Sample Size Calculator
Minimum sample size for a proportion with margin of error
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Need a fast answer on minimum sample size for a proportion with margin of error? Sample Size Calculator answers with the steps beside it. Drop Margin of Error (%), Expected Proportion (0-1) and Population Size (0 = infinite) into Sample Size — the figure refreshes as you type. Sample Size ties each output to its formula. Use Sample Size for a reliable number, fast. Sample Size runs in your browser. Math data stays in the tab. Sample Size sits in the Math section next to free online sample size calculator and sample size calculator margin of error confidence level population. Sample Size goes from question to answer fast. Try Sample Size now and keep it handy.
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, using Math conventions. With the defaults, sample size calculator gives a minimum sample size of n = 370.
- Inputs: Margin of Error, Expected Proportion, and Population Size.
- Output: the minimum sample size, and the operations that led to it.
- Method: the Math formula, applied to Margin of Error, Expected Proportion, and Population Size inside the browser tab.
Quick answer
sample size calculator returns a minimum sample size of n = 370 with the default inputs (margin of error of 5, expected proportion of 0.5, population size of 10,000).
How does the Sample Size Calculator 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. The minimum sample size is worked out on the device, so nothing about your inputs is transmitted.
How the Sample Size Calculator works
Rather than a single figure in a box, Sample Size Calculator hands back a minimum sample size plus its provenance: the inputs it used, the terms it applied, and the order it applied them in.
Using the Sample Size Calculator
- Margin of Error — a core sample size input applied directly — keep its units consistent with the label.
- Expected Proportion — one of the values sample size builds from; the minimum sample size reflects exactly what you type.
- Population Size — used in the first sample size stage, so entering it accurately beats any later refinement.
- Look for the step list under the figure on Sample Size Calculator: it names each operation, which is what turns a number into a checkable result.
- Use the share link from Sample Size Calculator to reopen a case later, change one value, and compare the new figure with the old one directly.
The formula behind the result
The relationship between the inputs is fixed by the formula, and Sample Size Calculator makes each substitution explicit so nothing about the result is hidden.
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
Understanding the result
The minimum sample size is the headline answer from Sample Size Calculator; the supporting figures beneath it and the step list give the context needed to judge it.
Where it helps
Where Sample Size Calculator earns its keep: planning a purchase, re-running the same case with a new figure, and spot-checking a quoted figure, and the smaller questions that sit around them.
Common mistakes
Comparing a sample size result with a quote that uses a different convention is not a like-for-like check, even when both numbers look similar.
Tip: Sample Size Calculator returns n = 370 at its defaults; double the Margin of Error (%) and it returns n = 96.
Assumptions and limitations
The minimum sample size Sample Size Calculator reports is only as complete as the inputs: anything the page does not ask for sits outside the calculation.
Why use this calculator
Because the sample size page shows its assumptions rather than burying them, you can see which ones your own case breaks.
Frequently Asked Questions
Which figure does sample size calculator produce?
Where a figure has to survive being questioned, Sample Size Calculator is the shortcut: the Math working is printed beneath the answer instead of assumed. Because the page doubles as documentation: Sample Size Calculator puts the formula, a worked example, and the assumptions right beside the calculator.
How is the minimum sample size calculated?
The first steps are formula: n₀ = z²·p(1−p)/e², then z = 1.96 (95%). Precision is maintained through every intermediate step in Sample Size Calculator, and rounding is applied only when the final value is formatted for display.
What should I have ready for Sample Size Calculator?
Sample Size Calculator needs Margin of Error, Expected Proportion, and Population Size and nothing else.
What if the Margin of Error (%) were twice as large?
At the defaults Sample Size Calculator returns n = 370; doubling Margin of Error (%) to 10 moves it to n = 96.
What does the result from this page’s calculator tell you?
The main number the sample size calculator returns is the minimum sample size for your exact inputs. Sample Size Calculator returns a point estimate for the values shown and says nothing about how confident you should be in those values.
What is the Sample Size Calculator best used for?
Reach for the sample size calculator when you need planning a purchase, re-running the same case with a new figure, and spot-checking a quoted figure without a spreadsheet open beside you. Enter the awkward number first in Sample Size Calculator — a decimal, or a figure with cents — and you will see early whether the minimum sample size behaves the way you expect.
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