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Sample Size Calculator for Research and Statistical Power

Calculate the minimum sample size for your study before collecting data. Choose a t-test, multiple regression, or SEM based on your research design and anticipated effect size.

A-priori sample size calculator for multiple regression

Freev2.0

This tool computes the minimum sample size a multiple linear regression needs, from the anticipated effect size (f²), the desired statistical power, the number of predictors, and the significance level.

Anticipated effect size (Cohen's f²)

0.02 small · 0.15 medium · 0.35 large

0.15
Desired statistical power

The standard academic benchmark is 0.80

80%
Number of predictors (k)

How many independent variables the model carries.

3

The conventional level is 0.05

Minimum sample sizeN = 77Predictorsk = 3Critical value (F)F = 2.73

Statistical power against sample size

k=3 · α=0.05 · target power 80%

Total sample size (N)0.00.20.40.60.81.077Total sample size (N)

The dashed line is the target power; the marked point is the smallest sample that reaches it. Move the pointer across the chart, or focus it with Tab and use the arrow keys, to read the power at any sample size. Home and End reach the axis limits.

Alternative description: a chart showing power rising with total sample size, reaching the 80% target at N = 77.

APA 7 reporting sentence (updates with your inputs)

An a-priori sample size analysis for a multiple regression model with (3) predictors, assuming an anticipated effect size of (f² = 0.15) and statistical power of (0.80) at a significance level of (0.05), indicated a minimum required sample of (N = 77).

What does this result mean?

With N = 77 participants you have 80% power to detect an effect of f² = 0.15 across 3 predictors at α = 0.05. A smaller sample weakens your ability to find the effect even when it is really there in the population.

Assumptions and limits

The result is computed in your browser; your inputs are never sent to the server.

This tool gives an initial estimate and does not replace a consultation. If your study design is more involved, start with a conversation.

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How do you calculate sample size for research?

This calculator estimates the number of participants needed to detect an anticipated effect before collecting data. It is for statistical power analysis in experimental and correlational studies, not for a population-survey margin-of-error calculation using Cochran's formula.

Choose the calculator that matches your research design

  1. Independent-samples t-test: Use it to compare the means of two independent groups. Set the anticipated Cohen’s d, power, and significance level.
  2. Multiple linear regression: Use it to test the model as a whole. Enter the anticipated f² and the number of predictors.
  3. Structural equation modelling: Use it when the design has latent variables and observed indicators. The tool considers both effect detection and model complexity.

Sample size questions

Is a rule of 30 participants enough?

No. It can suit some simple descriptions, but it does not establish sufficient power for a specified test or model. Sample size depends on effect size, power, significance level, and study design.

Why does the calculator use 80% power and 0.05 significance?

They are common starting points, not automatic choices. Increase power when missing an effect is costly, and document the rationale in your research plan.

Should I use this for a survey or an experimental study?

Use it for a study that tests a hypothesis or statistical model. Estimating a population proportion or survey margin of error needs different inputs and a different formula.

The power-analysis and test-selection principles follow established statistical references; see the NIST statistical handbook and Cohen reference on statistical power when documenting a methodological decision.