Mathematics Guide
Sample Size Mathematics
How many votes do you actually need to make a decision?
The Formula
For binary polling (where variance is maximized at a 50/50 split), the standard sample size formula is:
n = (Z² × P × (1-P)) / E²
Where:
- Z = Z-score derived from your confidence level (e.g., 1.96 for 95%)
- P = Population proportion (use 0.5 for maximum variance)
- E = Margin of error as a decimal (e.g., 0.05 for ±5%)
Applying the Math to Decisions
If your poll result is 51% vs 49% with a sample size of 100, the margin of error is nearly ±10%. The result is statistical noise. If the result is 80% vs 20% with the same sample size, the margin is ±7.8%. Because 80% minus 7.8% (72.2%) is still far above 50%, you can confidently declare a winner.
Run the numbers yourself
Don't do the math by hand. Use our interactive tool to calculate exactly how many votes you need before you can close the poll.
Open Calculator Tool