Coefficient of Variance Calculator
Tells you how risky or volatile a dataset is compared to its own average.
A percentage that lets you compare the risk of two different things — like two stocks — even if their prices are totally different.
Separate numbers with commas or spaces.
Coefficient of variation
22.77%
σ ÷ |μ| × 100 — relative volatility of your data
Moderate Spread — 22.77% is standard variability, common in biological data or weather patterns.
Mean (μ)
15.0000
Sample SD (s)
3.4157
Divisor n − 1
Count (n)
7
Step by step
- 1
Mean
Σx ÷ n = 15.0000
- 2
Deviation & variance
Σ(x − μ)² ÷ (n − 1) = 11.6667 → σ = 3.4157
- 3
CV
3.4157 ÷ 15.0000 × 100 = 22.77%
About this calculator
Standard deviation shows how far numbers move from the average, but it depends on the units you use. Elephant weights vary by 500 pounds; mouse weights by 0.5 ounces — you cannot compare those values fairly. The CV solves this by comparing the standard deviation to the mean as a percentage, letting you compare two datasets even in different units.
Imagine two friends guessing prices: both miss by $0.50 — one on a $1.00 candy bar, the other on a $20,000 car. Same absolute error, very different mistakes. The CV shows this difference by comparing the error to the size of the value.
Formula
CV = (Standard Deviation ÷ Mean) × 100%
How to use it
- 1
Raw Data mode: enter your numbers separated by commas or spaces — the calculator finds the mean, deviation, variance and CV step by step.
- 2
Known Stats mode: if your textbook already gives the mean and standard deviation, enter those two values directly.
- 3
Read the CV with its volatility scale verdict: green under 10% (high precision), amber 10–30% (moderate variance), red over 30% (high volatility).
Example: a week of measurements
10, 15, 12, 18, 20, 14, 16 → mean 15, sample SD 3.42, CV 22.77% — moderate spread. Press Reset to load these numbers.
How this calculator works — two modes
Raw Data mode (a list like 12, 15, 18, 20): Step 1 — add all numbers and divide by the count to find the mean. Step 2 — measure how far each number sits from that average. Step 3 — square those differences and average them into the variance. Step 4 — divide the standard deviation by the mean and multiply by 100.
Known Stats mode: your textbook already gives you the values — enter the mean and standard deviation, and the tool divides one by the other immediately. The volatility scale colors the result so you can read consistency at a glance.
0–10% High Precision · 10–30% Moderate Variance · 30%+ High Volatility
1. CV is a unitless measure
This is its most important property. You divide a value by another value in the same unit, so the units cancel: 5 meters ÷ 10 meters = 0.5 — meters disappears. That is why you can compare stock prices in dollars against real estate sizes in square feet directly.
2. The zero-mean problem
CV = σ ÷ mean, and dividing by zero is undefined — a mean of exactly zero kills the calculation. A mean very close to zero (like 0.001) is just as bad: the CV explodes into a huge, meaningless number. CV works best with data that is always positive, like height, weight or prices.
3. Sensitivity to outliers
CV depends on the mean, so extreme outliers throw it off — a billionaire walking into a room of regular workers shoots the average income up and distorts the CV. Always check your raw data for errors before calculating.
When to use this calculator
Investing & finance
Investors use CV as a risk-to-reward lens. Stock A returns 10% with 2% variation (CV 20%); Stock B returns 20% with 5% variation (CV 25%). B earns more, but A is safer — more consistency per unit of return.
Laboratory science
Scientists use CV to test equipment. A pipette that should dispense 10ml gets tested 100 times — the goal is the Relative Standard Deviation (another name for CV). Below 5% usually means the equipment is working correctly.
Manufacturing quality control
Tiny screws and giant bolts both vary by 1mm. For the bolt that is nothing; for the screw it is a serious defect. CV spots which machine needs fixing even when the absolute error looks identical.
In Excel: In Excel: =STDEV.S(range) / AVERAGE(range), formatted as a percentage.
Frequently asked questions
What is a good coefficient of variation?
It depends on the data. In chemistry labs a good CV is often below 2–3%. In surveys and social studies 10–15% is usually fine. In the stock market CV can exceed 20%. In general, lower means more stable data.
Can the coefficient of variation be negative?
Most of the time, no — standard deviation always stays positive. A negative average can produce a negative CV, for example with temperatures below zero, but many statisticians avoid CV with negative data because the result becomes hard to interpret. This calculator uses the absolute mean.
How is CV different from standard deviation?
Standard deviation shows spread in actual units — a price may change by $5. CV shows spread as a percentage of the value — the price changes by 10% of itself. Use standard deviation for one dataset; use CV when comparing different datasets.
Why do we multiply by 100 in the formula?
The raw division often gives a small decimal like 0.15. Multiplying by 100 turns it into 15%, which is much easier to read and compare.
Can I use this for simple lists of numbers?
Yes — Raw Data mode is built exactly for that. Enter test scores, temperatures, heights or any values, and the calculator does all the math for you.