Use this Sample Size Calculator to estimate how many observations are needed for a selected confidence level and margin of error when estimating a population mean or proportion.

Calculation Method

For a population mean:

n = (z × σ ÷ E)²

For a population proportion:

n = z² × p(1 − p) ÷ E²

If the expected proportion is unknown, p = 0.50 is commonly used because it gives the most conservative sample-size estimate.

When the total population size N is known and relatively small, finite population correction can be applied:

n = n₀ ÷ [1 + (n₀ − 1)/N]

Example

For a 95% confidence level, 5 percentage-point margin of error, and unknown population proportion:

z = 1.96

p = 0.50

n = 1.96² × 0.50 × 0.50 ÷ 0.05²

n ≈ 384.16

Always round required sample size up, giving 385 completed observations.

Important Note

This calculator plans sample size for confidence-interval precision, not statistical power. The formulas also assume an appropriate sampling design and do not automatically account for nonresponse, clustering, weighting, design effects, or biased sampling.

Source

• Penn State STAT 200 — Confidence Intervals and Sample Size