Standard Deviation from Range Calculator
Estimate a standard deviation quickly from the minimum and maximum using the range rule of thumb.
How it works
SD ≈ range ÷ 4 · (range ÷ 6 for larger samples) · range = max − min
The range rule of thumb gives a fast standard-deviation estimate when you only know the smallest and largest values. It works because in a roughly normal sample about 95% of data lies within ±2 SD of the mean — a span of four standard deviations — so dividing the range by 4 recovers an approximate SD. For larger samples the observed range tends to be wider (closer to six SD), so range ÷ 6 is the better divisor. Treat both as quick approximations, not substitutes for the true SD computed from all the data.
Worked example
For values spanning a minimum of 10 to a maximum of 90, the range is 80. The range rule gives SD ≈ 80 ÷ 4 = 20; for a large sample, 80 ÷ 6 ≈ 13.3 is a better estimate.
Sources: Range rule of thumb — Wikipedia
Frequently asked questions
How accurate is the range rule of thumb?
It is a rough guide, best for small-to-moderate, roughly normal samples. The range depends only on two extreme points, so a single outlier can distort it badly. Use it for a sanity check or a quick planning figure, then compute the exact SD when you have the full data.
When should I divide by 6 instead of 4?
The expected range in standard deviations grows with sample size — about 4 SD for a dozen points but nearer 6 SD for samples in the hundreds. So use ÷4 for small samples and ÷6 for large ones; other divisors from a statistical table refine it further.
Can I use this to plan a sample size?
Yes — when no pilot SD is available, estimating σ as range ÷ 4 from the plausible spread of your measurement is a common way to feed a sample-size formula. Just remember the resulting n is only as good as that rough σ.
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This calculator is for educational purposes. Double-check important results before acting on them.