Why the two distances need converting at all
The eighth mile is 660 feet and the quarter is 1,320 feet, so a quarter-mile run is exactly twice the distance. It is not twice the time, and it is not twice the speed, because the car is still accelerating throughout. The second half is covered much faster than the first, and the trap speed at the far end is higher.
Two conventional factors bridge the gap. Multiply eighth-mile ET by 1.5657 for the quarter-mile ET, and multiply eighth-mile trap speed by 1.25 for the quarter-mile trap. Both are empirical: they come from comparing large numbers of timeslips, not from a derivation. That is why you also see 1.55, 1.57 and other figures quoted, each fitted to a particular class of car.
You need the conversion whenever your home track runs one distance and the record, index or competitor you care about is quoted at the other. Bracket racers travelling between an eighth-mile and a quarter-mile facility need it to carry a dial-in across.
Where 1.5657 comes from, and what physics says it should be
The conversion factors are fitted, but there is a clean physical model behind them worth understanding, because it tells you when the factors will be too high or too low.
Suppose the car delivers constant power P from a standing start. Then the kinetic energy after time t is Pt, so ½mv² = Pt and v ∝ √t. Integrate: distance d ∝ t3/2. Invert that and t ∝ d2/3, while v ∝ d1/3.
Double the distance and you get the two constants this calculator reports:
- ET ratio = 22/3 = 1.587401
- Speed ratio = 21/3 = 1.259921
Compare those with the conventional 1.5657 and 1.25. The empirical ET factor is 1.5657 ÷ 1.587401 − 1 = 1.37% below the constant-power value, and the empirical speed factor is 1.25 ÷ 1.259921 − 1 = 0.79% below. Both point the same way: real cars beat the constant-power prediction over the second half of the track.
The reason is the launch. Constant power from time zero is an idealisation no car achieves — at the hit of the throttle the car is traction limited, the converter is slipping or the clutch is engaging, and the engine cannot deliver full power to the ground. All of that happens inside the first 660 feet. By the second eighth the car is hooked up, in a higher gear and closer to genuinely constant power, so it covers that half proportionally faster than the model predicts, and the ratio comes out below 22/3.
That also explains why the factor is not one number for all cars. A traction-limited high-power car spends more of the first eighth away from constant power and shows a lower factor; a heavy, low-power car that hooks easily and pulls hard from the start sits closer to the ideal.
Worked example: 8.00 at 85 mph in the eighth
A typical street car runs 8.00 seconds at 85 mph on an eighth-mile track. What would it have gone in the quarter?
- Quarter-mile ET. 8.00 × 1.5657 = 12.526 s.
- Quarter-mile trap speed. 85 × 1.25 = 106.25 mph.
- Constant-power ET. 8.00 × 1.587401 = 12.699 s, which is 0.17 s slower than the empirical figure.
- Constant-power trap speed. 85 × 1.259921 = 107.09 mph, 0.84 mph higher.
Sanity-check the numbers with average speeds. The eighth mile is 660 ft, and one mph is 1.466667 ft/s, so average speed = 660 ÷ (ET × 1.466667) = 450 ÷ ET. Here that is 450 ÷ 8.00 = 56.25 mph average against an 85 mph trap. For the quarter, average speed = 900 ÷ ET = 900 ÷ 12.526 = 71.85 mph against a 106.25 mph trap. Both averages sit well below their trap speeds, exactly as they must for a car that is still accelerating at the stripe.
Running it the other way: a 12.00 s, 110 mph quarter-mile car converts to 12.00 ÷ 1.5657 = 7.664 s and 110 ÷ 1.25 = 88.0 mph at the 660 ft mark.
How much to trust a converted number
Treat a converted ET as accurate to roughly a tenth of a second on a twelve-second car, and know which direction the error is likely to run.
The single factor hides real variation. The reference table below shows an 8.00 s eighth converting to anywhere between 12.400 s and 12.699 s depending on which factor you choose — a spread of 0.299 s. If you need better than that, the only reliable method is to measure your own car at both distances once and derive your personal factor by dividing.
Some patterns are consistent enough to use. Cars that are traction limited off the line — high power, small tyres, aggressive converters — tend towards factors at the low end. Cars that leave gently and pull steadily, including heavier, milder combinations, sit nearer the constant-power value. Anything that changes what happens in the first sixty feet without changing peak power moves the factor.
Trap speed converts more reliably than ET, because it depends on the whole run's energy rather than on how the first sixty feet went. If you are estimating power from a timeslip, prefer the trap speed route with the trap speed horsepower calculator, and use the quarter mile ET calculator when you want an ET predicted from weight and power rather than from another timeslip.
Quarter-mile ET from eighth-mile ET at several published factors
| Eighth-mile ET (s) | ×1.55 | ×1.5657 | ×1.57 | ×1.5874 (ideal) |
|---|---|---|---|---|
| 6.00 | 9.300 | 9.394 | 9.420 | 9.524 |
| 7.00 | 10.850 | 10.960 | 10.990 | 11.112 |
| 8.00 | 12.400 | 12.526 | 12.560 | 12.699 |
| 9.00 | 13.950 | 14.091 | 14.130 | 14.287 |
| 10.00 | 15.500 | 15.657 | 15.700 | 15.874 |
| 11.00 | 17.050 | 17.223 | 17.270 | 17.461 |
On an 8.00 s eighth the four factors span 12.400 to 12.699 s. That 0.299 s spread is the real uncertainty in converting someone else's timeslip.
Where conversions go wrong
- Converting a bracket dial-in and racing on it. A converted number is an estimate with a tenth or more of uncertainty, which is enough to lose a round. Use it to get in the ballpark on a new track, then make test hits.
- Mixing an eighth-mile ET with a quarter-mile trap speed. Some timeslips print incremental data including a 660 ft split on a quarter-mile track. That 660 ft ET is a genuine eighth-mile time, but the trap speed printed beside it is the 660 ft speed, not a full quarter-mile trap.
- Assuming one factor fits every car. The factor depends on how much of the run is traction limited, which varies enormously between a 3,800 lb street car and a Pro Mod.
- Forgetting the weather. Density altitude moves ET by more than the difference between two published conversion factors on many days. Check it with the density altitude calculator before concluding that a conversion is wrong.
- Comparing across track surfaces. Eighth-mile facilities and quarter-mile facilities prepare and groove their surfaces differently, and a car that hooks at one may not at the other. The conversion assumes an identical run, which is never quite true.
Why so much racing moved to the eighth mile
Eighth-mile racing is not simply a shorter version of the same sport. Shutdown areas are the practical driver: a car trapping over 200 mph needs far more room to stop than most facilities have, and stopping from an eighth-mile trap speed is a much easier problem. Many tracks that once ran the quarter now run the eighth for that reason alone.
Racing the eighth also changes what matters on the car. The launch and the first sixty feet occupy a larger share of the run, so converter stall, tyre choice, suspension setup and clutch management carry proportionally more weight, while peak power at the far end matters less. That is the same asymmetry that makes the conversion factor sit below the constant-power value, seen from the other side.
When you compare a car across the two distances, remember what is genuinely shared and what is not. Trap speed reflects the whole run's energy and converts fairly cleanly. ET carries all of the launch's variability, and converting it moves that variability along with it. If you want a figure that is independent of the distance altogether, work in power-to-weight with the power to weight ratio calculator and compare there.