The Verification Venue · one curve, ten miles an hour
The Ten Miles an Hour That Triple the Odds
Hit a person walking at 20 mph and, on the US average curve, about 1 in 14 are killed. At 30 mph it is about 1 in 5. That is roughly triple the odds for ten more miles an hour, and the number is not a slogan: it is a steep, nonlinear curve you can drag, audited against the study that published it.
The single most-cited modern US answer is Tefft (2011, AAA Foundation), fitted to NHTSA crash data for 422 pedestrians aged 15 or older struck by a single forward-moving car or light truck. Its average risk of death passes through 10% at 23 mph, 25% at 32 mph, 50% at 42 mph, 75% at 50 mph and 90% at 58 mph. Fit a logistic curve to those anchors and it reads about 7% at 20 mph and about 20% at 30 mph. Drag the two markers below and watch the gap steepen.
Panel A · The fatality curve
risk of death vs impact speed · drag the markersMarker A
20 mph
–% killed
Marker B
30 mph
–% killed
B versus A
–x
how much deadlier
Tefft is the US average (solid). Rosen is German data (dashed, lower). The 1970s THINK! curve is a red ghost: in 2010 the DfT acknowledged that its campaign had overstated fatality risk.
40 yr reproduces the population-average curve. Drag toward 70 and the whole curve lifts and steepens, so the 20-to-30 ratio edges up toward about 2.9x. Age model applies to the Tefft curve.
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Overlays the report's own published cells and checks the live fit against each.
Tefft's published anchors vs this page's live logistic fit
| Impact speed | Tefft published | Live fit here | Gap | Check |
|---|
The fit is forced through two anchors (10% @23, 50% @42) and reproduces the other three within a few points. A two-parameter logistic slightly under-reads the very top of the tail.
Two honest caveats before you trust that about 3x. First, it is not exactly 3x: on the US average adult curve it is about 2.7x (7.3% to 20.0%), edging up toward 3x for older pedestrians, whose curve is steeper (a 70-year-old runs about 2.9x, from roughly 13% to 37%). Flick the age slider to 70 and watch the curve lift and steepen. Second, studies disagree on the absolute number by two to three times. Switch the study to Rosen 2009 and 30 mph drops to about 7 percent. What is robust across every modern study is the shape (steep, nonlinear) and the direction and rough size of the 20-versus-30 gap. So we lead on the shape and the ratio, and we scope the absolute number.
The scary figure that was wrong for thirty years
"an 80% chance of death" at 40 mph: the DfT acknowledged the overstatement in 2010
The most-quoted sourced figure in this whole area was wrong for three decades. The UK THINK! / "Kill Your Speed" campaign told a generation that a pedestrian had a 20% chance of death at 30 mph and 80% at 40 mph. Those numbers were built on 1970s crash data and badly overstated the high-speed risk. On 17 September 2010, Road Safety GB reported the Department for Transport's acknowledgment and newer estimates of about 7% at 30 mph and 31% at 40 mph. Road safety minister Mike Penning said that "misleading statistics only serve to undermine our case, not help it." The revised figures are the British OTS and police fatal file estimates in Richards (2010), Table 4.1, not Rosen and Sander's German estimates, which are about 7% and 25%. Switch the study selector to the red 1970s THINK! ghost and watch its 40 mph point leap to about 85%, far above the modern curves: an illustration of the older claims. The lesson is doubly useful. 30 mph really is markedly (roughly triple) deadlier than 20 mph, and the graphic your driving instructor showed you was retired over a decade ago.
| Impact speed | Tefft 2011 (US avg) | Rosen 2009 (Germany) | 1970s THINK! (outdated) |
|---|
At very low absolute risk a ratio looks huge (Rosen's 30-versus-20 jump is a large multiple of a tiny number), which is exactly why we headline the US average adult curve's central estimate, about 3x, rather than any single ratio.
The other reason the faster car is deadlier
Fatality curves are indexed to impact speed, the speed at the moment of contact, which is lower than travel speed whenever any braking happened. That matters, because the 30 mph car is deadlier not only per impact but because it is far more likely to strike at speed at all. From one shared point where the driver first sees the pedestrian, the slower car can often stop clean while the faster car has barely begun braking. Run the bench: reaction distance (blue) is linear in speed, braking distance (red) is quadratic, and the residual speed feeds straight back up into Panel A.
Panel B · The street
shared sight line · blue = reacting · red = brakingCar A impact speed
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risk on the curve above
Car B impact speed
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risk on the curve above
Kinetic energy
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energy scales with speed squared
The sight-line margin: how far ahead the pedestrian is when the driver first sees them.
Detents: Alert 0.67 s, Typical 1.0 s, Distracted 1.5 s, AASHTO design 2.5 s.
At the default settings (15 m sight line, a typical 1.0 s reaction, dry road) the 20 mph car stops just before the line without contact, so 0% collision fatality risk. The 30 mph car, having spent about 13 m merely reacting, is still doing about 28 mph where the slower car had already stopped, which lands near 17% on the curve. Now drag reaction time to a texting 1.5 s: the 30 mph car has not touched the brake where the 20 mph car has fully stopped, and it strikes at the full 30 mph. The residual is not a fixed constant. It is roughly 20 to 30 mph depending on reaction time and grip, and that is the whole point of letting you set them.
The check: every number recomputed in front of you
Nothing here is stored. For your current settings the page recomputes the fit, the ratio and the stopping coupling from the same equations the offline verifier uses:
The offline gate recomputes all of it, two independent ways where it can: node research/how-much-deadlier-30-than-20/verify-how-much-deadlier-30-than-20.mjs. Free choices and scope. This page is about risk of death, not severe injury (Tefft's injury curve sits well to the left: 50% severe injury at 31 mph versus 50% death at 42 mph). The Tefft fit is a two-parameter logistic P = 1/(1+e-(a+bv)) forced through the report's 10% @23 and 50% @42 anchors (a=-4.857, b=0.115643/mph); it reproduces the other three published anchors to within about 4 points. The age term both shifts and steepens the logit line, logit += kA·(age-40) + kB·(age-40)·v, calibrated to ProPublica's reads of Tefft (a 70-year-old at about 13% at 20 mph and 70% at 40 mph, which back out a steeper older curve; it then reproduces a 30-year-old's 36% at 40 mph independently). Because an older pedestrian's curve is steeper, the 20-to-30 ratio edges up with age to about 2.9x rather than compressing; it is an approximation of Tefft's full age model. The German curve uses Rosen and Sander's published equation (2): P = 1/(1+e6.9-0.090v), with speed in km/h. The 1970s ghost is an illustrative logistic through 20% at 30 mph and 85% at 40 mph; those numbers appear only as a labelled, struck-out ghost and are never this page's own claimed risk. The stopping coupling uses d = v·tr + v2/2a with dry a = 6.6 m/s2 (≈ 0.67 g); the residual speed is strongly parameter dependent. All fatality curves are fit to crashes that were recorded, and faster crashes are likelier to be reported and reconstructed, which can bias the absolute risks upward (Rosen 2011 addresses this).
What is exactly true here, and what is a model
Robust across every modern study (the sourced physics and epidemiology). A pedestrian's risk of death rises steeply and nonlinearly with impact speed, and the curve is convex through the 20 to 40 mph band, so the gap from 20 to 30 mph is larger than the gap from 10 to 20 mph. The direction and rough size of the 20-versus-30 gap (roughly triple on the US average adult curve) is stable. Kinetic energy scales with the square of speed, so 30 mph carries (30/20)2 = 2.25 times the energy of 20 mph. Reaction distance is linear in speed and braking distance is quadratic, so from a shared sight line the faster car is much more likely to still be moving when it reaches the pedestrian.
Genuinely uncertain (the number, not the shape). The absolute probability of death at a given speed is contested: the US PCDS curve (Tefft) says about 20% at 30 mph, the German GIDAS curve (Rosen and Sander) says nearer 7 to 10%, a two-to-three-fold disagreement driven by country, era, car fleet, medical care, and how each study handles the selection bias that faster crashes are likelier to be recorded. We report the band and the reason rather than pretending one curve is the truth.
A model, not a measurement (the exact numbers). The Tefft curve is a two-parameter fit to the report's published anchors, reproduced within a few points; it is illustrative between them. The German curve uses Rosen and Sander's published equation (2). The 1970s ghost illustrates older claims. The age shift is a linear approximation calibrated to two points. The street simulation is a point-mass kinematic model: constant deceleration, no weight transfer, no anti-lock modulation, a single reaction time. These get the directions and rough magnitudes right without claiming to be any specific vehicle or crash.