How far could two free-running clocks diverge?

Enter non-negative accuracy bounds in parts per million. This linear model assumes initial alignment and constant errors within the chosen bounds.

Elapsed physical minutes since a common starting point.
Magnitude from 0 to 10,000; not a signed measured error.
The relative bound assumes opposite error directions.
Converts a time error to a fractional frame equivalent.

3.600 msClock A error bound
3.600 msClock B error bound
7.200 msMaximum relative error in this model
0.172800 framesRelative error as a frame equivalent
05:47:13.333Time from alignment for bound to reach one frame

60 minutes · 1 ppm per clock · 24 fps. Opposite error directions give a 2 ppm relative bound. Time to one frame is elapsed HH:MM:SS.milliseconds from alignment.

One ppm means one microsecond per second.

Parts per million express a fractional rate difference: 1 ppm = 1 / 1,000,000. At a constant error of 1 ppm, a clock can gain or lose 0.0036 seconds over an hour. That is 3.6 milliseconds, or 0.0001%; it is not a 1% error.

single-clock bound (seconds) = elapsed seconds × ppm / 1,000,000
relative bound (seconds) = elapsed seconds × (ppm A + ppm B) / 1,000,000
frame equivalent = relative bound × exact picture fps
seconds to one frame = 1,000,000 / ((ppm A + ppm B) × exact picture fps)

The sum covers the case where A runs fast and B runs slow at their respective bounds, or the reverse. It is a possible upper bound under these assumptions, not a prediction that both clocks will reach those errors.

Compare timing error with a picture interval.

Calculated hypothetical bounds after 60 minutes, at 24 fps
A / B accuracy boundsRelative boundFrame equivalent
1 ppm / 1 ppm7.200 ms0.172800 frames
2 ppm / 2 ppm14.400 ms0.345600 frames
1 ppm / 0 ppm3.600 ms0.086400 frames

At 24 fps, one picture interval is about 41.667 ms. A 2 ppm relative bound reaches that interval after 20,833.333 seconds, or about 5 hours 47 minutes. The fractional frame equivalent describes timing error; it is not a count of dropped or duplicated pictures.

If both clocks actually run at the same +1 ppm error, their relative rate error could be zero. Accuracy magnitudes alone do not reveal the actual signs or correlation. If both entered bounds are zero, the result is “No finite crossing in this model”; that is not a guarantee of zero real-world drift.

Verify which clock the specification describes.

Check the device model, software, temperature range, calibration and operating conditions attached to a ppm specification. Establish whether the timecode generator, sensor timing and audio sampling use the same oscillator or follow separate references. An accuracy claim for one clock does not automatically describe every recording subsystem.

Matching timecode labels alone does not prove sensor or audio-sample alignment. Initial offsets, reference loss and changing oscillator error can also affect a take. Use representative recordings and manufacturer instructions to verify the setup. This model neither measures hardware nor certifies a camera’s accuracy.

Fractional rates use 24000/1001, 30000/1001 and 60000/1001, rather than rounded decimals. Continue with timecode, genlock and word clock and camera sensor, project and timecode rates.

Technical references

Manufacturer references describe synchronization behaviour. The ppm inputs and worked examples here are hypothetical, not specifications for those products.