Quarter Mile Calculator

How this 1/4 mile calculator works

A quarter-mile pass is timed with light beams. The clock starts when the front tires leave the starting beam and stops when the car breaks the beam at the finish line, so the elapsed time, the ET, does not include the driver's reaction to the lights. The trap speed printed next to it is not the speed at the stripe but the average speed over the last 66 feet before it. Timers along the way record the 60-foot, 330-foot, eighth-mile and 1,000-foot times.

On the first tab the calculator works as a classic ET calculator: from two numbers, flywheel horsepower and race weight, it estimates both the 1/4 mile ET and the trap speed, and splits the pass at the eighth mile on the time bar. The other two tabs run the same drag racing formulas backward, turning the ET or the trap speed from a time slip into the power that would produce it.

Weight and power are all the formulas know. They describe a well-sorted car making a pass on a prepared dragstrip, with gearing and tires that suit it. Read the result as what the combination should be capable of; the gap between that and your time slip is what the launch, the gearing or the driver still has to find.

What to enter and where to find it

• Flywheel horsepower. Engine power at the crank, as rated or measured on an engine dyno. The formulas were fitted to flywheel figures. A chassis dyno reads lower because of drivetrain loss, so convert a wheel figure first with the whp to hp calculator.
• Race weight with driver. What the car weighs as it rolls into the lanes: fuel, driver and everything bolted on. Track scales are the best source; a brochure curb weight leaves out the driver and makes the estimate optimistic.
• ET and trap speed. Straight from the time slip of a normal pass. If your track prints weather-corrected figures as well, use the same kind every time you compare.

ET to horsepower or mph to horsepower: which to trust

Trap speed is the better measure of power. By the time a car reaches the speed trap it has long stopped fighting for grip, and the speed it carries through the lights depends mostly on how much power has been pushing how much weight. ET adds up the whole pass, and the first second decides a big part of it: a launch that spins the tires or bogs costs tenths that no amount of power gets back.

The numbers bear that out. Roger Huntington, who first fitted these formulas, noted that his trap-speed points lined up far better than his ET points and put the scatter down to differences in traction between cars. A later comparison against magazine road tests of production cars found the trap-speed formula explained about 91% of the variation between cars, the ET formula only about 62%. Part of that gap is a built-in bias: these constants were set for cars with race-car traction, and on the same road-test data a constant of about 6.1 fits the ET better than 5.825, so for a production car on ordinary tires expect a real ET roughly 5% (half a second or so) slower than the estimate. The trap-speed constant is off by only about 1% on the same data.

So when the two tabs disagree, believe the mph to horsepower result for power and treat the ET to horsepower result as a measure of how well the car leaves the line. If you race on an eighth-mile track, the 1/8 mile ET calculator converts your slip to a quarter-mile equivalent first.

Quarter mile ET formula and trap speed formula

These are empirical formulas: constants fitted to real passes, not laws of physics. The pair this quarter mile ET calculator uses, 5.825 and 234, is credited to drag racer and engineer Patrick Hale, who published it as a first-order estimate next to his drag racing simulation software. It descends from Roger Huntington's work for a hot rod magazine in the late 1950s; his trap-speed constant was 224, fitted to a few dozen road and strip tests.

1. ET (s) = 5.825 × (race weight in lb ÷ flywheel hp)^(1/3)
2. Trap speed (mph) = 234 × (flywheel hp ÷ race weight in lb)^(1/3)
3. Horsepower from ET = race weight × (5.825 ÷ ET)³
4. Horsepower from trap speed = race weight × (trap speed ÷ 234)³
5. 1/8-mile split ≈ ET ÷ 1.56 at a speed of trap speed ÷ 1.25

Why a cube root. If an engine delivered the same power at every speed with nothing lost on the way, the energy it adds, power × time, would all become ½ × mass × speed², and the car would reach a speed of (3 × power × distance ÷ mass)^(1/3). Physicist Geoffrey Fox used that model in the American Journal of Physics to explain Huntington's results. Over a quarter mile the ideal car would trap 281.1 × (hp ÷ lb)^(1/3) mph and run 4.80 × (lb ÷ hp)^(1/3) seconds.

Real cars trap at 234 × (hp ÷ lb)^(1/3) instead, which is what the ideal car would do with only about 58% of the flywheel power. The rest goes to drivetrain losses, the engine spending most of the pass below its peak power, gear changes, the grip-limited launch, spinning up the wheels and rotating parts, and air drag. The constants carry all of that on average, which is why the formulas need no other inputs, and why they cannot know about a car that is far from average.

How far off it can be. The formulas assume flywheel horsepower and race weight with the driver, the way they were fitted, and a car with good traction; Hale's ET constant in particular leans optimistic for production cars on ordinary tires, as explained above. For the same trap speed, Huntington's older constant gives about 14% more horsepower than Hale's: a fair picture of how much any horsepower figure worked out from a time slip depends on the formula behind it. The 1/8-mile split adds the spread of the conversion factors on top.

Worked example: from power to ET, and from a time slip to power

Three cases, worked out with the same functions that run the calculator.

Typical quarter mile ET and trap speed by power-to-weight

The table runs the formulas over the power-to-weight ratios you see at a dragstrip, from heavy cruisers down to serious race cars. The second column is the flywheel power a 3,400 lb car needs for each ratio; for any other weight only the ratio matters, so the times stay the same.

Because of the cube root, every 10% cut in weight per horsepower is worth only about 3.5% of ET and trap speed, and doubling the power cuts ET by about 21%. Taking weight out works exactly like adding power: what counts is the ratio.

Common mistakes

• Using wheel horsepower. The constants were fitted to flywheel power. A chassis-dyno figure makes the estimate slow; convert it first with the whp to hp calculator.
• Leaving out the driver. Race weight means the car as it runs, with the driver and fuel. Curb weight alone makes the estimate optimistic.
• Judging the engine by ET alone. ET depends on the launch as much as on the engine. If the ET says less power than the trap speed does, look at the launch and the 60-foot time before blaming the engine.
• Reading trap speed as the speed at the stripe. The figure on the slip is the average over the last 66 feet, and it is not the car's top speed either.
• Expecting the formulas to know your gearing. A car geared so it has to shift just before the lights, or one that runs out of gear early, will be slower than predicted. Check what speed each gear reaches with the gear ratio calculator.
• Comparing passes in different weather. Hot, humid air and altitude cost power. Compare slips from similar conditions, or the corrected figures if your track prints them.