Confidence Interval Calculator (Proportion)
Turn a single survey percentage into a confidence interval. Enter the sample size, the percentage who chose an answer and your confidence level.
Learn how to calculate it yourselfEnter your values
Results update as you type.
How to enter your data
In Sample size, enter how many people answered the question. In Percentage who chose the answer (%), enter the observed percentage, such as 75 for 150 out of 200 respondents. Choose a confidence level. Enter a count in the sample-size box and a percentage in the percentage box, without a percent sign.
Confidence interval
- Margin of error
- ±4.9%
Estimate a confidence interval for a population percentage. Enter the number who answered the question, the percentage choosing the answer of interest, and the confidence level. The interval reflects sampling uncertainty under the model assumptions, not bias or measurement error.
Calculate it yourself
Example: 60 of 100 respondents chose an answer. Build a 95% confidence interval around that percentage.
Follow this worked example, then repeat the steps with your own numbers.
Write the observed proportion
p = 60 ÷ 100 = 0.60; n = 100Calculate the standard error
SE = √[p(1 − p) ÷ n] = √(0.60 × 0.40 ÷ 100) ≈ 0.04899Find the margin of error
Margin ≈ 1.96 × 0.04899 = 0.09602The 95% normal-table multiplier is about 1.96. Keep extra decimal places until the final step.
Subtract and add the margin
(0.60 − 0.09602) × 100 ≈ 50.4%; (0.60 + 0.09602) × 100 ≈ 69.6%
This is the normal approximation used by this tool. It works best when both the number choosing the answer and the number not choosing it are reasonably large; it can be unreliable near 0% or 100%.
Check your answer in the calculatorUse your PaperSurvey.io results
Take a question’s percentage and response count into this calculator to build a confidence interval.
Where it is used
- Teachers: A teacher sees that 42 of 60 students passed a test and wants a likely pass-rate range for all their classes, not just this one group.
- Small-business owners: A cafe owner asks 80 customers whether they would come back, 68 say yes, and wants a realistic range for how satisfied all customers are.
- HR staff: An HR officer surveys 150 employees, 90 say they feel supported at work, and needs a range to report honestly to managers.
What a confidence interval tells you
A confidence interval is the range that very likely contains the true value for the whole population. A 95% confidence interval means that if you repeated the survey many times, about 95% of the intervals would contain the true value.
When should you use it?
Use this calculator when your survey answer is really a yes-or-no, or one choice against all the rest, and you want to know how much to trust that percentage. It fits questions like happy or not happy, pass or fail, would recommend or not, and voted yes or no. It works best when you asked only some of your people, a sample, and want to describe the wider group. Do not use it for averages of scores, prices or amounts. A separate mean calculator handles those.
What does the result mean?
The result is a percentage plus a range, for example 68 percent, from 58 percent to 78 percent. The percentage is what you found in your sample. The range shows where the true figure for your whole group is likely to sit. A narrow range means a precise, more trustworthy result. A wide range means you cannot be very sure yet. Bigger samples give narrower ranges. As a rough guide, many surveys aim for a give-or-take of about 5 percent or less, measured at 95 percent confidence.
Mistakes to avoid
Enter the sample size as a count and the observed share as a percentage. Use only people who answered the question in the sample size. A narrow interval does not guarantee a representative sample. Overlapping confidence intervals alone do not establish whether two groups differ; use an appropriate comparison test. Check the sampling assumptions before generalizing to the population.
How to use this calculator
- In Sample size, enter the number of people who answered the question, for example 200.
- In Percentage who chose the answer (%), enter the observed percentage, for example 75 for 150 out of 200 respondents.
- Choose a confidence level, usually 95%.
- Read the result: your percentage plus a range, for example 85% (from about 77% to 93%).
Worked example
Of 200 randomly sampled guests who answer a question, 150 say they enjoyed the event. Enter 200 in Sample size and 75 in Percentage who chose the answer (%). At 95% confidence, the interval is approximately 69% to 81%, subject to the sampling assumptions.
Frequently asked questions
Confidence interval vs margin of error?
The margin of error is half the width of the confidence interval. Add and subtract it from your result to get the interval.
What do I type in each box?
Enter the number who answered the question in Sample size, the observed percentage in Percentage who chose the answer (%), and your confidence level. For 150 of 200 respondents, enter a sample size of 200 and a percentage of 75.
Where do I get these numbers?
Count how many people answered the question and how many selected the answer of interest. Divide the selected count by the total answering and multiply by 100 to obtain the percentage input.
What does 95% confidence mean?
It means the true figure for your whole group is very likely to fall inside the range shown. If you ran the same survey many times, about 95 times out of 100 the real answer would land in that range.
What is the plus or minus number?
It is how far the result could stretch either side of your percentage, sometimes called the margin of error. A smaller number means a more precise result. Many surveys aim for about 5% or less.
How do I make the range narrower?
Ask more people. Larger samples give tighter, more reliable ranges. Roughly speaking, you need about four times as many responses to cut the range in half.
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