What Delta-V is and how it relates to whiplash injury
Updated 2026 · 3 min read
Delta-V is the abrupt change of speed a vehicle undergoes during the crash, not the speed it was travelling at. It is the quantity that correlates best with the severity of an impact, which is why it appears in almost every discussion about neck injury. But a Delta-V does not on its own decide whether there was an injury, and it is calculated with a margin of error that has to be declared.
What it actually measures
Picture a car stopped at a traffic light that is struck from behind. Before the impact it is doing 0 km/h; a tenth of a second later it is doing 12 km/h. That jump —12 km/h— is its Delta-V. The car that hit it was perhaps doing 25 km/h and dropped to 14 on impact: its Delta-V is 11 km/h.
Note that neither of the two Delta-Vs matches anybody's travelling speed. Confusing the two is a very common error in reports and in court submissions.
What shakes the occupant is the acceleration their own vehicle undergoes, and that acceleration is the Delta-V spread over the duration of contact, of the order of one to two tenths of a second. A truck travelling at 60 km/h that brushes another truck can produce less neck loading than a car striking a light vehicle at 20 km/h.
Why two cars in the same crash have different Delta-V
Because momentum is shared according to the masses. In an impact between two vehicles the following always holds:
In other words: the lighter vehicle always takes the larger Delta-V, in inverse proportion to its mass. If a 2,100 kg SUV runs into a 1,050 kg hatchback, the hatchback suffers twice the Delta-V of the SUV, in the same crash and at the same instant.
| Striking vehicle | Struck vehicle | ΔV of the struck | ΔV of the striker |
|---|---|---|---|
| 1,400 kg | 1,400 kg | equal | equal |
| 2,100 kg | 1,050 kg | double | half |
| 1,050 kg | 2,100 kg | half | double |
How it is calculated
In low-severity rear-end impacts the Delta-V does not come from skid marks —there are hardly ever any— but from the energy balance. The energy absorbed by the deformation of both vehicles is estimated and shared between them using conservation of momentum, allowing for the rebound (the coefficient of restitution).
Module 01 of this calculator does that calculation and returns the range, with the restitution curve as a function of closing speed and the correction for an off-centre impact.
Frequently asked questions
- Is Delta-V the same as impact speed?
- No. Delta-V is the change of speed a vehicle undergoes during the crash. The impact speed is the speed it was travelling at beforehand. In a rear-end impact the struck vehicle can be stationary —zero speed— and still have a considerable Delta-V.
- Is there a Delta-V below which whiplash does not occur?
- There is no universally accepted medical threshold. The literature discusses values of the order of 8 to 15 km/h: McConnell and the Quebec Task Force put the limit at 8 km/h, Castro between 10 and 15, and Kullgren and Krafft give a 10% risk at 8 km/h rising to 100% at 25 km/h. Spanish courts do not accept the threshold, on its own, as proof that no injury occurred.
- How accurately can a Delta-V be calculated?
- Checked against 312 instrumented rear-end tests, the median error is 9.6% and 96% of cases fall within ±30%, with a 7.2% tendency to over-predict.
- Why do the two vehicles have different Delta-V?
- Because it is shared in inverse proportion to the masses: m₁·ΔV₁ = m₂·ΔV₂ always holds. The lighter vehicle always suffers the larger Delta-V.
- Does Delta-V establish who was at fault?
- No. Delta-V measures the severity of the impact, not the mechanics of the manoeuvre. Liability requires avoidability, the pre-impact speeds and the trajectories, which are different calculations.