We asked "Claude" to estimate the percentage of vehicles thought to be exceeding the speed limit across the USA. The reply:

My best estimate: roughly 35–40% of vehicles on US roads are over the posted limit at any given moment.** A reasonable range is 25–50%. Only about 8–12% are more than 10 mph over. No one has directly measured an instant-in-time national figure. This estimate is built from the measured data below.

What has been measured (traffic engineering view)

The best national source is NHTSA's National Traffic Speeds Survey. Its latest round was in 2015. It measures *free-flow* traffic, meaning vehicles with enough space ahead to choose their own speed.
- **Freeways:** 70.1% of vehicles exceeded the limit by any amount, 44.9% by more than 5 mph, and 20.3% by more than 10 mph.
- **Arterials and collectors:** in the 2007–2009 survey, about 56% of traffic on arterials and collectors exceeded the speed limit. In 2015, 18.1 percent were traveling more than 10 mph over on major arterials, with a similar share on minor arterials and collectors.
- **Probe and AV observations:** a Texas probe-vehicle study found speeding most common late at night and on weekends, especially on 30 and 40 mph roads, where 43% of drivers exceeded the limit. Waymo's observations in San Francisco and Phoenix found almost half of nearby moving vehicles over the limit, and 6% at 10+ mph over.
- **Share of driving time:** Samsara's fleet telematics found drivers across all vehicle types spent 24% of their trip speeding, counting 1 mph or more over the limit.

**Why "at any given moment" is lower than the headline 56–70%**

The free-flow surveys leave out a lot of vehicles. In a snapshot of the whole country, many vehicles are stopped at signals, crawling in congestion, turning, or parked in traffic. None of them can be speeding. Snapshots also count vehicle-*time*, not miles. Slow urban streets take up a much larger share of vehicle-time than freeways do.

Here is my rough weighting by time on each road type:

| Road type | Approx. share of vehicles on the road | Over limit at a given moment | Contribution |
|---|---|---|---|
| Freeways | ~20% | ~60% (70% free-flow, less congestion) | ~12 pts |
| Arterials | ~45% | ~35% (56% free-flow, less signal and queue time) | ~16 pts |
| Collectors and local streets | ~35% | ~30% | ~10 pts |
| **Total** | | | **~38%** |

The answer also depends on the hour. Rush hour pushes it down, while nights and weekends push it up. IIHS found that when roads emptied in 2020, the proportion of vehicles exceeding the limit by 10+ mph rose 30–40% on all roads except rural arterials.

**Enforcement view**

Most agencies don't cite drivers in the 1–9 mph "tolerance band." The group that matters for enforcement is the 10+ mph segment. That's roughly 16–20% of free-flow traffic, or about 8–12% of vehicles at a random instant. Even that is far more than enforcement can reach. Automated enforcement changes behavior much more than patrols do. Montgomery County, Maryland's camera program reduced by 59 percent the likelihood of a driver exceeding the limit by more than 10 mph.

We asked "Claude": "Act as both a traffic engineer and traffic-enforcement official. Estimate the percentage of vehicles on US streets and highways that are traveling in excess of the speed limit at any given moment. If no statisticis are available, suggest a hypothesis for research on the topic."

*H₁: At a randomly sampled instant, the share of all US vehicles in motion on public roads that exceed the posted limit is significantly lower than the free-flow exceedance rate reported by NHTSA (56–70%), and falls between 30% and 45%. The rate varies mainly with (a) the share of vehicle-time spent in signal- or congestion-constrained conditions, (b) posted speed limit (lower limits produce higher exceedance), and (c) time of day.*

*H₀: The snapshot exceedance rate does not differ from the free-flow rate.*

How to test it:
- **Data:** a national connected-vehicle or telematics dataset, such as INRIX or Cambridge Mobile Telematics, matched to a speed-limit map. INRIX already reports the share of vehicles traveling more than X mph over the posted limit.
- **Sampling:** take random timestamps across a full year, stratified by hour, day, and season. For each one, record the instantaneous speed and limit of every active probe vehicle.
- **Weighting:** reweight the probe fleet to the national vehicle mix (heavy trucks often have speed governors) and the distribution of driving across road types.
- **Validation:** check against a fresh round of fixed-sensor surveys like NHTSA's. The 2015 national survey is now more than a decade old.
- **Outputs:** report the snapshot share at 1+, 5+, and 10+ mph over, separately for moving vehicles and all vehicles.

A caution on bias: probe data overrepresents newer vehicles with connected services. Speed-limit maps contain errors that can count drivers as speeding when they aren't, especially in school zones and work zones. Both need to be controlled.

Sources:
- [NHTSA Traffic Tech – National Traffic Speeds Survey III: 2015](https://www.nhtsa.gov/sites/nhtsa.gov/files/traffic_tech/812489_tt-national-traffic-speeds-survey-iii-2015.pdf)
- [NHTSA – National Traffic Speeds Survey II: 2009 (report 811638)](https://www.nhtsa.gov/sites/nhtsa.gov/files/811638.pdf)
- [Kockelman et al., UT Austin – Speeding in Texas (TRB)](https://www.caee.utexas.edu/prof/kockelman/public_html/TRB26SpeedingTexas.pdf)
- [Samsara – Distracted driving and speeding data insights](https://www.samsara.com/ca/blog/insights-distracted-driving-speeding)
- [Automotive Fleet – IIHS Virginia pandemic speeding study](https://www.automotive-fleet.com/10175396/speeding-risky-driving-prompted-by-pandemic-remains-a-reality)
- [Automotive Fleet – IIHS Montgomery County speed cameras](https://www.automotive-fleet.com/news/insurance-institute-decries-higher-speed-limits)
- [INRIX – Speed Distribution Profiles API](https://inrix.com/blog/introducing-the-inrix-speed-distribution-profiles-api/)