Sample Size Calculator for a Proportion
Required sample size to estimate a proportion within a margin of error.
Enter your values
Enter the expected proportion you are working with.
Enter the margin of error you are working with.
Choose one of: 90%, 95%, 99%.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- Required sample size
- 385
- z critical value
- 1.96
- Margin of error
- ±5%
Quick answer
Required sample size grows with confidence level and shrinks as the allowed margin of error increases.
n = (z²·p(1-p))/E²
At a glance
| What it does | Required sample size to estimate a proportion within a margin of error. |
|---|---|
| Category | Statistics |
| Inputs needed | Expected proportion, Margin of error, Confidence level |
| Main output | Required sample size |
| Formula | n = (z²·p(1-p))/E² |
| Cost | Free — no sign-up, no download |
How to use the Sample Size Calculator for a Proportion
- 1Enter your best estimate of the expected proportion (use 0.5 if unsure — it's the most conservative).
- 2Enter the acceptable margin of error and confidence level.
- 3The formula scales sample size with z² and shrinks it with the square of the margin of error.
Inputs explained
- Expected proportion
- Enter the expected proportion you are working with.
- Margin of error
- Enter the margin of error you are working with.
- Confidence level
- Choose one of: 90%, 95%, 99%.
Worked example
Using the values the calculator loads with:
Inputs
- Expected proportion0.5
- Margin of error0.05
- Confidence level95%
Results
- Required sample size385
- z critical value1.96
- Margin of error±5%
Frequently asked questions
Why use 0.5 for the expected proportion?
It maximizes p(1-p), giving the most conservative (largest) sample size when the true proportion is unknown.
Why does margin of error matter so much?
Sample size grows with the square of 1/E, so halving the margin of error roughly quadruples the required sample.
What do I need to enter into the Sample Size Calculator for a Proportion?
Just 3 values: expected proportion, margin of error, confidence level. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Sample Size Calculator for a Proportion work out the answer?
Required sample size grows with confidence level and shrinks as the allowed margin of error increases. It applies the formula n = (z²·p(1-p))/E² and shows the working so you can check each step by hand.
Is the Sample Size Calculator for a Proportion free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.