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Sample Size Calculator

Sample Calculator

Determine the optimal number of respondents needed for your research

60%
70%
80%
90%
95%
99%
Enter value between 1-30%
Typical values: 3-5%
Enter value between 1-99%
Use 50% for maximum variability
Must be positive number

Required Sample Size

Margin of Error Calculator

Calculate the confidence interval for your existing sample

60%
70%
80%
90%
95%
99%
Must be positive number
Enter value between 1-99%
Must be positive number

Margin of Error

Sample Size Calculator

Looking to calculate the ideal sample size for your research, survey, or experiment?
Our Sample Size Calculator helps you find the right number of people to include from your target population using a 95% confidence level.

Whether you’re dealing with a larger sample size or smaller samples, this tool considers essential factors like population size, margin of error, and confidence interval to ensure accurate results every time.

This size calculator is perfect for students, researchers, and professionals who need to determine sample size based on statistical power and random sampling techniques.
Try our calculator today and get instant, reliable results for your research.

Understanding Confidence Intervals and Sample Size in Statistics:

In statistics, we often estimate information about a population by studying a random sample.
For example, if p is the proportion of individuals with a specific trait (like brown hair), we can estimate p by selecting a sample of n individuals and calculating p̂ (sample proportion).

However, p̂ may differ from p due to sampling variation — that’s why we use a confidence interval to define how close our estimate is likely to be to the true value.

What Is a Confidence Level?

A confidence level represents how sure we are that the sample results reflect the population within a certain range.
Common levels include 90%, 95%, and 99%, each corresponding to a z-score value.

Confidence LevelZ-score (±)
0.901.64
0.951.96
0.992.58

For example, a 95% confidence level means that 95 out of 100 calculated intervals would contain the true population value.

Confidence Interval Formula (Proportion)

Formula:

p̂ ± z × √[ p̂(1 − p̂) / n ]

This tells us how far the observed sample proportion (p̂) might deviate from the true population proportion (p).

Finite Population Correction (FPC)

When the population size (N) is small, apply the Finite Population Correction:

√[ (N − n) / (N − 1) ]

This ensures more accurate confidence intervals for smaller or limited populations.

Example

Scenario:
A company has 120 employees, and 85 of them drink coffee daily.
Find the 99% confidence interval for coffee drinkers.

  • p̂ = 85 / 120 = 0.7083

  • z = 2.58 (for 99% confidence)

  • Apply the confidence interval formula and FPC (if needed)

The result gives a statistical range showing where the true proportion of coffee drinkers likely lies.

Sample Size Calculation Formula:

To determine the required sample size for a given confidence level and margin of error (ε), use:

n = (z² × p̂ × (1 − p̂)) / ε²

Example:
Estimate the proportion of supermarket shoppers who are vegan.

  • Confidence Level: 95% (z = 1.96)

  • Margin of Error: 0.05

  • Estimated Proportion (p̂): 0.5

Result:
Required Sample Size ≈ 385 respondents

If your estimated proportion changes (for example, p̂ = 0.06), simply recalculate using the same formula.

Why Use Our Sample Size Calculator?

  • Calculates precise sample size instantly

  • Adjusts for finite population

  • Supports different confidence levels (90%, 95%, 99%)

  • Perfect for academic research, market surveys, and data-driven studies

  • Uses statistical formulas trusted by professionals

Our calculator helps you save time and ensures your data-driven decisions are backed by solid statistical foundations.

Conclusion:

Understanding sample size, confidence levels, and margins of error is key to producing accurate and reliable research results.
Use our free Sample Size Calculator to make confident decisions backed by data and statistics — and ensure every survey or experiment yields meaningful insights.

Related Calculators:
Binary Calculator, Standard Deviation Calculator, Probability Calculator

External Resource:
Sample Size Determination

A Sample Size Calculator helps determine how many people or items you need in a survey or research study to get statistically valid results. It uses factors like confidence level, margin of error, and population size to estimate the ideal sample size.

The sample size directly affects how accurate your results are. A larger sample size gives more reliable results and reduces margin of error, while a smaller sample may not fully represent the target population.

You can calculate the sample size using this formula:
n = (z² × p̂ × (1 − p̂)) / ε²
Where:

  • z = Z-score (based on confidence level)
  • p̂ = estimated proportion of the population
  • ε = margin of error

Or, you can simply use our online Sample Size Calculator — it automatically applies this formula for you.

A confidence level represents how sure you are that your results reflect the true population. Common confidence levels include 90%, 95%, and 99%, with 95% being the most widely used in surveys and academic research.

The margin of error shows how much your survey results might differ from the actual population value. A smaller margin of error means more precision, but it usually requires a larger sample size.

Our Sample Size Calculator is based on well-established statistical formulas used by researchers and analysts worldwide.