QuantarizmQuantarizm
Calculators
Formula Library
Converters
Articles
QuantarizmQuantarizmMaking Numbers Meaningful.

Free math calculators, unit converters, and formula references — with clear steps.

Product

  • Calculators
  • Math
  • Financial
  • Formula Library
  • Converters
  • Articles

Company

  • About
  • Contact
Legal
  • Privacy Policy
  • Terms
  • Disclaimer
  • Cookies

© 2026 Quantarizm

Free tools · No account required

HomeCalculatorsConvertersFormula Library
  1. Home/
  2. Calculators/
  3. Math/
  4. Sample Size Calculator

Sample Size Calculator

Minimum survey sample size, margin of error from n, or mean-study sizing — with optional finite population correction.

Statistics

  • Average Calculator
  • Mean, Median, Mode, Range Calculator
  • Statistics Calculator
  • Standard Deviation Calculator
  • Number Sequence Calculator
  • Probability Calculator
  • Permutation and Combination Calculator
  • Sample Size Calculator
  • Z-score Calculator
  • Confidence Interval Calculator
  • P-value Calculator

How it works

n0 = z^2 p(1-p)/e^2; margin e = z sqrt(p(1-p)/n). Round up; shrink n when population N is known.

n=z^2 p(1-p)/e^2 · e=z sqrt(p(1-p)/n) · n_fpc=n0/(1+(n0-1)/N)

When to use

Use this tool when you need to: calc.net classic: 95% confidence, 5% margin, p=50% → about 385 people. Try margin-of-error mode with n=385 to verify ~5%.

How to use this tool

  1. Enter your values in the fields above.
  2. Review the formula and any mode options for your problem.
  3. Read the result and the step-by-step solution.

Calc.net classic: 95% confidence, 5% margin, p=50% → about 385 people. Try margin-of-error mode with n=385 to verify ~5%.

Frequently asked questions

What is the Sample Size Calculator?
n0 = z^2 p(1-p)/e^2; margin e = z sqrt(p(1-p)/n). Round up; shrink n when population N is known.
How do I use the Sample Size Calculator?
Enter the required values, then calculate. The Sample Size Calculator shows results, formulas, and step-by-step work when available. No account is required.
What formula does the Sample Size Calculator use?
n=z^2 p(1-p)/e^2 · e=z sqrt(p(1-p)/n) · n_fpc=n0/(1+(n0-1)/N)

You may also like

  • Average CalculatorArithmetic and weighted mean with a visual sum÷count layout and step-by-step work.→
  • Mean, Median, Mode, Range CalculatorArithmetic mean, median, mode(s), and range for comma-separated data — with ordered list, frequency table, and worked steps.→
  • Statistics CalculatorArithmetic and geometric means, σ and s, variance, quartiles, IQR, and Σx / Σx² from a comma-separated list.→
  • Standard Deviation CalculatorPopulation σ and sample s with variance, mean, sum, standard error, and margin of error for the mean.→
  • Number Sequence CalculatorArithmetic, geometric, and Fibonacci sequences: nth term, partial sum, and term list with clear formulas.→
  • Probability CalculatorIndependent two-event probabilities, solver, series of trials, normal range area, simple favorable/total, and Bayes.→

Browse categories

  • General
  • Geometry

Other categories

  • General
  • Geometry
All math calculators→

Popular

  • Percentage Calculator
  • Average Calculator
  • Fraction Calculator
  • Area Calculator
All math calculators→

Sample size calculator

Plan the minimum sample size for a proportion survey, reverse-engineer the margin of error from n, or size a study for a mean. Optional finite population correction when N is known.

Calculate

Confidence level

Confidence 90-99%. Margin as 5 or 0.05 (5 percentage points). Proportion as 50 or 0.5 — use 50% when unsure. Leave N blank for unlimited population.

Common confidence levels and z-scores
Confidence levelz-score (±)
70%± 1.04
75%± 1.15
80%± 1.28
85%± 1.44
90%± 1.64
95%± 1.96
98%± 2.33
99%± 2.58
99.9%± 3.29
99.99%± 3.89
99.999%± 4.42

Values match common textbook tables; the calculator uses a precise inverse normal for z from your confidence level.

Try an example

How it works

Sampling and confidence

Surveys and experiments study a finite sample and treat its characteristics as standing in for the whole population. The sample proportion p-hat is treated as roughly normal with variance p(1-p)/n. Larger n shrinks that noise; the confidence level says how often repeated intervals would cover the true p.

Confidence level and z

Common levels are 90%, 95%, and 99%, each with a two-sided z (about 1.64, 1.96, 2.58). At 95%, if you could resample infinitely often, about 95% of intervals built this way would contain the true parameter — not a claim that one realized interval is 95% likely after the fact.

Finding sample size

Set the maximum acceptable margin of error e, pick a confidence level (hence z), and a planning p-hat. Then n0 = z^2 p(1-p)/e^2. Use p=0.5 when unsure (most conservative). With known population N, correct with n = n0/(1+(n0-1)/N) and always round up. Classic: 95%, e=5%, p=0.5 → n≈385 unlimited.

Finding margin of error

Given n and p-hat, e = z sqrt(p(1-p)/n), or with finite N multiply the variance by (N-n)/(N-1). The approximate interval is p-hat ± e. This is the reverse of sample-size planning — useful after a survey finishes.

Sample size for a mean

When estimating a continuous mean with planning SD sigma, e = z sigma / sqrt(n) so n = (z sigma / e)^2. Optional finite-population correction matches the proportion case.

Related calculators

Probability, counting, sampling design, and normal-based inference tools work together. Descriptive statistics calculators help when you start from raw data.

  • Probability Calculator
  • Permutation and Combination Calculator
  • Z-score Calculator
  • Confidence Interval Calculator
  • P-value Calculator
  • Statistics Calculator