Sample Size Calculator

Determine the required sample size for surveys, experiments, and studies with precision control.

Last updated: March 2026

Calculator

Type

Confidence level

Margin of error (%)

Expected proportion (%)

Population size (optional)

Required sample size

385

z* (critical value)1.96

n (infinite pop)385

What is Sample Size Determination?

Sample size determination is the process of calculating how many observations (respondents, subjects, items) are needed to draw reliable conclusions about a population. It's a critical step in research design because collecting too few observations yields imprecise estimates, while collecting too many wastes resources and time.

The required sample size depends on: (1) confidence level (how certain you want to be), (2) margin of error (acceptable precision), (3) population variability (how spread-out the characteristic is), and (4) population size (for finite populations). Researchers balance statistical rigor with practical constraints like budget and timeline.

Sample size calculations differ for proportions (yes/no questions, like "Do you support Policy X?") and means (continuous measurements, like income or height). This calculator handles both common scenarios, with formulas based on the Central Limit Theorem and normal distribution.

How to Calculate Sample Size

Determine Your Study Parameters

1. Choose Study Type: Proportion (categorical) or Mean (continuous)

2. Select Confidence Level: 90%, 95%, or 99% (higher = larger sample)

3. Set Margin of Error: 5% (common), 3% (stricter), 10% (looser)

4. Estimate Variability: Expected proportion or std dev from prior research

5. (Optional) Enter Population Size: If finite, applies correction factor

Key Formulas

For Proportions:

n = (z² × p×(1-p)) / e²

For Means:

n = (z² × σ²) / e²

Finite Population Correction:

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

Common Z-Scores

90% Confidencez = 1.645

95% Confidencez = 1.96

99% Confidencez = 2.576

Real-World Example

Political Poll: Estimating Voter Support

Scenario:

Poll candidate support with 95% confidence and 3% margin of error

Prior polls suggest ~50% support

Input:

Type: Proportion

Confidence: 95% (z = 1.96)

Margin of Error: 3%

Expected Proportion: 50%

Calculation:

n = (1.96² × 0.5 × 0.5) / (0.03²)

n = (3.8416 × 0.25) / 0.0009

n = 0.9604 / 0.0009 ≈ 1,068

Result:

Sample Size: 1,068 respondents

Your poll must contact approximately 1,068 eligible voters. With this sample, you're 95% confident the true support is within ±3% of your poll result.

If true support is 50%, your poll will show 47-53% (~95% of the time).

Frequently Asked Questions

Why does confidence level affect sample size?

Higher confidence (99% vs. 95%) requires a larger critical value (z-score), which increases the sample size needed. You trade precision for statistical certainty.

What's margin of error (MoE)?

MoE is the acceptable difference between your sample estimate and true population value. 3% MoE means your poll result is within ±3% of reality. Smaller MoE requires larger samples.

How does expected proportion affect the calculation?

Proportions near 50% require the largest samples (maximum uncertainty). As proportion moves toward 0% or 100%, needed sample size decreases since there's less variability.

When should I use finite population correction?

Use it when your population is small or your sample will be >5-10% of population. For large populations (millions), it has minimal effect. It reduces required sample size slightly.

What if I don't know the expected proportion?

Use 50% (maximum conservative assumption). This gives the largest sample size. Once you have pilot data, you can recalculate with better estimates to potentially reduce it.

Is a larger sample always better?

More data improves precision, but costs and time increase. Find the minimum sample meeting your statistical needs. Beyond that, returns diminish. Context and budget matter.