# Margin of error calculator – use for free. Plus everything you need to know.

## Margin of error calculator

Use our margin of error calculator to determine how accurate your survey data is as a representation of the wider public.

You’ll need three numbers:

1. the total number of people your survey represents. For example, if you’re conducting a social housing survey, the total number of people in social housing in your domain will be the population size.
2. the sample size. this is how many people within the population that respond to your survey. their views are a sample of the total population and will be used to speak for the wider group.
3. confidence level. this number is how confident you are that the views expressed by the sample size are an accurate reflection of the total population. The higher the number, the more confident you are. (Note – we don’t offer a confidence level below 90% as anything below that is unlikely to represent quality survey data.)

Just input the relevant numbers and the calculator will determine the margin of error for your survey.

90% 95% 99%

## What is the margin of error?

The margin of error is an estimate of how accurate your feedback is – and how likely it is to reflect the opinions of people outside of your survey sample.

Aside from a census, most surveys will never reach an entire population – they reflect the views of a sample of the population.

Therefore, there’s always the question of whether the sample size matches up with what everyone else thinks.

This is where the margin of error comes in.

The larger the margin of error, the less confidence you should have in how closely the views expressed by the sample represent the views of the target population as a whole.

## How to calculate margin of error

Use our free margin of error calculator. It will be a mathematical sum made up of these 3 factors:

• Population size (overall)

How many people will the survey data represent?

For example, in social housing, you may have 50,000 tenants. So any feedback from a social housing survey will be understood to represent those 50,000 people – even if not all of them participated.

• Confidence level

How confident are you that the data accurately reflects the overall population of the people you surveyed?  It is usual to set this at 95% .

• Sample size

You will usually survey a certain number of people within a wider group – such as 1,000 social tenants out of 50,000 tenants in a social housing community.

The sample size of 1,000 will be used to understand the feelings and opinion of the 50,000.

## How to use margin of error

In a social housing survey, if 70% of social housing tenants respond they are happy with their provider, and if your margin of error is 3%, then you can estimate that between 67% and 73% of all social housing tenants are happy.

This is because your 3% margin of error reflects a possible change of 3% higher or lower than your survey results.

Once you know the minimum and maximum numbers you’re dealing with, you can begin plans for strategic action based upon your data.

Ultimately, taking margin of error into account means you can be more confident that you are unlikely to underestimate or overestimate how much your data reflects the wider population.

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