Introduction
The Margin of Error Calculator tells you how precise your survey results are. When you survey a group of people, you can't ask everyone in the whole population. Instead, you ask a smaller group — called a sample. The margin of error shows how close your sample's answers are likely to be to the true answer for the entire population.
For example, if a poll says 60% of people like a product with a margin of error of ±3%, the real number is most likely between 57% and 63%. A smaller margin of error means your results are more reliable. A larger one means there is more uncertainty.
To use this calculator, enter your confidence level, sample size, and population proportion. If you know the total population size, you can add that too for a more exact result. The tool will instantly calculate your margin of error, show you the confidence interval, give you a step-by-step solution, and display a chart so you can see how changing your sample size affects precision.
How to Use Our Margin of Error Calculator
Enter your survey details below to find out how precise your results are. The calculator takes your inputs and gives you a margin of error, a confidence interval, and a step-by-step breakdown of the math.
Confidence Level: Pick how sure you want to be that your results are correct. Most surveys use 95%. A higher number means more certainty, but it also makes the margin of error bigger.
Sample Size (n): Type in the number of people you surveyed. A bigger sample gives you a smaller margin of error, which means more precise results. If you need to figure out how many people to survey before running your study, try our Sample Size Calculator.
Population Proportion (p%): Enter your best guess for the percentage of people who hold the trait you are measuring. If you are not sure, leave it at 50%. This gives you the largest and safest margin of error.
Population Size (N): This field is optional. Enter the total number of people in the full group you are studying. If the group is very large or you do not know the number, leave this blank. When your sample is a large part of the population, filling this in will lower your margin of error.
What Is Margin of Error?
Margin of error tells you how close your survey results are to what the whole group really thinks. When you ask a small number of people a question instead of asking everyone, your answer won't be perfect. The margin of error is a range — shown as a plus-or-minus number — that tells you how far off your results might be from the true answer.
For example, if a poll says 60% of people like chocolate ice cream with a margin of error of ±3%, the real number is most likely between 57% and 63%.
How Is Margin of Error Calculated?
The margin of error formula is:
MOE = z × √(p(1 − p) / n)
Here is what each part means:
- z (Z-score): A number tied to your confidence level that comes from the normal distribution. A 95% confidence level uses a Z-score of 1.96. A higher confidence level means a larger Z-score and a wider margin of error. You can also think of this as a critical value for your chosen confidence level.
- p (Population proportion): Your best guess of the percentage of people who hold the trait you are measuring. If you don't know, use 50% — this gives you the largest and safest margin of error.
- n (Sample size): The number of people you surveyed. A bigger sample gives you a smaller margin of error.
What Is the Finite Population Correction?
When your sample is a large chunk of the total population, the basic formula overstates the error. The finite population correction (FPC) fixes this. It multiplies the margin of error by:
√((N − n) / (N − 1))
Here, N is the total population size and n is your sample size. This factor shrinks the margin of error because you have already surveyed a big part of the group. If your population is very large or unknown, you can skip this step.
What Is a Confidence Level?
The confidence level is how sure you want to be that your range captures the true answer. A 95% confidence level means that if you ran the same survey 100 times, about 95 of those results would contain the true value. Higher confidence levels give you more certainty but also produce a wider margin of error. To build a full interval around your survey result, use our Confidence Interval Calculator.
What Is a Good Margin of Error?
In most surveys and polls, a margin of error between 2% and 5% is considered good. Below 2% is excellent but usually needs a very large sample. Between 5% and 7% is still acceptable for many purposes. Anything above 7% means your results may not be reliable enough to draw strong conclusions. You can explore related measures of accuracy with our Percent Error Calculator or review spread in your data using the Standard Deviation Calculator.
How to Reduce Margin of Error
There are three main ways to make your margin of error smaller:
- Increase your sample size. This is the most common fix. More responses lead to more precise results. Use our Sample Size Calculator to find the exact number of responses you need for your target margin of error.
- Lower your confidence level. Going from 99% to 95% shrinks the margin of error, but you give up some certainty.
- Use a proportion closer to 0% or 100%. The margin of error is largest at 50% and gets smaller as the proportion moves toward either extreme. You usually can't control this, but it helps explain why some surveys have tighter results than others.