How to Determine Sample Size
Most people pick a sample size by gut feeling or by copying whatever their last project used, and both approaches waste either money or statistical power. The calculator above removes the guesswork by solving the standard formula directly — plug in your confidence level, margin of error, and an estimate of variability, and it returns the exact number of observations you need.
Two modes cover the vast majority of real-world studies. Proportion mode handles surveys where the outcome is a yes/no or percentage — voter preference, defect rates, conversion rates. You supply an estimated proportion (or leave it at 0.5 for the worst-case scenario) and the formula uses p̂(1 − p̂) to capture variability. Mean mode is for continuous measurements like test scores, response times, or revenue per customer. Instead of a proportion, you supply an estimated standard deviation, and the formula swaps in σ² for the variability term.
Both modes share the same skeleton: n₀ = z² × (variability) / E², where z comes from the confidence level and E is the margin of error you can tolerate. If you also know the total population, the finite population correction shrinks the sample — sometimes dramatically. A population of 500 with an initial n₀ of 385 drops the adjusted sample to about 218, which can cut fieldwork costs nearly in half.
Quick Reference Table
These numbers assume proportion estimation with p̂ = 0.5 and an infinite population — the most conservative scenario. Any prior knowledge that moves p̂ away from 0.5, or a known finite population, will reduce these counts.
| Confidence | MOE ±10% | MOE ±5% | MOE ±3% | MOE ±1% |
|---|---|---|---|---|
| 90% | 68 | 271 | 752 | 6,766 |
| 95% | 97 | 385 | 1,068 | 9,604 |
| 99% | 166 | 664 | 1,844 | 16,590 |
The jump from ±5% to ±1% is brutal — roughly 25 times more respondents for five times the precision. That tradeoff is exactly why ±5% remains the default for most applied research: the cost curve bends sharply past that point and the practical gain rarely justifies the extra recruitment effort.
Choosing Between Proportion and Mean Mode
The decision is straightforward once you think about what your data looks like. If every response falls into a category — yes/no, pass/fail, clicked/didn't click — use proportion mode. The variability maxes out at p̂ = 0.5 and you rarely need a pilot study to set up the calculation.
Mean mode requires more upfront knowledge because you need a reasonable estimate of the standard deviation. Run a small pilot of 20-30 observations, borrow the SD from a similar published study, or use the range/4 rule as a rough approximation. Getting σ wrong by a factor of two quadruples your required sample size, so it pays to be careful here.
When Finite Population Correction Matters
Textbooks treat populations as infinite by default, and for national surveys or large customer bases that assumption is fine. But the moment your population drops below a few thousand, ignoring the correction means you collect more data than necessary and spend budget you didn't need to spend.
The rule of thumb: if your initial sample size n₀ exceeds 5% of the population, apply the correction. For a company with 400 employees, the uncorrected formula says you need 197 for ±5% at 95% confidence. After correction, that drops to 132 — a third fewer interviews, same statistical guarantee.
Frequently Asked Questions
What sample size do I need for a survey?
At 95% confidence with a ±5% margin of error, the standard answer is 385 respondents for a large population. That number comes from z²×p̂(1−p̂)/E² with z = 1.96, p̂ = 0.5, and E = 0.05.
Tighten the margin to ±3% and you need 1,068. Push to ±1% and it jumps to 9,604. The cost-precision tradeoff gets steep fast, which is why most practical surveys settle on ±5%.
What is finite population correction?
It shrinks your required sample when the population is small enough that your sample covers a real chunk of it. The formula is n = n₀ / (1 + (n₀−1)/N), where N is population size.
Without it, you'd be told to survey 385 out of a town of 500 people — clearly overkill. After correction, that drops to about 218. The correction starts to matter once n₀ exceeds 5% of N.
Why use p̂ = 0.5 as default?
The product p̂(1 − p̂) peaks at exactly 0.25 when p̂ = 0.5. Any other proportion — 0.3, 0.7, 0.9 — produces a smaller product and therefore a smaller required sample.
Using 0.5 is the conservative play. It guarantees your margin of error holds regardless of the true proportion. If a pilot study gives you a better estimate, use it — you'll need fewer respondents.
How does confidence level affect sample size?
Higher confidence demands a larger z-value, and since sample size scales with z², the increase is steep. Going from 90% (z = 1.645) to 95% (z = 1.96) adds about 42% more respondents.
Jump to 99% (z = 2.576) and you nearly triple the 90% figure. Most fields default to 95% because it balances rigor against practical sample collection costs.
What margin of error should I use?
Match the margin to the stakes. Political polls need ±3% because a few percentage points determine elections. Market research on brand awareness works fine at ±5%.
Internal surveys where direction matters more than precision can get away with ±8-10%, cutting the sample by 75% compared to ±5%. Always weigh the cost of extra data against the cost of being wrong.