Seconds to Nanoseconds

Where a Nanosecond Becomes a Third of a Metre

Precise timing work is ranging work wearing a different hat. A GNSS receiver never measures distance directly — it measures how long a signal took to arrive, and every nanosecond of uncertainty in that measurement lands as just under thirty centimetres of uncertainty in the answer. The same arithmetic follows a telecom base station holding phase alignment, a substation stamping fault records, and an exchange proving which of two orders arrived first. Specifications get written in seconds; the error budget is spent in nanoseconds.

Conversion factor: 1 s = 1 000 000 000 ns, so multiply seconds by 10⁹. A 20 ns offset between a receiver clock and system time is 0.000 000 02 s; at 0.299 792 458 m of travel per nanosecond that same offset is 5.996 m of range.

What the Nanosecond Column Is Really Counting

The caesium definition underneath

Since 1967 the SI second has been 9 192 631 770 periods of the radiation from the hyperfine transition of caesium-133. Every figure you convert here inherits that definition, whatever the box on the rack claims.

29.98 centimetres per nanosecond

A radio signal covers 0.299 792 458 m in vacuum in one nanosecond. Multiply a timing error expressed in nanoseconds by that constant and you get the ranging error it produces, which is the figure a survey crew actually cares about.

Holdover starts when the antenna goes quiet

A disciplined clock is only as good as its own oscillator once the satellite signal disappears. Free-run stability is quoted as a bare fraction, and that fraction multiplied by the 86 400 s in a day is the error it accumulates.

Protocols sit orders of magnitude apart

Timestamps taken in software leave NTP on a public path near the millisecond mark, while stamping down in the network interface lets PTP work in the tens of nanoseconds over the same cabling.

Building a Time-Error Budget Line by Line

An error budget is a column of contributions — antenna cable delay, receiver granularity, oscillator drift, protocol asymmetry — that together have to stay under the specification. They arrive in mixed units, so the first job is getting every one of them onto the nanosecond scale.

Enter the allowance the specification gives you

Type the seconds figure on the left — 0.000001 for a one-microsecond limit, 0.0000001 for a hundred-nanosecond one. The nanosecond value appears as you type, and a comma is accepted in place of the decimal point.

Turn the nanoseconds into metres

Multiply the result by 0.299 792 458 to see what the line item costs in range. A 50 ns contribution is 14.99 m; tightening it to 5 ns brings that down to 1.499 m.

Reverse it when the counter speaks nanoseconds

A time-interval counter comparing two 1 PPS outputs reports in nanoseconds. Press the swap button (↔) to run ns → s and put the measurement back into the units the acceptance document was written in.

Move the digits into the test report

The copy control beside each field puts the number alone on the clipboard — no unit, no spacing — which is what a budget spreadsheet cell expects. Ctrl + C inside a field does the same thing.

Past ten seconds the output goes exponential: 10 s is 10 000 000 000 ns, and at that magnitude the field switches to scientific notation rather than printing eleven digits. Read 1.000000e+10 as ten billion nanoseconds — which is what you see when you convert a whole interval of free run instead of a single line item.

Timing Sources and What They Hold Over a Day

The first four rows are accuracies against UTC while a reference is present. The last four are free-run drift, worked out as the oscillator's fractional stability multiplied by the 86 400 s in a day — the same sum you make when someone asks how long a clock survives without its antenna.

Timing source	What the figure represents	Time error (s)	Time error (ns)
NTP over the public internet	Typical offset from UTC	0.005 s	5 000 000 ns
NTP on a well-run LAN	Typical offset from UTC	0.0001 s	100 000 ns
PTP with hardware timestamping	Offset from the grandmaster	0.0000001 s	100 ns
GNSS-disciplined clock, locked	1 PPS measured against UTC	0.00000002 s	20 ns
TCXO in holdover, 1 × 10⁻⁷	Drift accumulated in 24 h	0.00864 s	8 640 000 ns
OCXO in holdover, 1 × 10⁻⁹	Drift accumulated in 24 h	0.0000864 s	86 400 ns
Rubidium in holdover, 1 × 10⁻¹¹	Drift accumulated in 24 h	0.000000864 s	864 ns
Caesium beam standard, 1 × 10⁻¹³	Drift accumulated in 24 h	0.00000000864 s	8.64 ns

Six orders of magnitude separate the top row from the bottom, and the price list follows the same curve. That is why a holdover requirement is worth arguing over before anyone buys hardware: the gap between surviving an outage inside 1 µs and inside 100 ns is the gap between an oven-controlled crystal and a rubidium cell.

What the Converter Adds to Timing Work

Walk a budget without retyping

Both boxes stay editable and follow each other live, so you can step through 1 µs, 100 ns and 10 ns allowances one after another while the ranging arithmetic stays in your head.

Counter readings go back the other way

The swap control turns the page into ns → s, the direction you need once a measurement has come off the instrument and has to be reported against a written limit.

Microseconds sit one click away

Searchable dropdowns hold every time unit on both sides, so the same page takes a millisecond NTP figure or a microsecond holdover limit without opening another tab.

Eleven-digit answers stay legible

Results carry up to eight decimals with thousands spaced apart, and very large values shift into scientific notation instead of running off the end of the field.

Questions From the Timing Lab

How many metres of error does a 10 ns receiver clock error cause?

Multiplied by the speed of light it is 2.998 m — about three metres of pseudorange on every satellite being tracked. The saving grace is that a receiver's own clock offset is common to all of them, so the navigation solution estimates it as a fourth unknown alongside latitude, longitude and height, and it largely falls out. What does not fall out is error that differs from satellite to satellite: broadcast clock corrections, ionospheric delay, uncalibrated antenna and cable delays. Those nanoseconds turn straight into metres.

What does a "1 µs over 24 hours" holdover spec demand of an oscillator?

Divide the allowance by the interval: 0.000001 s spread across 86 400 s works out at a fractional frequency offset near 1.16 × 10⁻¹¹, and the device has to stay inside that for the whole day while temperature and ageing pull at it. A good oven-controlled crystal gets there if it has been disciplined long enough for its ageing rate to be learned and subtracted; a rubidium standard reaches it comfortably; a temperature-compensated crystal is around four orders of magnitude away and blows the budget within minutes.

Why can PTP reach sub-microsecond accuracy when NTP cannot?

It comes down to where the timestamp is taken and what the network does to the packet in between. NTP normally stamps in the operating system, so scheduling jitter and driver buffering land straight in the measurement. PTP stamps in the interface hardware as the packet crosses the wire, and the switches on the path are not passive: a transparent clock measures how long the packet sat inside it and writes that residence time into a correction field, while a boundary clock terminates the exchange and starts a fresh one downstream. Take out queueing uncertainty and path asymmetry and tens of nanoseconds become reachable.

Why is the second defined by an atom rather than by the Earth's rotation?

Because the planet is a poor clock. Length of day wanders by a millisecond or two, pushed around by tides, core–mantle coupling and the seasonal movement of air and water, and it does so unpredictably enough that nobody can publish the table in advance. A caesium transition behaves identically everywhere and always, which is why the 1967 redefinition moved the second onto 9 192 631 770 periods of that transition. Optical clocks are now several orders of magnitude better again, and are the reason a further redefinition is under discussion.

What does a leap second do to timestamped records?

It inserts an extra second into UTC so civil time keeps pace with the rotating Earth, and on the machines below it usually shows up as a repeated or stalled second. Timestamps can go backwards, ordering assumptions break, and any interval measured across the boundary is out by a full second — a billion nanoseconds, which is catastrophic on any scale discussed here. The usual defences are smearing the correction gradually across a day, or working internally on TAI or GPS time, neither of which contains leap seconds at all. International agreement is to stop inserting them by 2035.