Measurements Standard Deviation Calculator
Measure how widely your readings vary around their mean using population or sample standard deviation.
How to use Measurements Standard Deviation Calculator
1. Enter Measurements Values as matching lists where weights are used; separate numbers with commas, spaces, semicolons or new lines. 2. Choose Population or Sample mode. 3. Select Calculate or press Enter, then read standard deviation. 4. Copy result copies the answer; Reset clears the form. Do not use thousands separators inside lists.
Why use this tool?
Compare the variability of repeated readings of the same quantity under comparable conditions.
How the calculation works
Find the arithmetic mean, add the squared deviations from that mean, divide by count for Population or count − 1 for Sample, then take the square root. Sample requires at least two observations. Use one unit and the same measured quantity throughout. The result keeps that unit; the calculator does not assess instrument calibration or measurement uncertainty. Results use up to six decimal places, or six significant digits in scientific notation for nonzero magnitudes below 0.000001. Calculations use browser floating-point arithmetic. Each list supports up to 20,000 numbers. Entry and result magnitudes must not exceed 9,007,199,254,740,991; unrepresentable variance or weighted products are rejected. General descriptive-statistics reference: https://www.itl.nist.gov/div898/handbook/eda/section3/eda356.htm. Weighted conventions are defined explicitly on this page.
Example
For measurements 2.1,2.2,2.3,2.4 in Population mode, the standard deviation is 0.111803.
Practical tip
Use Population when describing the complete set of interest, or Sample when using observations to estimate a wider population’s variability.
Frequently asked questions
Which standard-deviation mode should I choose?
Population divides squared deviations by n. Sample divides by n − 1 and requires at least two values. Choose according to what the observations represent, not to obtain a preferred answer.
Are mixed units converted automatically?
No. Convert every reading to one unit before entering the list. A reading in cm and another in m must not be averaged or compared as if they shared a unit.
How should I separate numbers and interpret rounding?
Use commas, spaces, semicolons or new lines between entries. Enter 1000 rather than 1,000: commas separate observations. Repeated values are retained. Displayed results are rounded as stated; keep original readings for later calculations.