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Math

Sample Size Calculator

Find the exact number of survey responses you need

Survey Parameters

Use 50% if unknown — gives largest (safest) sample.

Enables finite population correction for smaller groups.

Presets:

Results

Required Sample Size371adjusted for 10,000 people
Confidence Level95.0%
Margin of Error±5.0%
Population Proportion50.0%
Z-Score1.9600
Population Size10,000
Sample Size (infinite pop.)385
Sample Size (your population)371
% of Population to Survey3.71%

Formula used

n = (Z² × p × (1 − p)) / e²

n_adj = n / (1 + (n − 1) / N)  ← finite pop. correction

Where Z = 1.9600 (z-score for 95% confidence), p = 0.50 (proportion), e = 0.05 (margin of error), N = 10,000 (population).

Common Z-Scores

80% → z = 1.281685% → z = 1.439590% → z = 1.644995% → z = 1.960099% → z = 2.575899.9% → z = 3.2905

Key Concepts

Sample Size
The number of respondents you need to survey to achieve statistical validity.
Confidence Level
How certain you want to be that the true value falls within the margin of error. 95% is the research standard.
Margin of Error
The maximum expected difference between your sample result and the true population value (±%).
Population Proportion
Your best estimate of the percentage who will answer 'yes'. Use 50% for maximum sample size when unknown.
Z-Score
The number of standard deviations corresponding to your confidence level, derived from the normal distribution.
Finite Population Correction
When your population is small, the required sample size shrinks. Enabled when you enter a population size.
About

Determine exactly how many survey responses you need with this free sample size calculator. Enter your desired confidence level (typically 95%), margin of error (±5%), and population size to instantly compute a statistically valid sample using Cochran's formula with finite population correction. Whether you're running a market research survey, academic study, or quality audit, get the right number in seconds.

FAQ
What confidence level should I use?+

95% is the standard for most research and surveys — it means you can be 95% certain the true population value falls within your margin of error. Use 99% for critical decisions (medical, financial) where higher certainty is worth a larger sample, or 90% for exploratory studies where speed matters more than precision.

Why does proportion matter, and what if I don't know it?+

Proportion (p) is your best estimate of the percentage of people who will answer 'yes' to your key question. It affects how variable responses will be. If unknown, always use 50% — this is the most conservative assumption and produces the largest (safest) sample size, guaranteeing your results are valid regardless of the true proportion.

When should I enter a population size?+

Enter your population size when surveying a defined, countable group — such as employees at a company, students in a school, or customers on a list. The calculator applies a finite population correction that reduces the required sample size, sometimes significantly. Leave it blank when surveying the general public or any large, effectively unlimited population.

What is margin of error and how small should it be?+

Margin of error (±%) defines the maximum expected difference between your sample result and the true population value. A ±5% margin is standard for general surveys. Smaller margins (±1–2%) require dramatically larger samples — halving the margin of error quadruples the sample size — so choose the largest margin that still meets your decision-making needs.

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