Relative Standard Deviation Calculator
Relative standard deviation, often shortened to RSD, scales the standard deviation by the mean so that spread can be compared across data sets of very different sizes. A raw standard deviation carries units and depends on magnitude, which makes a value like 15 hard to interpret on its own. RSD solves this by dividing the standard deviation by the mean and expressing the result as a percent, producing a unitless figure also known as the coefficient of variation. This calculator takes a standard deviation and a mean and returns the RSD as a percent. The method is the standard one used in analytical chemistry and laboratory quality control, where it is the usual measure of how precise a set of repeated measurements is. You enter the two figures, and the tool computes the RSD deterministically from the formula shown below, never estimated, so the worked example reconciles exactly with the result on screen. A small RSD signals tight, repeatable measurements; a large RSD flags wide variability relative to the average. Because it is scale-free, RSD is also useful in finance for comparing the relative volatility of assets. Use this tool to assess precision or to compare variability between experiments.
Relative standard deviation scales the spread by the mean: RSD = 100 x (standard deviation / mean). For a standard deviation of 15 and a mean of 120, the RSD is 12.50%.
Relative standard deviation formula
RSD = 100 x ( s / mean )
s = standard deviation
mean = average of the data
CV = s / mean (coefficient of variation, unitless)
Dividing the standard deviation by the mean gives the coefficient of variation, a unitless ratio. Multiplying by one hundred expresses it as a percent, the relative standard deviation, which can be compared across data sets of any scale.
Worked example
A set of measurements has a standard deviation of 15 and a mean of 120.
- Coefficient of variation = 15 / 120 = 0.125
- RSD = 100 x 0.125 = 12.50%
The relative standard deviation is 12.50 percent. These are the calculator's default inputs, so the result above matches the widget exactly.
RSD calculator: frequently asked questions
What is relative standard deviation?
Relative standard deviation, or RSD, expresses the standard deviation as a percentage of the mean. It is the coefficient of variation multiplied by one hundred. By scaling the spread by the average, RSD lets you compare the variability of data sets that have very different magnitudes or units.
How is RSD calculated?
Divide the standard deviation by the mean, then multiply by one hundred to express the result as a percent. For a standard deviation of 15 and a mean of 120, the RSD is 100 times 15 divided by 120, which equals 12.50 percent.
Why use RSD instead of standard deviation alone?
The standard deviation alone has units and depends on scale, so a spread of 15 means little without knowing the average. RSD removes the scale by dividing by the mean, producing a unitless percent. This makes it ideal for comparing precision across measurements, instruments or experiments.
Where is RSD commonly used?
RSD is a standard measure of precision in analytical chemistry and laboratory quality control, where repeated measurements of a sample are compared. It is also used in finance to compare the relative volatility of assets and in any field that needs a scale-free measure of variability.
What does a high or low RSD mean?
A low RSD means the measurements are tightly clustered relative to their average, indicating good precision. A high RSD means the values vary a lot compared with the mean. There is no universal threshold; acceptable RSD depends on the method and the field.
Official sources
- Measurement precision and statistics reference: US National Institute of Standards and Technology (NIST). As at 25 June 2026.
Reviewed by the CalculatorHub team, edited by James Graham, 25 June 2026. See our methodology. This is general information, not financial, tax, legal or investment advice.