What is Margin of Error?
Margin of error is a range of uncertainty in your survey data. It tells you how close your sample results are to what you would find if you surveyed every single person in the target group.
For example, imagine your survey shows that 60% of people like a new product. If your margin of error is 4%, the true answer for the whole population is likely between 56% and 64%. This concept is closely tied to sampling error, which happens anytime you study a sample instead of the entire group.
How to Calculate Margin of Error
You can calculate this number by hand if you do not have a margin of error calculator handy. The process requires a few specific statistical values.
The Margin of Error Formula
The standard formula is written as:
Margin of Error = Z * sqrt[(p*(1-p)) / n]
Here is what each part of the formula means:
- Z is your Z-score. This number changes based on your confidence interval. For a 95% confidence level, the Z-score is 1.96.
- p is your sample proportion. If you do not have a prior survey to base this on, you should use 0.5 (which represents 50%). This gives you the most conservative, safest estimate.
- n is your sample size, or the total number of survey responses you collected.
Note: If your sample size is more than 5% of your total population, you must use a finite population correction factor. Our calculator above does this for you automatically.
Step-by-Step Calculation Example
A neighborhood association polls 380 households out of 4,200 in the area. They want a 95% confidence level and have no prior estimate, so they use p = 0.5.
- Z for 95% confidence = 1.96
- p = 0.5, so p(1 − p) = 0.25
- n = 380
- 0.25 / 380 ≈ 0.000658
- √0.000658 ≈ 0.02565
- 1.96 × 0.02565 ≈ 0.0503
Without a finite-population correction, the margin of error is about 5.03%. Because 380 is more than 5% of 4,200, apply the correction √((4200 − 380) / 4199) ≈ 0.954. The adjusted margin of error is about 4.80%. Enter sample size 380, population 4200, and 95% confidence in the calculator above to match this.
Key Terms You Need to Know
To get accurate results from the calculator, you must understand the three inputs it requires.
Sample Size
Sample size is the exact number of people who completed your survey. A larger sample size gives you a smaller margin of error. The drop is not one-for-one. Doubling your sample size does not cut the margin of error in half, because the formula uses the square root of n. That is why going from 100 responses to 400 responses cuts the margin of error in half, while adding the same 300 extra responses later has a smaller effect.
Confidence Level
Confidence level represents how sure you can be that the true population answer falls within your margin of error. The most common choice is 95%. This means if you ran the same survey 100 times, the results would fall within your margin of error 95 times. You can also choose 90% or 99%. A higher confidence level means a larger margin of error.
Population Size
Population size is the total number of people in the group you are studying. If you are surveying voters in a small city of 50,000 people, your population size is 50,000. If you are surveying a massive country, you can often leave this blank or enter a very high number, because the math levels out when the population is extremely large.
How to Reduce Margin of Error in Your Survey
A high margin of error makes your data less useful. Here are the best ways to lower it.
Increase your sample size. This is the most reliable way to get a lower margin of error. Collecting more responses shrinks the range of uncertainty. In practice, collect as many responses as your time and budget allow, then check the result in the calculator above. If the margin of error is still too wide for the decision you need to make, you need more responses.
Lower your confidence level. If you drop your confidence level from 99% to 95%, your margin of error will go down. You trade a little bit of certainty for a tighter number range.
Reduce variability. If your audience mostly agrees on a topic, your margin of error will naturally be smaller. You cannot always control this, but it helps to write clear, unbiased survey questions.
Frequently Asked Questions
What is a good margin of error?
A good margin of error is usually between 3% and 5%. Most professional surveys and political polls aim for a margin of error around 3% or 4% at a 95% confidence level.
Is a 10% margin of error bad?
A 10% margin of error is generally considered high and unreliable for making precise business or political decisions. It means your results could be 10% higher or lower than the true value, which is a very wide range.
What is the standard margin of error for surveys?
The industry standard for most surveys is a 5% margin of error combined with a 95% confidence level. This provides a balance between statistical accuracy and the cost of collecting data.
Does population size affect margin of error?
Yes, but only up to a certain point. Population size greatly affects the margin of error in small groups, like a school of 500 students. However, for very large populations, the margin of error barely changes. A survey of 1,000 people has roughly the same margin of error whether the total population is 100,000 or 100 million.
Can margin of error be zero?
No, margin of error can never be zero in survey research. As long as you are collecting data from a sample instead of the entire population, there will always be some level of uncertainty.
What happens if margin of error is greater than the difference between two choices?
If the margin of error is larger than the gap between two options, the race or result is considered a statistical tie. You cannot confidently say one option is beating the other.