Coefficient of Variation Calculator
Calculate Coefficient of Variation ($\text{CV \%} = \frac{s}{|\bar{x}|} \times 100$), Relative Standard Deviation (RSD), mean, and variability risk levels.
Calculate Relative Variability (CV %)
Enter numbers separated by commas, spaces, or lines.
Calculation Results
Calculated using relative dispersion equations: \text{CV \%} = \left( \frac{s}{|\bar{x}|} \right) \times 100
Quick Summary
The Coefficient of Variation Calculator evaluates relative dispersion ($\text{CV \%} = \frac{s}{|\bar{x}|} \times 100$), standard deviation ($s$), mean ($\bar{x}$), and variability risk classification.
Formula Explanation
\text{CV \%} = \left( \frac{s}{|\bar{x}|} \right) \times 100
\text{Relative Standard Deviation RSD} = \frac{s}{|\bar{x}|}How It Works
Coefficient of variation (CV %) is a dimensionless measure of relative variability. The Coefficient of Variation Calculator divides standard deviation $s$ by absolute mean $|\bar{x}|$, expressing dispersion as a percentage to compare datasets across different measurement scales.
Step-by-Step Worked Example
Practical Problem: Calculate CV % for a manufacturing process sample: 100, 105, 95, 102, 98 ($n = 5$).
- Step 1: Calculate sample mean ($\bar{x}$): $(100+105+95+102+98)/5 = 500 / 5 = \mathbf{100.0000}$.
- Step 2: Calculate sample standard deviation ($s$): $\sum (x_i - 100)^2 = 0 + 25 + 25 + 4 + 4 = 58$; $s^2 = 58 / 4 = 14.5$; $s = \sqrt{14.5} = \mathbf{3.8079}$.
- Step 3: Divide standard deviation by mean: $3.8079 / 100.0000 = \mathbf{0.038079}$.
- Step 4: Convert to percentage ($\text{CV \%}$): $0.038079 \times 100 = \mathbf{3.81\%\text{ CV}}$.
- Step 5: Interpretation: The process exhibits low relative variability ($\text{CV} < 15\%$), indicating high consistency.
Real-World Calculation Examples
Scenario 1: Manufacturing Batch (100, 105, 95, 102, 98)
Parameters: Mean 100, SD 3.81
Result: 3.81% CV (Low variability quality control).
Scenario 2: Stock A vs Stock B Volatility Comparison
Parameters: Stock A (Mean $10, SD $2 $\rightarrow$ CV 20%); Stock B (Mean $100, SD $10 $\rightarrow$ CV 10%)
Result: Stock B has lower relative risk!
Scenario 3: Biological Assay Precision
Parameters: Mean 5.0, SD 1.2
Result: 24.00% CV (Moderate assay variance).
Scenario 4: Agricultural Crop Yield Stability
Parameters: Mean 180 bu, SD 36 bu
Result: 20.00% CV.
Key Benefits of Using This Calculator
Cross-Scale Unit Comparison
Compares variability across datasets with completely different units (e.g. height in cm vs weight in kg).
Risk Classification System
Classifies variability risk into Low (<15%), Moderate (15–30%), and High (≥30%).
Relative Standard Deviation (RSD)
Outputs RSD ratio ($s / \bar{x}$) used in chemical analytical validation.
100% Free & Client-Side
Executes locally in your browser with zero latency or web server transmission.
Frequently Asked Questions (FAQ)
What is Coefficient of Variation (CV %)?
CV % is standard deviation divided by mean expressed as a percentage ($\text{CV \%} = \frac{s}{\bar{x}} \times 100$).
Why use CV % instead of standard deviation alone?
Standard deviation depends on data scale; CV % standardizes variation relative to the mean, allowing direct comparison between different measurements.
What is Relative Standard Deviation (RSD)?
RSD is identical to CV, expressed either as a decimal ratio ($s / \bar{x}$) or percentage.
Can CV % be calculated if mean is zero or close to zero?
No — when mean approaches zero, CV % approaches infinity and is mathematically undefined.
What is a good CV % in analytical chemistry laboratory testing?
In analytical testing, a CV % under 5% indicates high laboratory repeatability and precision.
How do I calculate CV % in Excel?
Use formula =(STDEV.S(range) / AVERAGE(range)) * 100.
Is CV % suitable for interval scales like Celsius temperature?
No — CV % requires a true ratio scale with a non-arbitrary zero point (such as Kelvin or mass in kg).
What is Sharpe ratio relationship to CV?
CV % is the inverse of the signal-to-noise ratio ($\bar{x} / s$).
Can CV % exceed 100%?
Yes — if standard deviation is larger than the mean (high variance), CV % will exceed 100%.
How is CV % used in finance?
Financial analysts use CV % to measure risk per unit of expected return ($\text{Risk} / \text{Return}$).