: z-score * standard error * adjustment factor.

**The result is your margin of error**: This represents the range within which the true population parameter is likely to lie, with the specified level of confidence.

### What is population size?

Population size refers to the total number of people, elements, or units in the entire group or population that you are interested in studying.

Some other terms you may have seen used to refer to this are target population, target market, total population, or overall population.

It represents the entire pool from which a sample is drawn. In sample size calculations, knowing the population size is essential as it helps determine the required sample size to accurately represent the population.

### What is sample size?

Sample size represents the total number of completed responses for your survey or research project.

The sample size is a crucial factor in determining the margin of error. Generally, larger sample sizes lead to smaller margins of error, as larger samples provide more precise estimates of population parameters.

**Not sure what sample size you need? Use our sample size calculator.**

### What is confidence level?

The confidence level is the probability that the confidence interval, calculated from a sample, contains the true population parameter. It is expressed as a percentage and represents the level of certainty or reliability we have in our sample estimate.

For example, a 95% confidence level means that if we were to conduct the same study multiple times and calculate confidence intervals, we would expect about 95% of those intervals to contain the true population parameter.

Each confidence level is also associated with a z-score. The Z-score, also known as the standard score, is a statistical measurement that quantifies how many standard deviations a data point is from the mean of the dataset.

You can use our z-score table below to determine the score associated with each confidence level.

Confidence level | z-score |
---|---|

80% | 1.28 |

85% | 1.44 |

90% | 1.65 |

95% | 1.96 |

99% | 2.58 |

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