Archive

All past Fermi problems live here.

Energy Capital-to-capacity scaling

Duane Arnold nuclear restart electricity

Estimate how much electricity a restarted 615 MW nuclear plant could generate and how many years of gross power value would equal a $1.9 billion loan.

International trade Freight value and truckloads

Canada tariff-affected truckloads

Estimate how many daily truckloads are represented by about US$20 billion in U.S. goods affected by Canada's new counter-tariffs.

Solar manufacturing Material-cost scaling

Polysilicon solar panel cost

Estimate how much a fourfold polysilicon price premium adds to one solar panel and to a 1 GW solar project.

Federal budget Interest-cost scaling

Federal debt interest cost

Estimate the annual interest cost of $40 trillion in U.S. federal debt, then convert it into a per-household burden.

Advertising technology Internet-scale auction throughput

Google AdX auctions per second

Estimate how many ad auctions Google might run every second, then compare the flow with daily and annual ad-market dollars.

Climate Vehicle-emissions equivalence

Indonesia wildfire carbon vs cars

Estimate how many average U.S. gasoline cars driven for a year would match one week of reported Indonesian wildfire carbon emissions.

Meteorology Wind-field kinetic energy

Hurricane Karina kinetic energy

Estimate the kinetic energy stored in the hurricane-force wind field of a Category 4 Pacific storm, then compare it with household electricity use.

Natural hazards Warning-time throughput

Nepal glacier-collapse warning time

Estimate how much usable warning time communities 20 km downstream had before a glacier-triggered debris flow and flood arrived.

Aviation Transportation throughput

DXB passenger traffic drop

Estimate how many aircraft movements disappeared when Dubai International Airport lost 14.5 million passenger journeys in the first half of 2026.

Robotics Sprint power and battery energy

Tiangong robot sprint energy

Estimate the battery energy and peak power behind a humanoid robot running 100 meters in less than 9 seconds.

Climate Ocean heat content

Mediterranean upper-ocean heat

Estimate how much thermal energy is stored when the Mediterranean's upper ocean is warmed by about 2 degrees C.

Astronomy Probability and geometry

Satellite streak probability

Estimate when satellite constellations make long-exposure astronomical images likely to contain at least one bright streak.

Rocket reusability Manufacturing mass

Zhuque-3 booster reuse hardware

Estimate how much first-stage rocket hardware is saved when one recovered booster replaces fresh boosters across 20 launches.

Military logistics Mass-flow sustainment

Ulchi Freedom Shield logistics

Estimate food, water, fuel, and truckload logistics for an 18,000-troop exercise shortened from 11 days to five.

Media Human attention

Microdrama human attention

Estimate annual U.S. microdrama viewer-hours, episode-views, revenue per viewer-hour, and revenue per episode viewed.

Public health Healthcare throughput

MMR split healthcare workload

Estimate the extra clinic staff time, parent time, supplies, and appointment slots created if the combined MMR vaccine were split into separate visits.

Motorsports Aerodynamic power

Hydromax 406 mph power

Estimate the mechanical power and hydrogen use required for a hydrogen-burning streamliner to run a flying mile at 406 mph.

Oil spill Area and thickness scaling

Oman oil slick thickness

Estimate how thin 800,000 barrels of crude would be if spread over 2,000 km2, then work backward from realistic slick thickness.

Astronomy Explosion energetics

Wolf-Rayet supernova kinetic energy

Estimate the kinetic energy carried by supernova ejecta moving near 0.1c, then compare it with earthquakes, human energy use, and solar output.

Battery materials Material-flow scaling

CATL lithium mine EV batteries

Estimate how many EV battery packs one year of Jianxiawo lithium output could support, then compare that with China-scale EV production.

Humanitarian aid Mass-flow logistics

El Nino food aid logistics

Estimate the staple food, shiploads, truckloads, and global grain-production share needed if El Nino pushes 49 million more people into acute food insecurity.

Public health Contact tracing throughput

Congo Ebola contact tracing force

Estimate active contacts, daily monitoring interactions, and full-time tracers or mobile teams required during a fast-moving Ebola outbreak.

AI safety Rare-event testing throughput

Rare rogue AI behavior testing

Estimate how many tasks, parallel agents, and human reviewers are needed to catch a one-in-100,000 dangerous action within 30 days.

Energy transition Fleet stock and flow

Australia EVs and gasoline imports

Estimate whether additional Chinese EV imports can explain a substantial share of Australia's reported 15% gasoline-import decline.

Box office Attendance and capacity throughput

Spider-Man theater capacity

Estimate ticket sales, screenings, audience-hours, and the screen capacity used by a record $360 million opening weekend.

Wildfire evacuation Traffic flow

Spokane wildfire evacuation traffic

Estimate vehicles, lane-hours, traffic length, and outbound-lane needs for a 60,000-person wildfire evacuation.

AI infrastructure Capital-to-capacity scaling

Amazon AI capex power demand

Estimate how much continuous electrical load Amazon's $220 billion AI and data-center spending plan could eventually add.

Supply chains Backlog recovery

Japan quake production backlog

Estimate delayed auto and semiconductor output after the Kumamoto earthquake, then calculate how spare capacity controls catch-up time.

Military logistics Sorties and fuel

Iran strike wave logistics

Estimate strike sorties, aircraft-hours, jet fuel, tanker loads, and the hidden support package behind a two-hour strike wave.

Earthquakes Logarithmic scaling

Southwestern Japan earthquake energy

Estimate the energy released by a magnitude 7.1 earthquake, compare it with gasoline, household electricity, and Starlink reentry energy, then check the 6.8 sensitivity case.

Astronomy Orbital scaling

Betelgeuse companion orbit

Estimate the orbital period, orbital speed, and century-scale observing context for Betelgeuse's newly imaged companion.

Aviation Fuel burn and range

A350-1000ULR nonstop fuel efficiency

Estimate total jet fuel, fuel per passenger, and liters per passenger per 100 km for a 24-hour nonstop test flight.

Surveillance Computer vision throughput

Facial recognition at a mass protest

Estimate face detections, watchlist comparisons, false alerts, video storage, and human-review load during one protest day.

Agricultural biosecurity Biological supply chain

Distributing 500 million sterile flies

Estimate the mass, packed volume, and weekly aircraft release flights needed to distribute sterile screwworm flies at suppression scale.

Water infrastructure Construction quantity takeoff

Lake Powell boat-ramp extension

Estimate the ramp length, concrete volume, mass, truckloads, and cost needed if Lake Powell drops another 33 vertical feet.

Semiconductors Infrastructure scaling

AI-chip fabs as city-scale infrastructure

Estimate the power and water demand of four advanced semiconductor fabs, then compare the hub with city and metro-scale utility loads.

Air quality Exposure dose

Wildfire smoke exposure dose

Estimate the total extra PM2.5 mass inhaled across an affected region during one smoky wildfire day.

Hydrology Runoff rate

Texas flood runoff rate

Estimate the flood-wave flow produced when 10 to 20 inches of rain falls over a steep Texas Hill Country watershed.

Household budgets Weighted average

Import prices and household budgets

Estimate what a 7.1% rise in import prices might cost the average household after import exposure and pass-through are included.

Energy and defense Geometry and line of sight

Offshore wind radar horizon

Estimate whether large offshore wind turbines 20 to 60 km from shore are geometrically visible to coastal radar before Earth curvature hides them.

Public administration Operational throughput

Immigration arrest throughput

Estimate officer-days per arrest during a large enforcement surge, then compare full-network and field-team staffing assumptions.

Sports medicine Human thermal balance

World Cup hydration heat balance

Estimate how much heat a soccer player produces in one half, then convert that heat load into liters of sweat evaporation.

Volcanic hazards Atmospheric transport

Mayon ashfall distance

Estimate how far volcanic ash can drift downwind before settling, using plume height, wind speed, and ash settling speed.

Safety engineering Evacuation rate

Bangkok pub fire egress rate

Estimate how many usable doorway-equivalents a crowded pub would need to evacuate several hundred people before smoke conditions become life-threatening.

Energy Power and thermal physics

Heat dome AC demand in power plants

Estimate extra peak electrical demand from air conditioning during a large U.S. heat dome, then compare it with 1-GW power plants.

Energy supply chains Unit conversion

Strait of Hormuz oil in car fill-ups

Estimate how many average U.S. car fill-ups are equivalent to one day of oil normally passing through the Strait of Hormuz.

Sports Labor and time

World Cup fan time vs. worker-years

Estimate total human time spent inside stadiums by 2026 FIFA World Cup fans, then convert that collective attention into full-time work years.

Everyday life Counting and volume

America's daily coffee habit

An April 2026 survey reported that 66% of American adults drank coffee during the previous day. Estimate how many gallons that represents.