Sample Size Calculator
Estimate survey sample size from confidence level, margin of error, and optional population size. Free statistics planner.
Results
Recommended sample size
- Unlimited-population n
- 385
- Z-score used
- 1.96
You might also need
Educational estimates · not financial advice · free, no signup
Formula / how it works
n₀ = Z²·p·(1−p)/E²; finite population: n = n₀ / (1 + (n₀−1)/N). Default p=0.5.
Detailed guide
What it is, how to use it, how to read the numbers, common mistakes, a worked example, formulas, and FAQs.
What this calculator is
Classical stats, no mystery. The Sample Size Calculator on MyCalcsWorld uses textbook definitions so homework checks stay reproducible. What it does: Estimate survey sample size from confidence level, margin of error, and optional population. Typical inputs: Confidence level, Margin of error (%), Population (optional), Expected proportion (%). Demo defaults (confidence level 95, margin of error 5 %, population (optional) 0, expected proportion 50 %) currently resolve to Recommended sample size 385 in the live panel — change any field to explore sensitivity. Who it helps: students and analysts validating means, spreads, combinations, and classical probabilities on small datasets.
When to use / who it helps
- Planning a poll or customer survey.
- Seeing how tighter margins explode required n.
- Use the Sample Size Calculator to validate homework summaries or exploratory stats on small samples.
- State sample vs population formulas before comparing to a textbook key.
- Move to a full stats package for inference, A/B tests, or publication work.
How to use
Steps
- Choose 90/95/99% confidence.
- Enter margin of error % and optional population.
- Optionally set expected proportion (default 50%).
- Read recommended n.
- Optional: change one input to see how sensitive the result is.
- Open the Sample Size Calculator on MyCalcsWorld and skim the labeled fields before you type.
How to interpret results
- Finite-population correction lowers n when N is small relative to n₀.
- Z comes from the standard normal for the chosen confidence.
- Each result is driven only by the labeled inputs (Confidence level, Margin of error (%), Population (optional), Expected proportion (%)); anything not on the form (fees, holidays, clinical adjustments) is outside this estimate.
- Summary stats describe the sample you typed; they do not automatically generalize to a population.
- Watch sample vs population variance/std-dev definitions when matching homework keys.
Common mistakes & gotchas
- Using 99% confidence with a tiny budget and wondering why n is huge.
- Ignoring design effects for cluster samples.
- Using population variance when the homework wants the sample formula (or reverse).
- Typing unsorted or incomplete lists into: Confidence level, Margin of error (%), Population (optional), Expected proportion (%).
- Generalizing a tiny sample as if it were a population claim.
Worked example
Worked example — 95% confidence, ±5%, p=0.5
- Z ≈ 1.96; E = 0.05; n₀ = 1.96²·0.25 / 0.05² ≈ 385.
- Open the Sample Size Calculator (sample size) and note the starting defaults (confidence level 95, margin of error 5 %, population (optional) 0, expected proportion 50 %).
- Use these labeled inputs (the form defaults): Confidence level = 95; Margin of error = 5 %; Population (optional) = 0; Expected proportion = 50 %.
- Read the live result panel. With those defaults, MyCalcsWorld currently reports: Recommended sample size: 385.
Result: With defaults (confidence level 95, margin of error 5 %, population (optional) 0, expected proportion 50 %), the Sample Size Calculator shows: Recommended sample size 385.
To load the form's own demo values, tap Try example above the Calculate button.
How to calculate / formula
n₀ = Z²·p·(1−p)/E²; finite population: n = n₀ / (1 + (n₀−1)/N). Default p=0.5.
Frequently asked questions
Why default proportion 50%?
It maximizes p(1−p), giving a conservative (larger) sample size.
What if my population is 2,000?
Enter it — the finite correction reduces n versus the unlimited formula.
Is this for A/B tests?
It is a survey proportion formula; experiments often need power analysis instead.
Does 95% mean we are sure?
It refers to long-run coverage of the confidence procedure, not certainty about one sample.
Is this financial, medical, or legal advice?
No. MyCalcsWorld tools are educational estimators you can reconcile with professional advice for your situation.
What does the Sample Size Calculator on MyCalcsWorld actually compute?
Estimate survey sample size from confidence level, margin of error, and optional population. You enter Confidence level, Margin of error (%), Population (optional), Expected proportion (%), and the result panel updates in your browser.
What inputs does the Sample Size Calculator need?
The Sample Size Calculator asks for: Confidence level; Margin of error (%); Population (optional) — 0 = unlimited / unknown. Extra controls under “More options” can be left at their defaults.
What results does the Sample Size Calculator show?
The panel reports Recommended sample size. Each figure is recalculated whenever you change an input, so you can compare scenarios side by side.