Sample Size for 95% Confidence, ±5% Margin of Error
Required respondents assuming a 50% population proportion and an unlimited population. Use the calculator below to adjust any input.
Required Sample Size
385
Example
At 95% confidence with a 5% margin of error and a 50% assumed proportion, you need a sample size of at least 385 respondents.
Z-Score Used
1.96
Finite Population Correction
Not applied
Why Sample Size Matters
Sample size is the number of respondents or observations needed for a survey or study to produce results that reliably reflect the true population within a stated margin of error and confidence level. Too small a sample risks results that don't generalize; too large a sample wastes time and money collecting more precision than needed.
Confidence level is a measure of how certain you want to be that your sample's result falls within your stated margin of error — 90%, 95%, and 99% are the most common choices, each tied to a specific z-score from the normal distribution (1.645, 1.960, and 2.576 respectively).
Required sample size at other margins of error
| Margin of Error | Required Sample Size |
|---|---|
| ±1% | 9,604 |
| ±2% | 2,401 |
| ±3% | 1,068 |
| ±5% | 385 |
| ±7% | 196 |
| ±10% | 97 |
How Is Sample Size Calculated?
The base formula uses the z-score for your chosen confidence level, an assumed population proportion, and your target margin of error. If you provide a finite population size, a correction factor reduces the required sample — since sampling a larger share of a small population increases precision faster than the unbounded formula assumes.
Why 50% Is the "Safest" Proportion Assumption
The term p × (1 − p) is maximized when p = 50%, producing the largest possible sample size estimate for a given margin of error and confidence level. Using 50% when you don't have a prior estimate guarantees your sample is large enough regardless of how the actual population splits.
Margin of Error Shrinks Slowly as Sample Size Grows
Because sample size in the denominator is under a square root in the margin-of-error formula, cutting the margin of error in half requires roughly quadrupling the sample size — which is why going from a 5% to a 1% margin of error, a common ask, increases the required sample size by roughly 25 times.
When the Finite Population Correction Matters
The correction factor has almost no effect when your population is much larger than the unbounded sample size estimate (say, 20 times larger or more) — but it can meaningfully reduce the required sample when you're studying a small, well-defined group, like all employees at a single company.
Example — Your Current Inputs
At 95% confidence with a 5% margin of error and a 50% assumed proportion, you need a sample size of at least 385 respondents.
Additional Example — A National Opinion Poll
A national poll targeting 95% confidence and a ±3% margin of error, assuming a 50% proportion and an effectively unlimited population, needs about 1,068 respondents — close to the sample sizes commonly reported by major polling organizations.
About These Parameters
- Confidence Level
- How certain you want to be that the true population value falls within your stated margin of error across repeated sampling — 95% is the standard default across most fields.
- Margin of Error
- The maximum acceptable gap between your sample's result and the true population value. Smaller margins require dramatically larger samples due to the square-root relationship in the formula.
- Population Proportion
- Your best guess at how the population splits on the measured question. Use 50% if you have no prior information — it's the most conservative assumption.
- Population Size
- Optional — leave blank for large or unlimited populations. Providing a specific number applies the finite population correction, which can meaningfully shrink the required sample for small, well-defined groups.
Frequently Asked Questions
What sample size do most surveys use?
Many national polls target around 1,000-1,200 respondents, which produces roughly a ±3% margin of error at 95% confidence — a common industry standard balancing accuracy and cost.
Does a bigger population always need a bigger sample?
No — once a population is large relative to the required sample size, further population growth barely changes the needed sample at all. A poll of 1 million people and 1 billion people need almost the same sample size for the same margin of error and confidence level.
What if I don't know the population proportion?
Use 50% — it maximizes the required sample size, making it the safest assumption when you have no prior data on how responses will split.