Sample size calculator evaluated example 1
Use the page’s labelled starter inputs to verify Sample size calculator.
Inputs- Confidence level: 95
- Margin of error: 5
- Expected proportion: 50
- Population size: 10,000
Evaluated result: 370
Sample size calculator
Calculate sample size with explicit inputs, validation, and a documented formula.
Sample size calculator
Result370
What this calculator answers
Sample size calculator is a statistics and probability tool. Calculate sample size with explicit inputs, validation, and a documented formula. It uses only the values and choices shown on this page and does not infer hidden data.
Variables, defaults, and limits
- Confidence level
- Confidence level is a choice input. The displayed starter value is 95; it is an example, not a hidden assumption.
- Default: 95
- Accepted values: The field has no narrower HTML limit, but it must still satisfy the documented formula domain and produce a finite result. Available choices: 90, 95, 99.
- Margin of error
- Margin of error is a number input. The displayed starter value is 5; it is an example, not a hidden assumption.
- Default: 5
- Accepted values: Allowed range: 0.01 to 99.99. Numeric entries must be finite and unambiguous.
- Expected proportion
- Expected proportion is a number input. The displayed starter value is 50; it is an example, not a hidden assumption.
- Default: 50
- Accepted values: Allowed range: 0.01 to 99.99. Numeric entries must be finite and unambiguous.
- Population size
- Population size is a number input. The displayed starter value is 10,000; it is an example, not a hidden assumption.
- Default: 10,000
- Accepted values: Minimum: 1. Numeric entries must be finite and unambiguous.
Formula and calculation rule
p=x₃/100; n₀=z(x₁)²p(1−p)/(x₂/100)²; n=n₀/(1+(n₀−1)/x₄); x₁=Confidence level; x₂=Margin of error; x₃=Expected proportion; x₄=Population sizeSample size calculator evaluates the registered expression “p=x₃/100; n₀=z(x₁)²p(1−p)/(x₂/100)²; n=n₀/(1+(n₀−1)/x₄); x₁=Confidence level; x₂=Margin of error; x₃=Expected proportion; x₄=Population size” with the validated inputs. Full calculation precision is retained until the result is formatted for display.
Worked examples
Sample size calculator evaluated example 2
Change one valid input or choice and evaluate Sample size calculator again to check that the result responds deterministically.
Inputs- Confidence level: 95
- Margin of error: 6.25
- Expected proportion: 50
- Population size: 10,000
Evaluated result: 240
Assumptions
- Sample size calculator uses the visitor-entered values exactly as labelled; it does not retrieve private records or current rates.
- The calculation is limited to the declared relationship: p=x₃/100; n₀=z(x₁)²p(1−p)/(x₂/100)²; n=n₀/(1+(n₀−1)/x₄); x₁=Confidence level; x₂=Margin of error; x₃=Expected proportion; x₄=Population size.
- Intermediate values are not rounded; display rounding is applied only at the presentation boundary.
- The deterministic calculation runs locally and does not upload calculator inputs to the application API.
- The result is an educational arithmetic result and excludes facts that are not represented by an input.
Validation and boundaries
- Every visible required input must be present; a missing value is never replaced with zero.
- NaN, positive or negative infinity, unsafe overflow, and a non-finite final result are rejected.
- Field-specific minimums, maximums, and choices apply to Confidence level, Margin of error, Expected proportion, Population size.
- Zero, negative values, and discrete counts are accepted only when the displayed field definition permits them.
Review and correction links
Common mistakes
- Confirm the meaning and unit of Confidence level, Margin of error, Expected proportion, Population size before calculating; a numerically valid value can still use the wrong convention.
- Do not round intermediate values when checking the result, because early rounding can change the last displayed digits.
- Changing an unstated real-world assumption does not change the calculator until the corresponding displayed input is changed.
- Use the result as the answer to the displayed mathematical question, not to a different word problem with hidden conditions.
Frequently asked questions
- What question does Sample size calculator answer?
- Calculate sample size with explicit inputs, validation, and a documented formula. The implemented relationship is p=x₃/100; n₀=z(x₁)²p(1−p)/(x₂/100)²; n=n₀/(1+(n₀−1)/x₄); x₁=Confidence level; x₂=Margin of error; x₃=Expected proportion; x₄=Population size.
- Which inputs does Sample size calculator use?
- It uses the visible fields Confidence level, Margin of error, Expected proportion, Population size. No hidden value is substituted for an omitted required input.
- What happens when Sample size calculator receives an invalid or extreme value?
- The page rejects missing, ambiguous, out-of-range, or non-finite values and refuses to display a non-finite result.
- Why can Sample size calculator differ from another result?
- Different unit conventions, endpoint policies, fee or rate assumptions, formula domains, and premature rounding can produce a different answer.
- Can I use Sample size calculator as professional advice?
- No. It answers the displayed mathematical question and cannot account for omitted real-world facts.
- How can I verify the Sample size calculator result?
- Recalculate the two evaluated examples without rounding intermediate values and compare the declared formula or convention with NIST/SEMATECH e-Handbook of Statistical Methods.
Source and review scope
NIST/SEMATECH e-Handbook of Statistical Methods
Scope: NIST/SEMATECH e-Handbook of Statistical Methods is used to check the formula, definition, or convention relevant to Sample size calculator. The citation does not supply current personal, lender, tax, medical, or market data.
Source checked: