40-yard dash to 100m converter

A 40-yard dash is 36.576 m, a bit over a third of a 100m. Converting between them takes more than a ratio because the first 40 yards are almost all acceleration, while most of a 100m is run near top speed.

We model a sprint with a standard velocity curve, the same one Samozino et al.'s field method uses to profile sprinters: speed rises toward a top speed vmax as v(t) = vmax·(1 − e^−t/τ), where τ sets how quickly you get there. We fixed τ at 1.24 s by fitting the curve to Usain Bolt's ten official 10 m splits from his 9.58 in Berlin in 2009; the fitted curve misses his actual positions by 0.13 m on average. With τ fixed, one time pins your top speed, and the curve gives your time at any other distance.

As a check: the curve puts Bolt at 40 yards 4.19 s after his first movement. Interpolating his real splits gives 4.20 s.

A 40 is timed from your first movement, so there is no reaction time in it. A 100m is timed from the gun, so estimated 100m times add a 0.15 s reaction (Bolt's was 0.146 in Berlin).

Tyreek Hill has run both, which makes him a useful test case. His Pro Day 40 was 4.29, which converts to roughly a 9.8 100m. His 100m best, from high school in 2012, is 10.19. The marks are four years apart, but much of the gap comes from timing. A 40 starts when the athlete moves, often on a hand-started clock, while a 100m starts with a gun you have to react to.

Use the conversion to compare effort across the two events. A football player's sanctioned 100m will usually be slower than the time his 40 converts to. For athletes with times in both, see Tyreek Hill and Bo Jackson.