How many people do you need to survey before the results mean something? Ask too few and the numbers wobble. Ask too many and you waste time and money.
The Sample Size Calculator finds how many respondents a survey needs. You set the confidence level, margin of error, and population size. It suits researchers, students, marketers, and teams planning a poll.
Table of Contents
- What the Calculator Does
- How to Use It, Step by Step
- The Sample Size Formula
- Worked Example
- How to Read the Results
- What Changes the Sample Size
- Limitations and Assumptions
- FAQs About the Sample Size Calculator
What the Calculator Does
The tool plans a survey that estimates a percentage, such as how many customers say yes. It updates as you change any input.
- Required Sample Size: the main result, rounded up to a whole respondent.
- Z-Score Value: the critical value for your confidence level.
- Infinite Population Base: the sample size before any population adjustment.
- Population Sampling %: your sample as a share of the population.
- Recruit for 10% Dropout (Sample / 0.9): how many surveys to send if one in ten people will not finish.
- Copy Sample Plan copies a text summary, and Reset restores the sample values.
How to Use It, Step by Step
- Pick a Confidence Level (%): 90%, 95%, or 99%. The sample value is 95%.
- Enter the Margin of Error (±%) from 0.1 to 50, such as 5 for plus or minus 5 points.
- Enter the Population Size as a whole number of at least 1. Leave it blank if the group is very large or unknown.
- Enter the Response Proportion (P) as a percent from 1 to 99. Use 50 if you have no estimate.
- Read the required sample size, then check the four cards below it.
- Press Copy Sample Plan to paste your plan into a document.
The Sample Size Formula
The tool uses Cochran's formula for a proportion. It then shrinks the answer when the population is small enough to matter.
Z² × p × (1 - p)÷E²=Base n0→Sample Size
- n0 = Z² × p × (1 - p) ÷ E², where p and E are written as decimals.
- If you enter a population N, the tool uses n = n0 ÷ (1 + (n0 - 1) ÷ N).
- Required sample = n, rounded up, and never above N. Base = n0, rounded up.
- Recruit = required sample ÷ 0.9, rounded up, using exact whole-number math.
- Z is fixed at 1.644854, 1.959964, or 2.575829 for the three confidence levels, shown with six decimals.
Worked Example
Ana runs a customer survey for a club with 500 members. She wants 95% confidence, a 5% margin of error, and p = 50%.
| Result | Calculation | Output |
|---|
| Base n0 | 1.959964² × 0.5 × 0.5 ÷ 0.05² | 384.15, so 385 Respondents |
| Adjusted n | 384.15 ÷ (1 + 383.15 ÷ 500) | 217.49 |
| Required Sample Size | 217.49 rounded up | 218 Respondents |
| Population Sampling % | 218 ÷ 500 × 100 | 43.60% of Pop |
| Recruit for 10% Dropout | 218 ÷ 0.9 = 242.2, rounded up | 243 Surveys |
With the sample values of 20,000 people, the tool shows 377 respondents. With a blank population, 99% confidence, and a 3% margin, it shows 1,844 respondents.
How to Read the Results
Required Sample Size is the number of completed responses you need. Infinite Population Base is the answer if your group were huge. Comparing the two shows how much a small population saves you.
Population Sampling % shows the sample as a share of your population, such as "1.88% of Pop". With a blank population, the card reads Infinite instead.
The recruit card shows how many surveys to send. For the sample values, 377 respondents become 419 surveys. If a finite population is too small, the card adds "(more than the population)".
What Changes the Sample Size
The margin of error has the biggest effect. Halving it, from 5% to 2.5%, roughly quadruples the base sample. Higher confidence also raises the number, because the Z value grows.
The proportion matters too. A 50% proportion gives the largest sample, which is why it is the safe default. If past surveys say about 20% of people answer yes, the base drops to 246.
Population size only helps when the sample is a notable part of it. For a population of 20,000, the saving is small. For 500, it is large.
After collecting data, the confidence interval calculator shows how precise your mean is. The z-score calculator explains the critical values behind each confidence level.
The probability calculator helps with chance questions. You can summarize your responses with the standard deviation calculator or the average calculator. More tools are in the math and science calculators hub.
Limitations and Assumptions
- The formula fits a yes or no style question about a proportion, not a study of means.
- It assumes a simple random sample. Clusters, strata, and weighting need other methods.
- Only the 90%, 95%, and 99% confidence levels are offered.
- The margin of error must be 0.1 to 50, and the proportion must be 1 to 99. Other entries show a message.
- A population of 0, a negative number, or a decimal is rejected. Leave the box blank for unlimited.
- The recruit card assumes exactly 10% dropout, not a response rate model you choose.
- Low response and biased sampling can hurt a survey more than a small sample does.
FAQs About the Sample Size Calculator
What sample size do I need for a 95% confidence level and 5% margin of error?
For a very large population with p = 50%, the tool shows 385 respondents. A population of 20,000 gives 377.
What should I enter if I do not know the population size?
Leave the box blank. The tool then skips the population adjustment and shows the unlimited result.
Why is the default proportion 50%?
A proportion of 50% produces the largest required sample. It is the cautious choice when you have no earlier estimate.
Why does the recruit card divide by 0.9 instead of adding 10%?
If 10% of invitees drop out, only 90% finish. Dividing by 0.9 gives enough surveys to still reach your target.
Why does a small population need fewer respondents?
Each person you sample from a small group tells you more about everyone left. The finite population step reflects that and lowers the number.
Does a larger sample guarantee accurate results?
No. A larger sample narrows random error only. Bias from who answers, or how you ask, is not fixed by size.
This calculator gives general estimates only and is not professional advice. Reviewed for general accuracy by Prof. Dr. Khalil Mudassar, PhD.