Sample Size Calculator
Minimum sample size for a proportion with margin of error
Whether you are estimating or double-checking a figure, Sample Size Calculator handles sample size calculator margin of error confidence level population instantly. You provide Confidence Level; the tool does the rest in real time. Every answer includes a transparent breakdown you can repeat by hand. Perfect for budgeting, planning, or checking someone else’s figures. Everything runs in your browser — your inputs are not sent to our servers, and it works offline after the first visit (currency conversion needs a live connection). Searching for sample size calculator margin of error confidence level population or free online sample size calculator? This tool covers it — free, fast, and private. Bookmark it and the answer is always one click away.
What does the Sample Size Calculator do?
Sample Size Calculator works out the minimum sample size from the Margin of Error, Expected Proportion, and Population Size, following standard Math conventions — the page defaults produce a minimum sample size of n = 370.
- Inputs: Margin of Error, Expected Proportion, and Population Size.
- Output: the minimum sample size, plus the intermediate steps behind it.
- Method: the standard Math formula, evaluated entirely in your browser.
Quick answer
With the default inputs (margin of error of 5, expected proportion of 0.5, population size of 10,000), sample size calculator returns a minimum sample size of n = 370. Assumptions and limits are summarized below.
How does it work?
Sample Size Calculator computes the minimum sample size directly from your inputs — the Margin of Error, Expected Proportion, and Population Size feed the formula. Nothing is uploaded: the math runs locally in your browser and the result appears as you type.
How the Sample Size Calculator works
Use Sample Size Calculator when the minimum sample size needs to be right the first time: it evaluates your inputs against the standard Math method and shows the working, not just the answer.
Using the Sample Size Calculator
- Margin of Error — a core input the formula applies directly — keep the units consistent with the label.
- Expected Proportion — one of the values the calculation builds from; the result reflects exactly what you type here.
- Population Size — used in the first stage of the calculation, so entering it accurately matters more than any later refinement.
- The output panel in sample size calculator leads with the headline result and follows with the steps behind it, so the value can be checked rather than assumed.
- Iterate. Vary the inputs one at a time; the movement in the figure shows which lever matters most for your sample size question.
The formula behind the result
The engine behind Sample Size Calculator evaluates the inputs in a single pass — no hidden iterations or adjustments — so the result you see is exactly what the formula produces for the values you entered.
Worked example: with margin of error of 5, expected proportion of 0.5, population size of 10,000, this sample size calculation returns n = 370. The same run reports Uncorrected (infinite): 385 | Finite-population correction applied.
The steps it follows:
- Formula: n₀ = z²·p(1−p)/e²
- z = 1.96 (95%)
- n₀ = 1.9600² × 0.5 × 0.50 / 0.050² = 384.2
- Finite correction: n = n₀/(1+(n₀−1)/N) = 370
Substitute your own values and the same steps produce your answer — that is the point of a calculator that shows its working.
Understanding the result
Interpret the minimum sample size against the inputs that produced it — the same number from different inputs can mean different things, which is why the pairing is always shown.
Where it helps
Typical uses for Sample Size Calculator include planning and budgeting, comparing scenarios side by side, and double-checking the minimum sample size — anywhere the figure needs to be defensible rather than guessed.
Common mistakes
Rounding intermediate values by hand introduces error Sample Size Calculator does not have; it keeps full precision internally, so trust the displayed figure over mental arithmetic.
Tip: Run Sample Size Calculator twice with deliberately low and high inputs; the spread tells you how sensitive the figure is, which a single run never shows.
Assumptions and limitations
Results from Sample Size Calculator are estimates computed from the values entered; real-world outcomes can differ when fees, taxes, or conditions not modeled here apply.
Why use this calculator
Because the page doubles as documentation: Sample Size Calculator puts the formula, a worked example, and the assumptions right beside the calculator.
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Frequently Asked Questions
What does the Sample Size Calculator calculate?
Every run of Sample Size Calculator evaluates the Margin of Error, Expected Proportion, and Population Size you enter, applies the standard Math formula, and reports the figure with each step listed for review. Because the working is visible: Sample Size Calculator shows each operation behind the result in the steps panel, so you can verify the result instead of trusting a black box.
How is the minimum sample size calculated?
The first steps are formula: n₀ = z²·p(1−p)/e², then z = 1.96 (95%). Sample Size Calculator lists every intermediate step in the result panel, so the derivation of the output can be checked line by line.
What do I need to use the Sample Size Calculator?
The Margin of Error, Expected Proportion, and Population Size it asks for, or the page defaults if you just want to see the calculation work. Each input maps directly to the formula, and changing any one of them recalculates the minimum sample size instantly.
What does the result from the Sample Size Calculator mean?
The main number the sample size calculator returns is the minimum sample size for your exact inputs, and the supporting figures and step list give it context. The model behind Sample Size Calculator covers the standard case; special cases, edge values, or jurisdiction-specific rules may need manual adjustment.
When is the Sample Size Calculator most useful?
Common scenarios for Sample Size Calculator: planning and budgeting, comparing scenarios side by side, and double-checking the minimum sample size. The step list makes it equally useful for learning the method and for double-checking someone else's numbers. Run Sample Size Calculator twice with deliberately low and high inputs; the spread tells you how sensitive the minimum sample size is, which a single run never shows.