Calculator
Sample Size Calculator
Estimate sample size from confidence level, margin of error, population, and expected proportion.
AnswerCanvas Calculator
Sample Size Calculator
Required sample size
385
Assuming a large/unknown population.
- Base sample size (infinite population)
- 385
- Finite population correction applied
- No
- Required sample size
- 385
- Z-critical value used
- 1.960
Result chart
Formula
Base sample size: n₀ = (z² × p × (1−p)) ÷ e², where z is the critical value for your confidence level, p is the expected proportion (50% gives the most conservative/largest required sample, since p×(1−p) is maximized there), and e is the desired margin of error. If sampling from a known finite population, the finite population correction n = n₀ ÷ (1 + (n₀−1)/N) reduces the required sample size somewhat.
Worked example
Targeting 95% confidence with a 5% margin of error and a conservative 50% expected proportion (no population size limit): requires a sample of about 385 - a commonly cited standard sample size for general surveys at this precision level.
Money-page insight
Using 50% as your expected proportion assumption is the standard conservative choice when you genuinely don't know what proportion to expect - it produces the LARGEST required sample size (since p×(1−p) peaks at p=50%), which protects against being under-sampled if your true proportion turns out to be near 50%.
Calculation history
Stored locally on this deviceHow the sample size calculator works
How to use this calculator
Adjust the assumptions on the left and the result updates instantly. Use the summary as a planning estimate, then compare it with quotes, local rules, lender disclosures, or professional guidance for decisions involving taxes, loans, construction, or health.
Useful next steps
Learn more
Stage 1 - Inputs
Collect the required sample size planning values and confirm that each value is physically and logically possible.
Stage 2 - Formula
Base sample size: n₀ = (z² × p × (1−p)) ÷ e², where z is the critical value for your confidence level, p is the expected proportion (50% gives the most conservative/largest required sample, since p×(1−p) is maximized there), and e is the desired margin of error. If sampling from a known finite population, the finite population correction n = n₀ ÷ (1 + (n₀−1)/N) reduces the required sample size somewhat.
Stage 3 - Substitute values
Replace each variable in the formula with the current input value. This keeps the calculation transparent and easy to audit.
Stage 4 - Intermediate calculations
Calculate the supporting values first, such as totals, rates, balances, volumes, or ratios, before producing the final result.
Common mistakes
- Mixing units, such as monthly and annual rates, inches and feet, or gross and net income
- Entering rounded guesses when exact quotes or measurements are available
- Ignoring fees, taxes, risk factors, local rules, or physical constraints
- Treating an estimate as a final professional decision
Tips
- Change one input at a time to understand sensitivity
- Use conservative assumptions when the result affects safety, debt, taxes, or health
- Save or print the result with assumptions before comparing alternatives
- Recheck units whenever a result looks surprisingly large or small
Sample Size Calculator mastery
Estimate sample size from confidence level, margin of error, population, and expected proportion.
Use this statistics calculator as a working model: enter realistic inputs, read the primary answer first, then use the supporting rows to understand what changed and why.
Read the result correctly
Treat the primary answer as the headline result and the supporting values as the evidence trail behind it.
Improve accuracy
Small input changes can shift the output. Recheck units, time periods, percentages, and any assumptions before using the result.
Use it professionally
Save or print the result with the inputs visible so the calculation can be reviewed, repeated, or compared later.
Expert suggestions
Professional perspective
How to get more value from the sample size calculator
A strong calculation is not only a final number. It is a repeatable way to compare choices, understand assumptions, and see which inputs deserve the most attention.
Start with a baseline
Use the most realistic inputs you have today before testing optimistic or conservative cases.
Change one variable
Adjust one assumption at a time. This makes cause and effect easier to understand.
Keep the evidence visible
Save or export the result with inputs included so the answer can be checked later.
Learning path
What to understand next
- Understand the main formula
- Review the assumptions
- Compare alternate scenarios
- Decide what information would improve accuracy
Statistics insight guide
Understand the answer
Use the sample size calculator as a decision aid, not just a number.
A calculator is most useful when the result, assumptions, and practical meaning are read together. Use the output as a structured estimate and review the inputs before making a decision.
The primary answer summarizes the model. Supporting values explain the path from inputs to output and reveal which assumptions matter most.
The result usually changes when units, rates, time periods, quantities, prices, thresholds, or rounding assumptions change.
Confirm that each input uses the intended unit, time period, percentage basis, and sign. A correct formula can still produce a poor estimate from inconsistent inputs.
Use extra care when the answer affects money, health, safety, legal exposure, construction quantities, or long-term planning.
Accuracy checklist
- Confirm every unit before comparing outputs.
- Use current inputs rather than outdated estimates.
- Test at least one conservative and one optimistic scenario.
- Review whether rounding changes the practical decision.
How professionals use this
- Document the inputs beside the result.
- Compare scenarios instead of relying on a single run.
- Share the assumptions when asking for review.
- Use expert review for high-stakes decisions.
Frequently asked questions
- Why does 50% expected proportion require the largest sample?
- The p×(1−p) term is maximized at p=0.5 (0.25) and shrinks as p moves toward 0% or 100% - this reflects that proportions near the extremes are inherently easier to estimate precisely than proportions near the middle.
- What is the finite population correction for?
- When sampling a significant fraction of a KNOWN, limited population (not from an effectively infinite pool), you need proportionally fewer samples to achieve the same precision - this correction reduces the required sample size accordingly.
- Why is 385 such a commonly cited sample size?
- It's the result of this exact formula at the very common combination of 95% confidence, 5% margin of error, and 50% expected proportion - which is why you'll see it referenced so often as a standard survey sample size.
- What does the Sample Size Calculator calculate?
- Estimate sample size from confidence level, margin of error, population, and expected proportion.
- How should I read the Sample Size Calculator result?
- Read the primary answer first, then review the supporting values, formula notes, assumptions, and expert suggestions. The supporting values explain why the answer moved and which inputs deserve more attention.
- Which input matters most in the Sample Size Calculator?
- The most important input depends on the calculator, but the highest-impact variables are usually rates, time periods, quantities, income, balance, measurements, or unit choices. Change one input at a time to see which variable drives the result.
- Why might my Sample Size Calculator result differ from another website?
- Different calculators may use different assumptions, rounding rules, formulas, default values, tax years, unit conversions, or included costs. Compare the formula and assumptions before comparing final answers.
- Can I use this statistics result for an important decision?
- Use the result as a structured estimate and learning tool. For financial, tax, medical, legal, construction, or safety-sensitive decisions, verify the inputs and review the output with a qualified professional.
- How often should I update the inputs in the Sample Size Calculator?
- Update the inputs whenever the underlying facts change: rates, prices, measurements, dates, balances, income, rules, or goals. Outdated inputs create outdated answers.
- What is the safest way to compare scenarios?
- Keep all inputs the same except one variable. That makes it clear whether the difference came from rate, time, quantity, price, measurement, or another assumption.