Sample Size Calculator

Sample Size Formula (for proportions):

n = (z² × p × (1-p)) / e²

With finite population correction:

n_adj = n / (1 + (n - 1) / N)

Where:

• n = required sample size (before population correction)
• z = critical value for the confidence level (see table below)
• p = estimated proportion (use 0.5 if unknown — this gives the largest, most conservative sample size)
• e = margin of error expressed as a decimal (e.g., 0.05 for plus or minus 5%)
• N = total population size (optional — only needed if your population is small and known)

Critical values by confidence level:

When to use this calculator: Use it whenever you are planning a survey, poll, or research study and need to know how many responses are required for statistically reliable results. It is commonly used in market research, academic studies, quality control, and public opinion polling.

Practical Example: You want to survey customers about a new product. You want 95% confidence with a margin of error of plus or minus 5%, and you have no idea what proportion will say yes (so use p = 0.5). n = (1.960² x 0.5 x 0.5) / 0.05² = (3.8416 x 0.25) / 0.0025 = 385 responses

If your total customer base is only 2,000 people, the finite correction reduces this: n_adj = 385 / (1 + (385 - 1) / 2000) = 385 / 1.192 = 323 responses

Quick reference table (95% confidence, p = 0.5):

Common Mistakes:

• Using p = 0.5 when you already have a reasonable estimate — this overestimates the required sample
• Forgetting the finite population correction when surveying a small, known group
• Confusing margin of error with confidence level — they are independent settings