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Standard Deviation Calculator
Find population or sample standard deviation instantly. Paste in a list of numbers and see the mean, variance, median, mode, and the full deviation breakdown.
Separate values with commas, spaces, or line breaks.
Results
Population statistics for 8 values
Count
8
Mean
21.25
Median
22
Mode
22
Range
18
Min
12
Max
30
Sum
170
Variance
31.6875
Standard Deviation
5.6292
Step-by-Step Breakdown
Standard deviation is based on the squared distance each value is from the mean.
Mean
21.25
Sum of Squares
253.50
Formula
σ² or s² = 253.50 ÷ 8
SD = √31.6875 = 5.6292
| Value | Value - Mean | (Value - Mean)² | Std Devs from Mean |
|---|---|---|---|
| 12 | -9.25 | 85.5625 | -1.6432 |
| 15 | -6.25 | 39.0625 | -1.1103 |
| 18 | -3.25 | 10.5625 | -0.5774 |
| 22 | 0.75 | 0.5625 | 0.1332 |
| 22 | 0.75 | 0.5625 | 0.1332 |
| 24 | 2.75 | 7.5625 | 0.4885 |
| 27 | 5.75 | 33.0625 | 1.0215 |
| 30 | 8.75 | 76.5625 | 1.5544 |
Sorted Data Distribution
See how far each point sits from the mean in standard deviation units.
Negative values are below the mean, positive values are above it, and values near 0 are close to average.
EveryCalc calculators are designed for fast, practical estimates with transparent inputs and no required account. We use plain formulas, visible assumptions, and related tools so visitors can check the result from more than one angle.
Results are informational only. For financial, tax, legal, medical, construction, or other high-impact decisions, verify the output against primary sources or a qualified professional.
Learn more about our review process on the EveryCalc methodology page.
How this calculator works
What this page estimates
This Standard Deviation Calculator is built to give a quick, browser-based estimate for standard deviation. Find population or sample standard deviation instantly. Paste in a list of numbers and see the mean, variance, median, mode, and the full deviation breakdown. The inputs stay on the page during normal use, and the result should be treated as an estimate for planning, comparison, or education rather than professional advice.
Calculation approach
The calculator applies the standard relationship implied by the inputs, then formats the answer so it can be checked and reused. For math & education tools, the most important step is using consistent units, rates, time periods, and assumptions before comparing the result with another calculator or outside quote.
Example workflow
For example, start with a realistic value you already know, change one input at a time, and watch how the answer moves. That makes it easier to tell whether the result is being driven by the main amount, the rate, the time period, or a unit conversion.
Practical checks
- Use current, real-world numbers when the result affects money, health, tax, or legal decisions.
- Run a low, base, and high case when the inputs are estimates.
- Check the related calculators below when the next decision depends on a different assumption.
How to interpret the standard deviation result
Best use
Use the result to learn a formula, check homework, verify a percentage, or understand the steps behind a number.
Cross-check
Compare the output with the method your class, textbook, spreadsheet, or teacher expects, especially when rounding rules are specified.
Watch for
A calculator can confirm arithmetic, but it cannot decide which formula a word problem requires. Read the setup before trusting the answer.
This page belongs to the Math & Education calculator library, so the answer should be read in the context of the decision you are modeling rather than as a universal rule.
Before relying on this standard deviation estimate
Most calculator mistakes come from the inputs, not the arithmetic. Use this short audit before you reuse the answer in a spreadsheet, quote, application, or important conversation.
Match the expected method
Teachers, textbooks, spreadsheets, and tests may require a specific formula, rounding rule, or notation format.
Inspect the setup
The calculator can check arithmetic, but the user still has to choose the right formula for the word problem or assignment.
Show the work when needed
Use the result to verify steps, then write out the method when an answer alone is not enough.
Rerun this page when the formula, rounding instruction, units, or assignment requirements change.
How to Use
- Paste or type your numbers into the input box using commas, spaces, or line breaks.
- Choose whether you want population standard deviation or sample standard deviation.
- Review the summary cards for mean, median, mode, variance, range, and standard deviation.
- Use the breakdown table to see each deviation from the mean and how the variance was calculated.
Frequently Asked Questions
What is the difference between population and sample standard deviation?
Population standard deviation uses every value in the full dataset and divides by N. Sample standard deviation is used when your data is only a sample of a larger population, so it divides by n - 1 to reduce bias.
What does standard deviation tell you?
Standard deviation measures how spread out your values are around the mean. A small standard deviation means the numbers cluster tightly around the average, while a larger one means the data is more spread out.
How is variance related to standard deviation?
Variance is the average of the squared deviations from the mean. Standard deviation is simply the square root of the variance, which brings the result back to the original unit of the data.
Why do some datasets have no mode?
A mode is the most frequent value. If every number appears only once, there is no mode because no single value occurs more often than the others.
Can I use decimals and negative numbers?
Yes. This calculator accepts whole numbers, decimals, and negative values, as long as they are separated by commas, spaces, or line breaks.
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