Sample Size Calculator: Surveys & MOE

Confidence	Z
70%	1.036
75%	1.150
80%	1.282
85%	1.440
90%	1.645
92%	1.751
95%	1.960
96%	2.054
97%	2.170
98%	2.326
99%	2.576
99.5%	2.807
99.9%	3.291
99.99%	3.891
99.999%	4.417

How to Use the Sample Size Lab

Leave either Sample Size or Margin of Error empty to solve. The Statistical Summary shows the result, Z-score, standard error, and confidence gauge. Copy result & formula for reports.

At a Glance

Solve for n

Enter Confidence Level, Margin of Error (%), and Proportion. Leave Sample Size empty. The dashed border marks the solved field.

Solve for Margin of Error

Enter Sample Size, Confidence Level, and Proportion. Leave Margin of Error empty to get ±e.

Finite Population

Optional: enter Population Size for

n_adj = n / (1 + (n−1)/N)

. Reduces required n when sampling a large fraction of the population.

Sample Size Calculator: Survey Sample Size & Margin of Error

Free sample size calculator for surveys. How many people to survey? Solve for sample size or margin of error. 95% confidence, ±5% margin. Finite population correction. Z-score reference. No sign-up.

What This Sample Size Calculator Does

This sample size calculator solves for sample size or margin of error when estimating a population proportion (e.g. survey approval, response rate). Leave one field empty: Margin of Error empty → solve for how many people to survey; Sample Size empty → solve for margin of error. Uses

n = [z² × p × (1−p)] / e²

with optional finite population correction

n_adj = n / (1 + (n−1)/N)

. Confidence levels 70%–99.999%; Z-score reference table; Logic Trace with Step 1 and Step 2 (FPC). Results rounded up (Math.ceil) per statistical best practice. Free online; all calculations local.

Sample Size Formula: Proportions and the 95% / ±5% Benchmark

For a population proportion:

n = z² × p × (1−p) / e²

At 95% confidence (z = 1.96), p = 0.5, and ±5% margin (e = 0.05), n ≈ 385; the standard survey sample size for many studies. Reverse:

e = z × √[p(1−p)/n]

gives margin of error from a given n. With finite population N, adjust:

n_adj = n / (1 + (n−1)/N)

. Use 50% proportion when unknown (conservative); prior estimates yield smaller n.

How to Use This Calculator

Leave one field empty to tell the calculator what to solve, then fill in the remaining parameters.

Solve for Sample Size:

Leave Sample Size empty. Enter Confidence Level, Margin of Error (%), and Population Proportion. The calculator returns the minimum n required, rounded up per statistical best practice.
Solve for Margin of Error:

Leave Margin of Error empty. Enter Sample Size, Confidence Level, and Population Proportion. The calculator returns ±e as a percentage.
Confidence Level:

Select from 70% to 99.999%. The corresponding Z-score is applied automatically (e.g., 1.96 for 95%).
Population Proportion:

Use 50% when unknown for the most conservative (largest) sample size. Enter a prior estimate (e.g., 30%) for a smaller required n.
Population Size (Optional):

For finite populations, enter total N. The finite population correction reduces required n when your sample is a large fraction of the population.

Sample Size Calculator FAQ

How do I calculate sample size for a survey?

Use

n = [z² × p × (1−p)] / e²

where z comes from your confidence level (1.96 for 95%), p = expected proportion (0.5 when unknown), e = margin of error as decimal (0.05 for ±5%). Leave Sample Size empty; enter Confidence Level, Margin of Error, and Proportion. With a finite population, use:

n_adj = n / (1 + (n−1)/N)

Results use Math.ceil to round up, statistical best practice for whole units.

What sample size do I need for 95% confidence and 5% margin of error?

At 95% confidence (z ≈ 1.96) and ±5% margin with p = 0.5, n ≈ 385. This is the classic survey benchmark: ~400 responses gives ±5% at 95% confidence for large populations. Use the calculator to adjust for different confidence levels, margins, or finite populations.

Why use 50% for population proportion when unknown?

p = 0.5 maximizes p(1−p) = 0.25, yielding the most conservative (largest) sample size. When the true proportion is unknown, 50% ensures your sample is large enough. With a prior estimate (e.g. 30% approval), enter it for a smaller required n.

What is the finite population correction?

When sampling from a finite population N, required n is reduced:

n_adj = n / (1 + (n−1)/N)

Equivalent to:

n × N / (n + N − 1)

Enter Population Size in the calculator; Step 2 of the Logic Trace shows the adjustment. Matters when your sample is a large fraction of N.

Mathematical Reference Note

Calculation Logic: This tool uses standard mathematical algorithms. While we strive for accuracy, errors in logic or user input can result in incorrect data.

Verification: Results should be cross-checked if used for important academic, professional, or personal calculations.

Standard Terms: This tool is provided free of charge and as-is. CalcRegistry provides no warranty regarding the accuracy or fitness of these results for your specific needs.