What Is Raosoft Sample Size?
The sample size for a survey depends on four things: how much error you can accept (margin of error), how confident you want to be, how large the population is, and how split you expect the answers to be. Setting the response distribution to 50 % is the conservative choice because it gives the largest sample.
The calculator also shows the sample size without the finite population correction, the z critical value used, and the margin of error implied by the result. A lookup table and chart let you compare several margins and confidence levels at once.
The sections below show the formula, define each variable, work through an example and answer questions such as what happens when the population is very large and how to treat low response rates.
How to Use the Raosoft Sample Size Calculator
- Enter the margin of error you can live with, for example 5%.
- Pick the confidence level (95% is standard).
- Enter the size of the population, or leave it at a large default if it is unknown or very large.
- Leave the response distribution at 50% unless you have good evidence about the likely split.
- Use the result as the number of completed responses you need, and plan for non-response.
Raosoft Sample Size Formula
Sample size with finite population
Margin of error for a given n
Raosoft Sample Size Variables Explained
| Symbol | Meaning | Notes |
|---|---|---|
| n | Recommended sample size | Rounded up |
| N | Population size | Use a large number if unknown |
| E | Margin of error | As a proportion, e.g. 5 % = 0.05 |
| z | Critical value for the confidence level | 1.96 for 95 % |
| p | Expected response distribution | 50 % is the most conservative |
Raosoft Sample Size Worked Example
With the example values loaded in the calculator above, the steps are:
- x = z² × p(1 − p) = 1.96² × 0.5 × 0.5 = 0.960365.
- n = N·x ÷ ((N − 1)·e² + x) = 1500 × 0.96036 ÷ ((1499) × 0.0025 + 0.96036) = 305.99.
- Round up to 306.
Result: Recommended sample size = 306.
Worked Example: A Survey of 1,500 Members
A club has 1,500 members and wants ±5% at 95% confidence, using the cautious 50% response distribution. Then x = 1.96² × 0.5 × 0.5 = 0.9604, and n = 1,500 × 0.9604 ÷ (1,499 × 0.0025 + 0.9604) = 306 after rounding up.
Without the population correction the answer would be 385, so knowing the group is small saves about 80 responses. Tightening the margin to ±3% raises the requirement to 624. These counts are the completed responses you need, not the invitations you send. If only part of those invited reply, divide by the expected response rate.
Understanding the four inputs
A “±5% at 95% confidence” statement means: if you repeated the survey many times, in 95 out of 100 the true population percentage would be within 5 points of the percentage you observed.
| Input | Meaning | Typical value |
|---|---|---|
| Margin of error | How far the sample result may be from the true value | 3% to 5% |
| Confidence level | How sure you want to be that the true value lies within the margin | 95% |
| Population size | Number of people in the group you want to describe | Known or large |
| Response distribution | Expected share answering a particular way | 50% when unknown |
Why more responses give diminishing returns
Precision improves with the square root of the sample size. Moving from ±10% to ±5% costs about three times as many responses; moving from ±5% to ±2.5% costs four times more again. The chart shows how steeply the curve climbs as the margin shrinks, which is why most surveys stop around ±3% to ±5%.
Does the population size matter?
Only when it is small. Once the population exceeds about 20,000 the required sample hardly changes: it is around 377 for ±5% at 95% whether the population is 20,000 or 20 million. For a population of a few hundred the required sample is a large share of it, so enlarge your effort to reach most of them.
Things the formula does not handle
- Non-response: if only 30% of invitations are answered, invite about three times as many people as the sample size.
- Bias: a large sample drawn from the wrong people is still wrong.
- Subgroups: if you need results for subgroups, size each separately.
- Clustered designs: cluster sampling needs a design-effect adjustment (see the Cochran calculator).
Where Raosoft Sample Size Is Used
Survey sample size
Find the number of responses needed for your margin of error and confidence level.
Finite populations
Apply the population correction when the group is small.
Reading the table
See sample sizes for several margins and confidence levels at once.
Response distribution
Test how the expected split changes the sample size.
Common Raosoft Sample Size Mistakes to Avoid
- Always report the margin of error and confidence level with survey results.
- Round up.
- Increase the sample for subgroup comparisons.
- When in doubt use 50% for the response distribution.
Raosoft Sample Size Terms and Definitions
- Response distribution
- The expected percentage of respondents giving a particular answer; 50% is the most conservative choice.
Raosoft Sample Size FAQs
How do I use the Raosoft sample size calculator?
Enter your margin of error, confidence level, population size and expected response distribution. The tool returns the number of responses needed.
What is a good sample size for a survey?
For ±5% at 95% confidence, about 385 completed responses for a large population. Smaller populations need fewer.
Why is the response distribution 50% by default?
Because it maximises the variability p(1 − p), so the resulting sample size works whatever the true split turns out to be.
Does this match the original Raosoft results?
The formula is the same, so results should agree for the same inputs. Small differences can arise from rounding.
What if I don’t know my population size?
Use a large number. Above about 20,000 the result barely changes.
How many people should I invite?
Divide the sample size by the response rate you expect. With a 20% response rate you need five times as many invitations as responses.
Why does the Raosoft calculator give 377 and not 385?
At ±5% and 95% confidence with a 50% response distribution, an unlimited population needs 385. Raosoft's default population is 20,000, and the finite population correction brings the answer down to 377. Enter 20,000 here to match it.
How does the population size change the answer?
Only when the population is small. At ±5%, 95% and 50%, a population of 500 needs 218 responses, 1,500 needs 306, 20,000 needs 377 and 100,000 needs 383.
What happens if I use a 99% confidence level?
The sample grows. For a population of 20,000, ±5% and 50%, 99% confidence needs 643 responses instead of 377 at 95%.