Statistics
Sample Size Calculator
Use your desired confidence, margin of error, and response distribution to size surveys with or without a finite population.
Estimate how many responses you need for surveys or polls with margin of error and confidence tuning.
Sample size with finite correction
n₀ = (Z² × p(1 − p)) / E² n = n₀ / [1 + (n₀ − 1)/N]
Z is the critical value for the confidence level, p is the assumed response proportion, E is the margin of error, and N is the population (optional).
How to use
- Pick a confidence level to set the Z-score.
- Enter the acceptable margin of error and expected response distribution.
- Optionally add a population size to apply the finite population correction.
Example
Input: Confidence = 95%, Margin of error = 5%, Distribution = 50%, Population = 10,000
Output: Sample size ≈ 385 without population, ≈ 370 with finite correction
Student-friendly breakdown
This walkthrough emphasizes the most searched ideas for Sample Size Calculator: sample size calculator, survey sample size calculator, sample size margin of error, finite population sample size calculator. Start with the formula above, then follow the guided steps to double-check your work. For quick revision, highlight the givens, plug into the equation, and finish by verifying your units.
Need more support? Use the links below to open the long-form guide, browse additional examples, or hop into adjacent calculators within the same topic. Each resource is interlinked so crawlers (and readers) can discover the next best action within a couple of clicks—one of the easiest ways to lift topical authority.
Deep dive & study plan
The Sample Size Calculator is a go-to tool whenever you need to estimates the responses needed to hit a target margin of error and confidence level.. It focuses on sample size, margin of error, confidence level, which means searchers often arrive with intent-heavy queries like “how to sample size calculator quickly” or “sample size calculator formula explained.” Use this calculator to capture those intents and keep learners on the page long enough to send positive engagement signals.
Under the hood, the calculator leans on z is the critical value for the confidence level, p is the assumed response proportion, e is the margin of error, and n is the population (optional).—that’s why we surface the full expression (“n₀ = (Z² × p(1 − p)) / E² n = n₀ / [1 + (n₀ − 1)/N]”) directly above the interactive widget. When you embed that formula inside H2s or supporting paragraphs, you help both humans and crawlers understand what entity the page represents.
Execution matters as much as the math. Follow the built-in procedure: Step 1: Pick a confidence level to set the Z-score. Step 2: Enter the acceptable margin of error and expected response distribution. Step 3: Optionally add a population size to apply the finite population correction.. Each numbered instruction is short enough to scan on mobile but descriptive enough to satisfy Google’s Helpful Content guidelines. Encourage students to jot down units, double-check signs, and compare answers with the Example card to build confidence.
The Example section itself is packed with semantic clues: “Confidence = 95%, Margin of error = 5%, Distribution = 50%, Population = 10,000” leading to “Sample size ≈ 385 without population, ≈ 370 with finite correction.” Pepper similar narratives throughout your copy (and internal links from related guides) so canonical search intents are answered without pogo-sticking back to Google.
Quick retention checklist
- Speak the formula aloud (or annotate it) so the relationships stick.
- Write each step in your own words and compare with the numbered list above.
- Swap in new numbers for the Example to make sure the calculator (and your logic) handles edge cases.
- Link out to at least two related calculators to keep readers exploring your topical hub.
FAQ & notes
What response distribution should I use?
If you do not know the true proportion, use 50%. It produces the largest (safest) sample size requirement.
Can I model different confidence levels?
Yes—switch between 80%, 85%, 90%, 95%, or 99% confidence to see how the Z-score scales the required sample.
What formula does the Sample Size Calculator use?
Z is the critical value for the confidence level, p is the assumed response proportion, E is the margin of error, and N is the population (optional).
How do I use the Sample Size Calculator?
Pick a confidence level to set the Z-score. Enter the acceptable margin of error and expected response distribution. Optionally add a population size to apply the finite population correction.