A Margin of Error Calculator That Is Simple and Efficient to Use

The word “error” is a somewhat triggering word for bookkeepers and accountants alike. Locating an unexpected error in a balance sheet can sap hours and hours of valuable time from a day. Fortunately, today we will only discuss a predicted error, the Margin of Error. 

Using the tips outlined in this article, you will understand and use margin of error calculators, while also increasing your knowledge of the methods and procedures needed when looking at your clientele.

Margin of Error Validity

Let’s say you flip a coin 100 times. Since there is a 50% chance that a coin will land on “heads,” the average statistical results will be 50 times heads and 50 times tails. However, it is not likely you will get this exact result. 

Therefore, mathematicians in the field of statistics developed a separate label to account for the degree of error that the solution will deviate. This is also known as the Margin of Error. 

Having the ability to recognize and calculate the margin of error is a necessary skill for any small business owner. This metric comes in handy when deciphering survey data and asking for input from your customers.

Define Your Population

In statistics, a population is a pool of individuals from which a statistical sample is drawn within a study. A population represents every member who is grouped by a common trait or characteristic.

Understanding a business’s population parameters is necessary to determine decisions or predictions based on your survey data. 

For example, say you want to determine the most popular social media platform your subscribers use. You may send a survey to your subscribers (your defined population) and ask them to select an answer from a specific set of selections.

While it would be wonderful if 100% of your survey recipients responded, that’s uncommon. In this example, you’ll use your responses as your sample and infer that the patterns in their responses hold for the rest of your subscribers.

In other scenarios, you may not be able to survey the entire population due to cost and time constraints. Instead, you’ll attempt to pick a representative subset to survey and use those results to draw conclusions.

In either case, the margin of error determines how accurate the sample is to the entire population.

Simple Margin of Error Calculator

Using this quick formula allows calculating the margin of error to be simple and easy.

simple margin of error equation

Let’s say you received 2000 responses to your query about social media platforms. In this case, the margin of error would be .022. Therefore, there is a 2.2% margin of error in your sample. 

Extended Margin of Error Calculator

Here is the universal formula for calculating the margin of error for a sample.

extended margin of error equation

Z = Z score; this is already calculated. You can reference the following Z Score Table.

p̂ = sample size proportion

n = sample size

Step 1: Calculate p̂ by calculating the number of respondents that you are selecting. Ex: you can look at each social media site individually then compare it to the entire sample. The p̂ value is represented by a percentage of respondents. See the example below for more detail.

Step 2: Find Z Score corresponding to a 95% confidence level or 1.96 in this case.

Step 3: Calculate and convert to a percentage.

Using the social media example again, let’s say the company conducted the survey and found that 30% of their customers prefer Facebook as their social media platform. Since you are comparing 30% of users that preferred Facebook to the 70% that preferred a different platform, here is how the equation would look:

extended margin of error equation example

When we input these numbers, our answer is 2.0%, slightly different from the easy formula. 


Using samples of a population for survey data will always provide a range, not a specific number. Therefore, the margin of error reveals the imprecision within the sample. 

The only real way to reduce your margin of error and improve your cash flow is to increase your sample size and get more respondents. The smaller the margin of error, the more confidence you may have in your results. The bigger the margin of error, the farther they can stray from the views of the total population.

Finally, the margin of error calculators offers a certain statistical way of predicting the accuracy and reliability of your survey results compared to the entire population.  


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