# MARGIN OF ERROR CALCULATOR

Simple and accurate margin of error calculator allows researchers to check if their sample size relative to the population is within an acceptable region of rejection.

### Margin of Error Calculator

## Calculate Margin of Error with this Tool

Variables related to Margin of Error

**Provide the population size for the target population that your survey results will be representing**

This is the total population of your target audience. Some examples may include

- The United States of America (330 million)
- Monthly Spotify users (286 million)
- Amount of electrical engineers in the United Kingdom (55 thousand)

**The sample size is there to check what margin of error you will receive based on the population size.**

The sample size represents the * amount of responses * that is acceptable to the researcher.

You want to get a sample size large enough to get the margin of error to be at most 5 percent. That is an acceptable range in social sciences. However, increasing the sample size relative to your population size will allow the data to have less margin of error.

*Margin of error decreases as sample size increases.*

Trying to figure out margin of error effects the sample size? Use our sample size calculator

**Select the reliability level**

This is a measurement of how acceptable your inferences can be made based off of the data that you collected.

A higher confidence level is a more accurate representation of the target population. A confidence level of 99% means that you are 99% certain that your sample represents the population.

*Increasing the confidence level will increase the margin of error.*

**This is your estimated sample size based on the inputs provided**

The calculator uses a p-value of 0.50 which is the standard distribution or deviation recommend for most research where you don’t know the previous or actual deviation.

Find your target Population and test different sample sizes in order to find an acceptable margin of error. The most commonly used confidence level is 95% and 5% for margin of error are for research.

If you already have a target margin of error and are trying to find what sample size you need, please refer to our sample size calculator

## How to Calculate Margin of Error

If you are calculating the margin of error, you are looking for how precise your results reflect the target population. When designing a survey, you use a sample size where the participants are in your target population. A higher sample size relative to the target population will lower your margin of error, which will increase the accuracy of your results. The accepted margin of error in research is 5 percent.

Using this calculator allows calculating the margin of error to be simple and easy. You can raise or lower the sample size in order to find what margin of error you’d like to place in your study.

### Choose the alpha level and corresponding confidence level

The sum between alpha and confidence interval always equals 1. So if you want your alpha to be .05, then your confidence level will be .95 or 95%. The alpha is the probability of rejecting the null hypothesis of the survey. In other words, alpha is the percent of your study that does not reflect the target population.

Generally, 0.05 is the accepted alpha level. Other common alpha levels are .1, .02 and .01. If you can’t decide which alpha level to use, set alpha to 0.05.

### Estimate the standard deviation

When it comes to standard deviation, unless you have access to raw data in research prior to what you are conducting, set it to .5.

Please note: if you plan to use a standard deviation value other than 0.5, you must replace 𝜎 with the true population standard deviation.

### Find the Z-score for the confidence level

Here are the most commonly used confidence levels along with their Z scores. Z score is the number of standard deviations away from the mean. The confidence level is the probability of that Z score.

If you have a different alpha, the Z score can easily be found using a Z score table, which can be found in most statistics books. Assuming you’re conducting a two-tail test, subtract alpha divided by 2 from 1. Then find the closest probability value in the Z score table and add your Z score row + column.

For example, when you’re trying to find a Z score for a two tail test at alpha = .05. 1-(.05/2) = .975. On the 1.9 row and the .06 column, you will find .9750. This means your Z = 1.96

### Common confidence levels with Z scores

Confidence Level | Z-Score |

90% | 1.645 |

95% | 1.96 |

98% | 2.33 |

99% | 2.575 |

### Margin of Error formula

z= z score, 𝜎 = population standard deviation, n = sample size

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