Calculate exactly how many people you need to survey for a given precision. Explore cost-precision tradeoffs and discover how polling organizations design surveys with stratification and weighting.
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Calculator Inputs
How close to the true value do you need?
Confidence Level
95% CI: if you repeated the survey 100 times, ~95 would include the true value
Use 50% if unsure: this gives the largest (most conservative) sample size
FPC reduces required n when population is small relative to sample
Required Sample Size
1,068
Survey 1,068 people to estimate the proportion within ±3% with 95% confidence
Standard Error
1.530%
Actual MOE
±3%
p(1-p)
0.2500
Formula
n = z² × p(1−p) / MOE²
Practical Estimates
Total budget
$5,340
Adjusted contacts needed
1,335
with 20% non-response
Time estimate
11 days
at 100 surveys / day
Cost-Precision Curve
Drag the gold dot to explore how sample size affects margin of error
Key insight: Notice the curve flattens: diminishing returns after ~n=400. Doubling sample size beyond that barely shrinks the MOE.
MOE Comparison Table
Based on 95% confidence, p = 50%. Highlighted row matches your current MOE setting.
| MOE | Required n | Cost | Time |
|---|---|---|---|
| ±1% | 9,604 | $48,020 | 97 days |
| ±2% | 2,401 | $12,005 | 25 days |
| ±3%current | 1,068 | $5,340 | 11 days |
| ±5% | 385 | $1,925 | 4 days |
| ±10% | 97 | $485 | 1 day |
Key insight: Halving MOE quadruples sample size: precision is expensive.
Survey Design Principles