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Find the margin of error of a survey proportion.
Results update as you type.
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a percentage it is z*·√(p(1 − p) / n), where p is the sample proportion, n the sample size and z* the critical value for your confidence level (1.96 for 95%). The default 50% proportion gives the most conservative (largest) margin, because the quantity p(1 − p) peaks at p = 0.5, which is why pollsters often quote it. To halve that margin, you would need roughly four times the sample. To halve that margin, you would need roughly four times the sample.It reports the margin of error, the confidence-interval bounds around your proportion and the full interval width, and a table shows how it shrinks as the sample grows. To halve that margin, you would need roughly four times the sample.It reports the margin of error, it reports the margin of error.ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:ItWorked example:
Tambayoyi da ake yi da yawa
Me ya sa wani misali mai girma ya rage ma'aunin kuskure?
The margin shrinks with the square root of the sample size, so quadrupling n halves the margin of error. This diminishing return is why very large samples are needed to push the margin below one or two percentage points.
Me yasa 50% ke da ma'aunin diff?
The quantity p(1 − p) is largest at p = 0.5, so assuming a 50/50 split produces the widest, most conservative margin of error. Using it guarantees the true margin is no larger than reported.
Ta yaya zan iya ƙididdige ma'auni na kuskure?
Multiply the critical value z* for your confidence level by the square root of p(1 − p) ÷ n. For p = 0.5, n = 1000 and 95% confidence, that is 1.96 × √(0.25 ÷ 1000) ≈ 3.1 percentage points.
Mene ne bambanci tsakanin ma'auni na kuskure da tsakanin lokaci na aminci?
The margin of error is the half-width; the confidence interval is the full range you get by adding and subtracting the margin from your result. A 48% result with a 3-point margin gives a confidence interval of 45% to 51%.
Shin, yawan jama'a mai girma yana buƙatar wani yanki mai girma na kuskure?
Ba. A bayan mutane dubu kaɗan, yawan jama'a ba zai iya shafar matsin lamba ba - abin da yake da muhimmanci shi ne girman misali. Wannan shi ne dalilin da ya sa zabukan kasa da zabukan birni za su iya raba matsin lamba guda tare da adadin masu amsawa guda.
Ta yaya mataki na aminci zai canza ma'auni na kuskure?
A higher confidence level uses a larger z*, which widens the margin. Moving from 95% (z* = 1.96) to 99% (z* = 2.576) increases the margin by about 31% for the same sample.
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[Translation temporarily unavailable. Please try again.] Anything you omit uses the same default this page is pre-filled with; an unknown parameter is a 400, never a silent zero. [Translation temporarily unavailable. Please try again.] →
Endpoint
GET https://calculator.free/api/v1/margin-of-error/curl
curl "https://calculator.free/api/v1/margin-of-error/?n=1000&p=50&conf=1.96"JavaScript fetch()
const r = await fetch(
"https://calculator.free/api/v1/margin-of-error/?" + new URLSearchParams({
"n": "1000",
"p": "50",
"conf": "1.96"
}));
const data = await r.json();
console.log(data.results);Results are estimates for general guidance only, not financial, medical or tax advice.