# Quarter Mile Calculator

By Steven Wooding
Last updated: Jun 25, 2020

If you're thinking of entering your car into a drag race and are wondering how well it would perform, then this quarter-mile calculator is for you. It combines a quarter-mile time calculator and a quarter-mile speed calculator. Using only your car's power and weight, it will estimate its 1/4-mile elapsed time (ET) and final speed (trap speed). With this quarter-mile ET calculator, you can:

1. Set a target time for your drag race.
3. Learn how reducing the car's weight affects its performance.

In this article, you'll also learn about the history of attempting to calculate the elapsed time and speed over a quarter-mile, using only the vehicle's power and weight.

## Huntington's quarter-mile ET and speed formulas

Back in the 1950s, engineer and automotive enthusiast Roger Huntington wanted to determine a mathematical relationship between a vehicle's power, weight, and performance over a 1/4-mile distance (a typical track length used in drag racing). His solution was to record the elapsed time and final speeds of different vehicles, plot the data on a graph, and find a line-of-best-fit to the data.

For the elapsed time, common sense dictates that the heavier a vehicle is, and less horsepower it has, so the longer the ET over a quarter-mile distance will be. So he plotted the data on a graph of weight/power against the 1/4-mile elapsed time and derived the following empirical equation (a quarter-mile ET calculator):

`ET = 6.290 * (weight / power)¹ᐟ³`

where:

• ET is the elapsed time over a quarter-mile distance.
• 6.290 is an empirically derived constant.
• weight is the total weight of the vehicle (including the driver) in pounds.
• power is the peak engine power at the clutch (net power) in horsepower.

When it comes to plotting the final speed, it makes more sense to plot the power-to-weight ratio (more power and less weight means more speed) along the x-axis. The Huntington empirical formula for the final speed is, therefore:

`final speed = 224 * (power / weight)¹ᐟ³`

where:

• final speed is the speed of the vehicle at the quarter-mile mark.
• 224 is an empirically derived constant.
• weight is the total weight of the vehicle (including the driver) in pounds.
• power is the peak engine power at the clutch (net power) in horsepower.

Don't worry if you only know your vehicle's weight and power in metric units, our 1/4-mile calculator will handle all the unit conversions for you!

## Fox's quarter-mile time and speed equations

Later on in the 1960s, a physics professor named Geoffrey Fox at the University of Santa Clara proposed a theoretical basis for Huntington's formula. He wrote up his theory in a 1973 article in The American Journal of Physics entitled, On the Physics of Drag Racing, coming up with the following significant variables that affect the ET and trap speed:

• vehicle weight.
• engine power.
• friction of the tire on the track.
• aerodynamic drag.
• moment of inertia.
• frictional loss due to moving parts.
• gear ratios and gearbox type (e.g., manual or automatic).
• vertical and horizontal centre of gravity.

Fox concluded that the power and the weight of the vehicle are the major factors in determining the final speed, making it more useful than the ET if you want to estimate the horsepower of a vehicle. The other factors can significantly affect the elapsed time. However, Fox made similar measurements to Huntington and refined the constants in his equations resulting in the following formulas:

`ET = 6.269 * (weight / power)¹ᐟ³`

`final speed = 230 * (power / weight)¹ᐟ³`

## Hale's quarter-mile speed and ET formulas

In the 1980s, drag racer, engineer and computer programmer Patrick Hale produced software that took all the variables listed above into account to estimate the ET and trap speed. However, he also produced similar formulas to estimate the performance values from just the power and weight:

`ET = 5.825 * (weight / power)¹ᐟ³`

`final speed = 234 * (power / weight)¹ᐟ³`

## How to use the 1/4-mile calculator

1. First, decide which formula to use. Fox's or Hale's is likely to give more accurate results than Huntington's as they are more recent and more likely to apply to modern vehicles.

2. Enter the total weight of the car and driver. For a standard car, you can look up its weight in the manual or search for it online. If you have a custom vehicle, visit a weighing station to measure its mass.

3. Enter the car's peak power output. For an unmodified engine, you'll find it in the manual, quoted at a particular engine speed, measured in revolutions per minute (rpm). If you have modified the engine, take it to a garage to test its peak power output.

When performing the quarter-mile run, you need to maintain the peak power rpm over the entire distance. The start will be the hardest part, as you are accelerating from a standing start. As you drop the clutch, the engine revs could significantly decrease if you don't smoothly engage the first gear.

4. The results section shows you the estimated elapsed time over the 1/4-mile, and the final speed at the quarter-mile point.

The calculator can also be used in reverse to estimate your car's power given a measured quarter-mile elapsed time or final speed. To do this, put in its weight and then enter a value for either the time or the speed.

## Comparison of the three equations with a worked example

Let's compare the three formulas by way of a worked example. The car we'll use is the Mercedes W10 Formula One car, with a peak horsepower of around 975 hp and a weight of 1638 lb (743 kg). Taking into account the driver's weight (let's use Lewis Hamilton, who weighs 150 lb), that makes a total weight of 1788 lb. Plugging these numbers into Huntington's equations gives:

`ET = 6.290 * (weight / power)¹ᐟ³ = 6.290 * (1788 / 975)¹ᐟ³ = 7.699 seconds`

`final speed = 224 * (power / weight)¹ᐟ³ = 224 * (975 / 1788)¹ᐟ³ = 183 mph`

Now for Fox's equations:

`ET = 6.269 * (weight / power)¹ᐟ³ = 6.269 * (1788 / 975)¹ᐟ³ = 7.673 seconds`

`final speed = 230 * (power / weight)¹ᐟ³ = 230 * (975 / 1788)¹ᐟ³ = 187.9 mph`

And finally, Hales equations:

`ET = 5.825 * (weight / power)¹ᐟ³ = 5.825 * (1788 / 975)¹ᐟ³ = 7.13 seconds`

`final speed = 234 * (power / weight)¹ᐟ³ = 234 * (975 / 1788)¹ᐟ³ = 191.17 mph`

We can see that Huntington and Fox give very similar ETs, but Hale gives a significantly shorter elapsed time. The trap speed results are more spread out, ranging from 183 mph for Huntington to 191 mph for Hales. The results are similar from all three equations, and they give a good first-order approximation of the quarter-mile performance figures without considering some of the other variables that are difficult to determine.

Steven Wooding
Equation
Huntington
Weight
lb
Power
hp(l)
Results
Elapsed time
sec
Trap speed
mph
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