The basics
Before launching a survey, you need to know how many people to ask. Too few responses and your data is noise; too many and you're wasting resources. The sample size calculator uses your confidence level, acceptable margin of error, and expected response pattern to determine the minimum number of respondents required.
How it works
The calculator combines three key inputs to find your sample size. Your confidence level sets how certain you want to be (95% is standard in most research). Your margin of error defines the acceptable range around your results—a 5% margin means if 60% say "yes," the true figure is probably between 55% and 65%. The response proportion is your educated guess about how the population will answer (50% is safest if you're unsure). For small populations, you also enter population size; for national surveys or large markets, you leave it unlimited.
These values feed into a statistical formula that accounts for the variability in your data and the precision you need.
The formula
n = (z² × p × (1 − p)) / e² (for unlimited populations)
Where:
- z = critical value for your confidence level (1.645 for 90%, 1.96 for 95%, 2.576 for 99%)
- p = expected response proportion (as a decimal: 0.5 for 50%)
- e = margin of error (as a decimal: 0.05 for 5%)
- n = required sample size
For finite populations, a finite population correction is applied to reduce n slightly.
Worked example
Imagine you're a coffee brand planning to survey customers about a new product. You want 95% confidence and a 3% margin of error. You don't have prior data, so you assume a 50% split in opinion.
Inputs:
- Confidence level: 95%
- Margin of error: 3%
- Response proportion: 50%
- Population size: 0 (unlimited)
Calculation:
- z = 1.96 (for 95% confidence)
- p = 0.5
- e = 0.03
- n = (1.96² × 0.5 × 0.5) / 0.03²
- n = (3.8416 × 0.25) / 0.0009
- n = 0.9604 / 0.0009
- n ≈ 1,068 respondents
So you'd need about 1,068 completed surveys. If you relax the margin of error to 5%:
- n = (3.8416 × 0.25) / 0.05²
- n = 0.9604 / 0.0025
- n ≈ 385 respondents
Notice how tightening the margin of error from 5% to 3% nearly tripled the sample size.
Things to watch
Response rate matters in practice. The calculator tells you how many completed responses you need. If your survey has a 40% response rate, you'll need to contact roughly 2.5× the calculated sample. Plan your outreach accordingly.
Confidence level and margin of error trade off. Moving from 95% to 99% confidence increases your sample size significantly. Similarly, cutting margin of error from 5% to 3% is expensive in sample terms. Understand your actual business tolerance before choosing.
Use 50% if uncertain. If you have no pilot data on response proportions, defaulting to 50% is statistically prudent—it maximizes sample size, so you won't undersample. Once you have real preliminary results, recalculate for a more efficient design.
This is an estimate based on statistical theory, not a substitute for research methodology advice.