Calculated using standard mathematical and industry formulas.
Free online Sample Size Calculator calculator and unit conversion tool for everyday, engineering, and home projects.
How to use this calculator?
Select your desired confidence level (95% is standard).
Enter your acceptable margin of error in percent.
Use 50% for estimated proportion unless you have a prior estimate.
Enter population size if finite (leave 0 for large/unknown populations).
Read the minimum sample size required.
Formula & calculation method
Sample size formula
n₀ = (z* × p × (1−p)) / E² · With finite population: n = n₀N / (n₀ + N − 1)
z* = confidence level critical value, p = estimated proportion, E = margin of error (decimal), N = population size.
Step-by-step calculation example
95% CI (z*=1.96), MOE=5% (E=0.05), p=50%: n₀ = (1.96² × 0.25) / 0.0025 = 384.16 → n = 385.
Key insights to remember
The classic result: for a 95% CI and ±5% MOE, you need n ≥ 385 (infinite population).
Sample size grows with the square of z* and shrinks with the square of MOE — halving MOE quadruples required n.
Using p = 0.5 maximises required sample size, providing a conservative estimate.
Finite population correction reduces sample size for small populations: n_adj = n₀N / (n₀ + N − 1).
How to interpret your results?
Margin of error vs sample size trade-off
A smaller MOE requires a much larger sample. Going from ±5% to ±2.5% quadruples the required sample.
Conservative 50% estimate
When you have no prior estimate of the proportion, use p = 0.5. This maximises variance and gives the largest required sample.
Frequently asked questions
How do I use the Sample Size Calculator calculator?
Enter your numerical input and select desired units to get instant accurate results.
How accurate are the conversions?
Conversions use official ISO conversion factors for maximum precision.
Does it convert metric and imperial units?
Yes, seamless conversions between metric (meters, kg) and imperial (feet, lbs) are supported.
Is my data stored?
No, all calculations execute 100% locally in your browser with zero data logging.
Can I use this for DIY or engineering projects?
Yes, it provides reliable estimates for construction, crafting, science, and everyday math.
What if I enter invalid inputs?
The calculator will display a friendly error prompt if non-numeric values are entered.
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