Fractional Frame Rates: 23.976, 29.97, and 59.94
These familiar fractional frame rates are exact integer rates divided by 1.001.
| Familiar label | Exact rate | Exact picture duration | Duration in milliseconds, rounded |
|---|---|---|---|
| 23.976 fps | 24000/1001 fps | 1001/24000 s | 41.7083 |
| 29.97 fps | 30000/1001 fps | 1001/30000 s | 33.3667 |
| 59.94 fps | 60000/1001 fps | 1001/60000 s | 16.6833 |
These familiar decimals name precise rational frame rates. Each is its corresponding integer rate multiplied by 1000/1001. The displayed decimal is rounded; use the fraction for timing calculations.
The picture duration is the reciprocal of the rate. At 24000/1001 fps, every constant-rate picture occupies 1001/24000 second. Its spacing can be perfectly regular: “fractional” refers to the rate's value, while variable describes spacing that changes.
Calculate a whole sequence
Take exactly 86,400 pictures.
At 24 fps:
86,400 ÷ 24 = 3,600 seconds.
At 24000/1001 fps:
86,400 × 1001 ÷ 24,000 = 3,603.6 seconds.
The same picture count lasts 3.6 seconds longer. Its duration increases by exactly 0.1%; its playback rate is multiplied by 1000/1001.
This calculation explains a subtitle or audio version that starts aligned but gradually diverges after the picture sequence is retimed. Moving the start by a fixed offset does not change the duration difference. Retiming a fixed sequence and converting its picture allocation while preserving duration are different operations.
The film-to-television ratio
Fractional film and field rates retain the same useful ratio:
(60000/1001) ÷ (24000/1001) = 2.5 fields per film picture.
Four film pictures therefore span ten field intervals. That is the basis of the repeating 3:2 pulldown relationship at these rates. The 1001 denominator cancels exactly; rounding the rates to decimals is unnecessary for the calculation.