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Get to know the appropriate sample size to meet a given set of constraints accurately and quickly using the sample size calculator.
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Find out the target population you need to interview as a representative of the whole population using this sample size calculator. The tool provides accurate results without any manual calculation.
Sample size refers to the number of individuals whose data you collect to accurately reflect the population's opinions or results. Simply put, it is a subset of the population participating in a survey or research.
When conducting surveys in a large population, calculating the sample size is crucial because it is impractical to collect feedback from everyone. Determining sample size allows you to draw conclusions about the entire population based on a subset. Statistical sample distribution is important for researchers, marketers, economists, government agencies, and scientific studies. If you need quick results, you can use our minimum sample size calculator to complete the calculation instantly.
To calculate sample size, you need to consider a few important factors:
The margin of error is the range within which you expect your results to fall. It can be positive or negative and is usually expressed as a percentage (e.g., ±5%). It is also called the confidence interval.
The confidence level indicates how reliable your estimate is within the margin of error. Higher confidence levels mean your estimate is closer to the true population value. Its calculation is based on probability.
Population size is the total number of individuals in the population. If the population is very large and unknown, an estimate like 100,000 can be used. For large populations, sample size does not change significantly, so this estimate is accurate enough.
Standard deviation shows the variation of individual responses around the mean. Low values indicate responses are close to the mean, while high values indicate greater spread.
The Z-score represents your confidence level as a percentage (e.g., 90%, 95%, 99%).
Formula: z = (x – μ) / σ
Use the following formulas depending on population type:
Infinite Population:
\(\text{Sample Size} = \left(\dfrac{\text{Confidence Level} \times \text{Standard Deviation}}{\text{Margin of Error}}\right)^2\)
Finite Population:
\(\text{Sample Size} = \dfrac{n \times N}{n + N - 1}\)
Where:
You can also use a free population proportion calculator to calculate the sample size quickly and accurately. Our sampling distribution calculator can help you calculate probabilities for any value.
| Confidence Level | z-score |
| 80% | 1.28 |
| 85% | 1.44 |
| 90% | 1.65 |
| 95% | 1.96 |
| 96% | 2.05 |
| 98% | 2.33 |
| 99% | 2.58 |
Suppose the standard deviation is 2, the confidence level is 95%, and the margin of error is 5. How do we calculate the sample size for an infinite population?
Sample size formula for infinite population:
\(\text{Sample Size} = \left(\dfrac{1.96 \times 2}{0.05}\right)^2 = (78.4)^2 \approx 6147\)
Our online population calculator makes sample size calculation effortless. Users just need to follow these steps:
Inputs:
Output:
Source: Geopoll – Confidence Interval, and Wikipedia – Sample Size Determination
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