Standard Deviation Calculator
Compute mean, standard deviation, variance, standard error and confidence intervals from repeated measurements.
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About standard deviation in surveying
Standard deviation (σ) measures the spread of repeated measurements around the mean. In surveying, multiple observations of the same angle, distance, or GNSS position are essential to quantify precision. A small σ means observations cluster tightly; a large σ indicates noisy data.
This calculator computes both sample σ (using n-1 in the denominator) and population σ (using n). Sample σ is used when the dataset represents a subset of a larger population (the normal case in surveying). The standard error is σ/√n — how precisely the mean is determined — and shrinks as you take more measurements.
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Practical use cases
Assessing repeatability of GNSS occupations: take 10+ short epochs and compute σ to judge site quality.
Evaluating total station distance measurements: multiple pointings reveal instrument noise and atmospheric effects.
Checking level readings: repeated foresight readings should have σ below 1-2 mm for precise work.
Statistical QC on traverse angles: σ of forward/backward differences reveals systematic errors.
Frequently asked questions
Sample vs population standard deviation?
Sample σ (divide by n-1) is an unbiased estimator when you have a sample from a larger population. Population σ (divide by n) is used when you have the entire population. In surveying, sample σ is the standard.
What is the relationship between σ and precision?
Precision = 1σ (68% of measurements fall within). 2σ ≈ 95% confidence, 3σ ≈ 99.7%. Specifications often require 2σ.
How many measurements do I need?
For reasonable σ estimate: minimum 5 repetitions. For tight estimates: 10-30. The standard error (σ/√n) shows the diminishing-returns curve.
What does the confidence interval mean?
The 95% CI gives the range within which the true mean likely falls. A narrow CI means the mean is well-determined.
Related tools
Combine with our error propagation calculator for multi-measurement combinations.