We approximate the spatial and temporal distribution of the Pigouvian kilometre tax for road traffic in the most urbanized part of Sweden, with four million inhabitants and a similar "degree of urbanization" to the Netherlands and the UK, in a future scenario where most vehicles are electric. We apply the national transport model and include all links and four time-of-day periods. We find that roughly half of the vehicle kilometres travelled in Ma center dot lardalen has a marginal external cost (congestion and other external costs included) below 0.04 euro/km which is below the fuel tax in 2019). The mean marginal external cost is higher, at 0.09 euro/km. Our focus is not the exact numbers but the magnitudes and the vast variation across links in a country-like region: 90 percent of the revenue is collected on 10 percent of the road network. Hence, a nation-wide kilometre tax, implying high enforcement cost, is likely not the best option. Instead, the marginal external cost could probably be internalized fairly accurate by a congestion tax in the big cities in combination with for instance an ownership tax. We find that the Pigouvian tax would cover the public costs for our target road system. We relate our findings to the mainstem fiscal tax literature.