|Nice start, Mr. Johnson. But we think you need much more data to show statistical significance.|
Nuclear power is considered cheap compared to electrical power from fossil fuel burning plants. In price comparisons featuring the generation costs, it is with US $0.025 per kWh featured as the cheapest to generate energy.  The total costs of the power also needs to include the capital costs for building the plant and by costs for decommissioning, which bring nuclear power to its current selling price of about US $0.108 per kWh (2013).  However, additionally there is some cost related for nuclear waste storage and accidents that occur costs and/or require insurance as well. While the generating and capital costs are necessarily included in any business calculation, costs incurring much later (such as decommissioning costs) and/or costs which have a very low probability to arise and therefore a high uncertainty (such as accident related costs) are hard to budget for. The very limited information on the risks of nuclear power cause nuclear accidents to be not insurable on the marketplace.  Therefore typically the government steps in in addition to limited liability insurances of the nuclear power plant providers with additional guarantees for accidents above the market insurable levels. An interesting question is now if the total price for nuclear power set by governments for the nuclear power reasonable and covering costs related to disasters? This question is hard to analyze as both actual costs and probabilities of disasters are hard to come by. Even in the event of past disasters, significant portions of the cost are in the future and oftentimes government controlled. Additionally these estimates typically only consider monetary costs, e.g. the damage to an economy, so suffering in addition to actual economic damages is oftentimes not considered.  Still this might be sufficient as a first order approximation using the limited data of rough estimates available. To get a better understanding on the topic, a comparison between the value of the produced nuclear and the estimated costs of nuclear accidents so far can be made.
As a back of the envelope calculation, the total amount of nuclear energy produced in history of mankind can be estimated easily by multiplying the timescale in which nuclear power has been used by the average power generation per year. Since 1954 nuclear power plants have been supplying power to the grid, with a current generation of 2620 billion kWh (as of 2010).  The increase in nuclear power production that happened from 1954 until 2013, which while not exactly linear can be reasonably well approximated by a linear ramp up. Therefore having an average generation of about half the current production (rounded to) 1300 billion kWh and a timescale of about 60 years, we can estimate the total amount of generated nuclear power in history of mankind with
|1300 × 109 kWh/year × 60 years = 7.8 × 1013 kWh|
or 2.8 × 10 20 joules. While a price increase from US $0.015 per kWh in the early 1970s until now US $0.108 per kWh took place due to many reasons, including inflation, energy crisis, new regulations, more expensive new power plants etc., for simplified calculation just the costs now are considered (which therefore includes the inflation consideration but not the others).  Using for simplicity US $0.10 per kWh (US $0.108 per kWh in 2018) as a current price or value of the generated electricity, we can estimate the respective value of the nuclear energy generated by humankind up to date.  This yields a total estimated value of all nuclear energy produced until now (as of 2013) of about US $7.8 trillion (2013).
There have been only a handful of severe nuclear accidents, and the two biggest nuclear accidents: Chernobyl (1986), Fukushima (2011) shadow all other nuclear accidents including Three Mile Island (1979) in consequences and costs.  Therefore we focus only on major accidents, knowing that all added costs from all smaller accidents have no significant additional effect on the total costs. Exact costs of these accidents are hard to come by, however different studies estimated economic damages of these nuclear accidents in the following ranges. The Chernobyl accident costs were estimated in 1992 at 180 billion DM (about 90 billion Euro, not inflation-adjusted), more recently estimates have risen to hundreds of billions including US $235 billion (for Belarus alone in 2003). [4,7,8] The Fukushima accident costs estimates range from US $10 billion (government pledge for cleanup costs) to more than US $100 billion. [9,10] For the Three Mile Island accident, US $2.4 billion of damages were estimated.  Already here the trend is visible that the Three Mile Island accident is much less costly then Fukushima or Chernobyl accidents.
Comparing the rough estimates of the nuclear accident costs to date totaling somewhere in the high US $100 billion with the economic value of nuclear power of about US $7.8 trillion, so far the economic value of nuclear energy generated is about one order of magnitude higher than estimated nuclear accident costs. Breaking down the accident related costs to a kWh (assuming again a price of US $0.10 per kWh), they are on the order of US $0.01 per kWh. While the accident related costs - broken down to a kWh level - are with US $0.01 per kWh rather low and does not change the economics much, still they cannot be neglected. This is especially true in a country that experienced a major nuclear accident (such as Ukraine, Belarus and Japan) and has to foot the bill for these damages and oftentimes make up a significant chunk of the GDP for years up to decades (Belarus and Ukraine still spend around 6% of GDP in the early 2000s on Chernobyl related programs.  Looking at accidents it is also informative to look at the worst-case scenario. If such a worst-case nuclear accident occurred in a highly populated area in Germany, costs were estimated to 10 trillion DM (1992, about 5 trillion Euro, not inflation adjusted), which is comparable to the total value of the energy produced. 
Not many large-scale nuclear accidents cases have been happened to date, which makes it hard to estimate probabilities. While the two major nuclear accidents (Chernobyl and Fukushima) can give some limited some indication of the occurrence, it is hard to estimate actual costs, which have big error bars. The current selling price (including not only generating but all capital costs) seems reasonable, so the price would not change much if current estimates of nuclear accident costs would be added or subtracted. Considering the actual value of the nuclear power produced to day, accidents related cost estimates are a fraction thereof. Although it is not negligible, it does not change the economics much, especially as nuclear power is not cheapest option anymore. 
© Daniel Bechstein. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
 "Electric Power Annual 2011," U.S. Energy Information Administration, January 2013, Table 8.4.
 "Annual Energy Outlook 2012," U.S. Energy Information Administration, DOE/EIA-0383 (2012), June 2012.
 G. Skough, "Development Risks, Strict Liability, and the Insurability of Industrial Hazards," The Geneva Papers on Risk and Insurance 23, 247 (1998)
 H.-J. Ewers and K. Rennings "Economics of Nuclear Risks - A German Study," in Social Costs of Energy: Present Status and Future Trends, ed. by O Hohnmeyer and R. Ottinger (Springer, 2012), pp 150-166.
 "International Energy Outlook 2013," U.S. Energy Information Administration, DOE/EIA-0408(2013), July 2013.
 B. L. Cohen, The Nuclear Energy Option: An Alternative for the 90's (Plenum, 1990).
 "Chernobyl's Legacy: Health, Environmental and Socio-Economic Impacts and Recommendations to the Governments of Belarus, the Russian Federation and Ukraine, Second Revised Version (2003-2005)," Int. Atomic Energy Agency, IAEA/PI/A.87 Rev.2/06-09181, April 2006.
 G. Kastchiev et al., "Residual Risk: An Account of Events in Nuclear Power Plants Since the Chernobyl Accident in 1986," Greens in the European Parliament, May 2007.
 G. Brumfiel and I. Fuyuno, "Japan's Nuclear Crisis: Fukushima's Legacy of Fear," Nature 483, 138 (2012).
 M Schneider, A. Froggatt and S. Thomas, "Nuclear Power in a Post-Fukushima World," Worldwatch Institute, April 2011.
 B. K. Sovacool, "The Costs of Failure: A Preliminary Assessment of Major Energy Accidents 1907-2007," Energy Policy 36, 1802 (2008).