How big is a nanosecond?

Nanoseconds are hard to argue about because nobody has any intuition for them. Fortunately there is a conversion that gives you one, and it is worth committing to memory before anything else on this site.

Light travels about 30 cm in a nanosecond. About a foot.

That single fact turns a great many timing questions from abstract into physical:

Time Distance
1 ns ≈ 30 cm — about a foot
100 ps ≈ 3 cm — a little over an inch
30 ps ≈ 9 mm — the width of a little finger
1 ps ≈ 0.3 mm — about the thickness of a business card
Manhattan, priced in nanoseconds — a long block is about 900 ns, a short one about 250. From The Last Nanoseconds to UTC, given in the building at the center of the frame.

Why this is the most useful thing here

Because it makes errors comparable to objects.

A foot of extra antenna cable is about a nanosecond and a half — light does a foot per nanosecond, but coax does about two thirds of that, which is a page of its own. A GNSS antenna surveyed a meter too high is three nanoseconds. The difference between two ends of a rack is under a nanosecond, and the difference between two buildings on a campus is not.

And it works in the other direction, which is where it earns its keep in arguments: if somebody claims a system holds a hundred picoseconds, they are claiming to control something to about an inch. That is a claim you can inspect by looking at the room.

The picosecond trap

Small units are easy to mis-convert, and one mis-conversion in particular catches people who know exactly what they are doing.

A picosecond is 0.3 mm — genuinely tiny, easy to dismiss as unphysical. But timing specifications are rarely for one picosecond. Thirty picoseconds is 9 mm, which is a perfectly ordinary distance you could point at.

Convert the number you were given, not the unit

The instinct is to convert “a picosecond” and judge plausibility from that. The quantity that matters is whatever multiple of it is actually being claimed, and the difference between 0.3 mm and 9 mm is the difference between “impossible” and “the width of your little finger”.

What it looks like across a real site

Half a mile of datacenter campus. Time crosses it to within 200 ps; UTC arrives to within about ±15 ns. From The Last Nanoseconds to UTC.

From a talk on getting to the last nanoseconds of UTC:

We do lose a little bit of precision when we get to a half-mile campus like this one in New Jersey — maybe only within 200 picoseconds over a half-mile campus. But that’s two orders of magnitude better than the accuracy of our clocks.

Two things worth extracting. Distributing time across half a mile costs about 6 cm of equivalent distance error — small. And it is two orders of magnitude below what the clocks themselves manage, which tells you where the money should go, and it is not the cabling.

That ratio is the useful shape: once you can convert time to distance, you can see which term in your error budget dominates without measuring anything. The same campus makes the point about matching acquisition to distribution, where the seventy-five-fold gap between the two is the whole argument.

There is a companion conversion worth having in the same pocket. This page turns time into distance; how big is a degree? turns coordinates into distance — which is what you need the moment somebody hands you a latitude and longitude and you have to decide how many of its digits to believe.