Sample size Calculator

Looking to calculate the ideal sample size for your research or survey?
Our Sample Size Calculator uses a 95% confidence level to help you determine the right number of people to survey from your target population.
Whether you’re working with a larger sample size or smaller samples, our tool considers the margin of error, population size, and confidence interval to give accurate results.
This tool is perfect for researchers needing to determine sample size based on statistical power and random sample techniques.
Try our size calculator to get a precise estimate today.

Understanding Confidence Intervals and Sample Size in Statistics

In statistics, we often infer information about a population by studying a finite sample. For example, if p is the proportion of individuals with brown hair in a population, we can estimate p by selecting a sample of n individuals and calculating p̂, the sample proportion. However, p̂ will generally differ from p due to sampling noise.

Statistics of a Random Sample

The sample proportion p̂ is normally distributed with mean p and variance p(1-p)/n. This is a result of the Central Limit Theorem. The confidence interval indicates the range within which p̂ is likely to fall. The confidence level tells us how often this interval will contain the true p across multiple samples.

Confidence Level

The confidence level reflects the likelihood that the sample reflects the population within a chosen interval. Common levels include 90%, 95%, and 99%, each associated with a specific z-score.

Confidence Interval

A confidence interval is an estimated range likely to include the true population parameter. For example, a 95% confidence interval means that 95% of such intervals from repeated samples would contain the true value. The width of the interval depends on:

• Sample size
• Confidence level
• Variability in the sample

Equation for Confidence Interval (Proportion)

Confidence Interval:
p̂ ± z * sqrt[ p̂(1 - p̂) / n ]

Finite Population Correction (FPC)

When the population size is finite, apply the FPC:

sqrt[ (N - n) / (N - 1) ]

This adjustment corrects for the fact that samples are not independent when drawn from a small population.

Example

Given that 120 employees work at Company Q, and 85 drink coffee daily, find the 99% confidence interval:

• p̂ = 85/120 = 0.7083
• z = 2.58 for 99% confidence
• Apply formula with FPC if needed

Sample Size Calculation

To determine required sample size for a given confidence level and margin of error ε:

n = (z² × p̂(1 - p̂)) / ε²

Example

Estimate proportion of U.S. supermarket shoppers who are vegan:

• Confidence Level: 95% ⇒ z = 1.96
• Margin of Error: ε = 0.05
• Estimated Proportion: p̂ = 0.5
• Required Sample Size: ~385

If updated info gives p̂ = 0.06, recalculate using this value.

Refrence:

Use our Number Sequence Calculator to find missing terms, generate sequences, and solve pattern-related problems.

For advanced statistical analysis, you can use the Sample Size Calculator by Calculator.net to compute precise values for different confidence levels and margins of error.