yCalculator

Standard Deviation Calculator

Last updated: April 2026

Enter your dataset

Separate numbers with commas, spaces, new lines, or tabs. Use sample for most real-world datasets where your data is a subset of a larger group.

8 numbers entered

Standard deviation (s)

2.13809

Variance (sĀ²)

4.571429

Supporting stats

Count (n)
8
Mean
5
Sum of squares
32
Variance
4.571429
Std deviation
2.13809

Deviation table

xMeanx - mean(x - mean)^2
25-39
45-11
45-11
45-11
5500
5500
7524
95416
Sum0 OK32

Normal distribution visual

mean68-95-99.7 rule

The 68-95-99.7 Rule

In a normal distribution, 68% of data falls within +/-1 standard deviation, 95% within +/-2, and 99.7% within +/-3.

+/-1s: 2.86191 to 7.13809
+/-2s: 0.72382 to 9.27618
Step-by-step working
  1. Find the mean: (2 + 4 + 4 + 4 + 5 + 5 + 7 + 9) / 8 = 40 / 8 = 5.
  2. (2 - 5)^2 = (-3)^2 = 9
  3. (4 - 5)^2 = (-1)^2 = 1
  4. (4 - 5)^2 = (-1)^2 = 1
  5. (4 - 5)^2 = (-1)^2 = 1
  6. (5 - 5)^2 = (0)^2 = 0
  7. (5 - 5)^2 = (0)^2 = 0
  8. (7 - 5)^2 = (2)^2 = 4
  9. (9 - 5)^2 = (4)^2 = 16
  10. Sum the squared deviations: 9 + 1 + 1 + 1 + 0 + 0 + 4 + 16 = 32.
  11. Sample variance with Bessel's correction: 32 / (8 - 1) = 32 / 7 = 4.571429.
  12. s = sqrt(4.571429) = 2.13809.

Related calculators

Mean, median and modeZ-score calculator

Population vs sample standard deviation

Population standard deviation divides by N. Sample standard deviation divides by n - 1 because sample data usually underestimates the spread of the full population.

Why divide by n - 1?

Bessel's correction adjusts for the fact that a sample mean is estimated from the same data, giving a less biased estimate of population variance.

What does standard deviation tell you?

A small standard deviation means values cluster near the mean. A large standard deviation means values are more spread out.

Standard deviation vs variance

Variance is the average squared deviation. Standard deviation is the square root of variance, so it is expressed in the same units as the original data.

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.

Related Math calculators

math calculators

Triangle Calculator

Solve any triangle using SSS, SAS, ASA, AAS, SSA, right triangle, and Pythagorean theorem modes

Calculate ā†’

math calculators

Area Calculator

Calculate the area of common 2D shapes with formula substitutions and unit conversions

Calculate ā†’

math calculators

Volume Calculator

Calculate the volume and surface area of common 3D shapes with full working and practical litre conversions

Calculate ā†’

You might also need

math calculators

Mean, Median, Mode and Range Calculator

Calculate mean, median, mode, range, quartiles, variance, and standard deviation from any dataset

Calculate ā†’

math calculators

Z-Score Calculator

Calculate z-scores, percentile ranks, and standard normal distribution probabilities

Calculate ā†’

math calculators

Probability Calculator

Calculate basic probability, combined events, conditional probability, and binomial probability

Calculate ā†’