Slovin’s Formula Calculator

N
e

Sample size (n):

200

Conversion steps:

n = N / (1 + N × e2)

n = 400 / (1 + 400 × (0.05)2)

n = 400 / (1 + 400 × 0.0025)

n = 400 / (1 + 1)

n = 400 / (2)

n = 200

∴ Sample size (n) = 200

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What is Slovin's Formula?

Slovin's Formula is a statistical equation used to estimate the ideal sample size for surveys or research studies when the population size is known. It helps ensure that your data collection is both cost-effective and statistically accurate, especially for large populations where surveying everyone is impractical.

This method is commonly used in fields such as education, marketing, business, and social sciences where sample-based surveys are required.

Slovin’s Formula Equation

The formula is:

n = N / (1 + N × e²)

Where:

  • n = required sample size
  • N = population size
  • e = margin of error (in decimal)

How to Use the Slovin’s Formula Calculator

  1. Enter the Population Size (N): Provide the total number of people in the population you want to study.
  2. Enter the Margin of Error (e): Choose how much error you’re willing to tolerate (e.g., 0.05 for 5%).
  3. Click Calculate: The calculator will compute the sample size needed for statistically significant results.
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Example Calculation

If your target population is 10,000 people and you accept a margin of error of 5% (0.05):

Using Slovin’s Formula:

n = 10000 / (1 + 10000 × 0.05²)

n = 10000 / (1 + 10000 × 0.0025)

n = 10000 / (1 + 25)

n = 10000 / 26

n ≈ 385

You would need to survey approximately 385 individuals to get reliable survey results.

FAQs about Slovin’s Formula

What is Slovin's Formula used for?

It is used to determine the appropriate sample size needed for research when the population is known and a margin of error is set.

What is a good margin of error?

A 5% (0.05) margin of error is commonly used for 95% confidence level. Lower margins increase accuracy but require a larger sample size.

Can I use Slovin’s Formula for small populations?

Yes, but for very small populations, it’s often better to survey everyone or use exact statistical methods instead.

What if I don't know the population size?

Slovin’s Formula requires a known population. If unknown, use other statistical sampling methods like Cochran’s formula.