Sample Size Calculator

Last updated: April 2026

Sample size calculator

Estimate how many responses you need for statistically useful survey or research results.

Confidence level

Margin of error %5% is standard for many surveys.Population proportion %Use 50% if unknown for the most conservative sample size.Population sizeEnter 0 to assume an infinite population.

Required sample size

385

Supporting info

Confidence level: 95%
Margin of error: +/-5%
Z-score used: 1.96
Population size: Not applicable
Adjusted sample: Not applicable
Sampling fraction: Not applicable

Sensitivity table

Margin	90% CI	95% CI	99% CI
1%	6,766	9,604	16,590
2%	1,692	2,401	4,148
3%	752	1,068	1,844
5%	271	385	664
10%	68	97	166

Step-by-step working

Z = 1.96 for 95% confidence.
n = (Z^2 x p x (1-p)) / e^2.
n = (1.96^2 x 0.5 x 0.5) / 0.05^2.
n = (3.8416 x 0.25) / 0.0025.
n = 384.16. Round up: n = 385.
No finite population size entered, so the infinite population sample size is used.

What is statistical significance?

Statistical significance means your result is unlikely to be due to random chance alone.

Confidence level vs confidence interval

The confidence level is how often the method should capture the true value. The interval is the estimated range.

Why use 95% confidence?

95% confidence is a common balance between reliability and a practical sample size.

How population size affects sample size

For small finite populations, the required sample can be adjusted downward because each response covers a larger share of the group.

What does this mean?

This calculator is designed to help you understand the likely number before you make a decision or start an application.

Your result should be checked against official UK guidance, especially if your circumstances include dependants, exemptions, prior leave, or a complex immigration history.

Treat the figure as a planning tool rather than legal advice. Where the answer affects an application deadline or major payment, speak to an authorised adviser.

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