Chronograph SD and ES Calculator
Paste a string of velocities. Get the average, standard deviation, and extreme spread. No signup, nothing stored, and it works on a phone at the bench.
Results appear here as you paste.
These numbers are only useful next to the load that produced them: bullet, charge, seating depth, brass, and the day's conditions. HandloaderPro keeps the string with the recipe, and imports Garmin Xero and LabRadar files directly. Free for 14 days, no card.
What the numbers mean
What is extreme spread (ES)?
The difference between the fastest and slowest shot in the string. It is only two data points, so it is less informative than SD, but it is the number that shows a flier most clearly: one shot 60 fps off the rest moves ES a lot and SD only a little.
What is standard deviation (SD) for a chronograph string?
A measure of how tightly the velocities cluster around the average. Lower is more consistent. Velocity variation is what spreads vertical at distance, so SD is the number to chase for long-range loads. This calculator uses the sample standard deviation (n-1 divisor), the same formula chronograph apps report.
How many shots do I need for a useful SD?
A 3-shot SD is approximately meaningless. A 10-shot SD starts being useful, and a 20-shot SD is honest. The calculator flags any string under 10 shots as a small sample.
Can I paste a table copied from my chronograph app?
Yes. Shot numbers, 'fps' labels, and blank lines are ignored. Any number under 100 is treated as a shot number rather than a velocity, so a pasted table with a shot column gives the right answer. Velocities can be fps or m/s; the math is the same.
What to write down with them
The string is the result. The load is the cause. Average, SD, and ES are worth nothing in two years unless they sit next to the bullet, powder charge, primer, brass and its firing count, seating depth, and the temperature that day. The guide on what to record from a chronograph session covers the short list.