Our margin of error calculator has the objective of showing the researcher how much they can trust in the outcome that was obtained during the survey application phase of their research project. .

Most surveys are run with research purposes, based on the compiled information for a study sample, and not the total population, and because of this, the margin of error is an item to consider when running the sampling.

The **margin of error calculator** measures the maximum amount by which the outcome of our sample might differ from the total population. Given that most responses from a survey can be presented in terms of percentages, the result of the calculation is too shown as a percentage.
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If you want to know more about sampling, we recommend you visit our article: Types of sampling.

As a first step, set the size of the total population considered for your research project in the indicated box.

Then set a confidence level. The most common standard value to researchers is 95%. Remember: the narrower the confidence level, the broader the margin of error.

Finally, set the **sample size**. To do this you should already know the sample size concerning the total population. If you don’t know it yet, check out our **Sample Size Calculator**.

There! Automatically, you’ll be able to know the ideal margin of error (MoE) for the research project you’re working on.

Total Population

Confidence Level

Sample Size:

Margin of error:

The margin of error is the considered amount of error that might be in a random sampling process for any research project, especially when running the questionnaires or surveys.

It’s an important value to be aware of during any research project since it determines the possible confidence level regarding the outcome of the entire research.

The narrower the margin of error, the broader the degree of certainty on the outcomes of the research.

Learn how to determine the sample size.

Two pieces of information are needed to calculate the margin of error for a sample. The margin of error is calculated from:

- The sample size (number of individual respondents)
- The level of confidence for the outcome (generally established at 95% in the research industry).

To calculate it, the following formula is needed:

Where σ (the population’s standard deviation) is divided by the square root of the n (sample size) and the result is multiplied times z (tabulation based on the determined confidence level value).

Z value | Confidence Level (in percentage) |
---|---|

1.28 | 80% |

1.44 | 85% |

1.65 | 90% |

1.96 | 95% |

2.58 | 99% |

Say you have a new milkshakes business, and you’re training new employees to fill the cups with the right amount of ice cream, 10oz each.

Therefore, you want to calculate the average weight of the cones produced during a workday, including the margin of error. Instead of weighing each cup, you ask every employee to weigh and register randomly a sample of the served cups, and take notes.

For 50 sampled cups, you found an average of 10.3oz. Say the standard deviation for that population is 0.6oz. So, how would you calculate the margin of error with a confidence level of 95%?

Based on the 50 cups sample, the average weight is 10.3oz with a margin of error of approximately 0.17oz. In other words, the possible interval for the average weight of all the big seize cones produced for a workday, is estimated (with a confidence level of 95%) between 10.30 - 0.17 = 10.13oz and 10.3 + 0.17 = 10.47oz.

If you are about to run a research project, and you want to collect the appropriate number of samples, we have a few suggestions for you:

**Identify the sample for your total population.** Only in this way will you be able to know whether your margin of error is the right one.
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**Establish the accuracy percentage you would like to achieve.** To do so, you need to measure both the margin of error and the confidence level of your sample, it depends on this how much your outcomes will differ from your responses.

**Establish the sample size.** How many people would you need to survey for your research project? Remember to consider as part of your sample only the respondents that completed the survey.

**Define the response rate.** This regards the result obtained from dividing the participants' percentage that responded to the survey by the people that received it.

Now that you’ve followed these steps, you know exactly how many people should receive your survey for you to obtain the desired outcome.

The **margin of error calculator** is a way of measuring how effective is your survey. The narrower the margin of error, the more confidence you can have in the results. The broader the margin of error, the further the opinions from the total population.

We hope this tool will be quite useful for your research (or other projects). Remember that with QuestionPro you’ll be able to use these values to obtain a real value thanks to our Survey Software.

You can start right now to use **QuestionPro for free**, or connect with one of our executives to clear your doubts about our platform.

Finally, we recommend the following read: Population vs. Sample.

YYou know the number of surveys you must run for your study to have a valid range, do you need an automatic tool to collect and analyze data? In QuestionPro we can help you. What are you waiting for?.