Napkin Math Tool
Quantity
0 | individual person |
1 | nuclear family, small friend group, car pool, small team |
2 | extended family reunion, classroom, apartment building, small company |
3 | elementary school, village, large wedding, medium company office |
4 | large high school, small town, popular concert, large corporation office |
5 | major sports stadium, medium-sized city, large university, industry convention |
6 | large metropolitan area, small country, global company workforce |
7 | large urban area population, mid-sized country, global social media platform users |
8 | Japan's population, global corporation's customer base, global sport viewership |
9 | India or China's population, Facebook users, global television audience |
10 | world population + historical population, estimated global internet users by 2030 |
11 | estimated human historical total, ants on Earth, trees on Earth |
12 | estimated stars in the Milky Way, global annual digital information in bytes |
Probability
-10 | practically impossible, every atom in your body quantum tunneling simultaneously one foot to the left |
-9 | astronomically unlikely, shuffling a deck and getting cards in perfect sequential order, specific molecular-level event |
-8 | nearly inconceivable, winning national lottery jackpot twice in a row with single tickets, specific quantum tunneling event |
-7 | virtually impossible, same person being struck by lightning twice in a lifetime, specific major asteroid impact in a given year |
-6 | exceptionally uncommon, random person winning a specific state lottery, fatal reaction to a well-tested vaccine |
-5 | extremely rare, winning $100+ in a specific scratch-off lottery ticket, specific major earthquake occurring on a given day |
-4 | highly improbable, winning a specific 4-digit lottery number, being struck by lightning in your lifetime |
-3 | 0.1%, rare event, being dealt a royal flush in poker, dying in a car accident in a given year (US) |
-2 | 1%, very unlikely, winning a specific raffle with 100 tickets, professional athlete having career-ending injury in a given game |
-1 | 10%, moderate chance, rolling a 1 on a 10-sided die, rain in Seattle on a random day, minor side effect from medication |
0 | 100%, absolute certainty, guaranteed outcome, mathematical proof, sunrise tomorrow, death eventually occurring |
Time (seconds)
-9 | fastest computer operations |
-8 | light traveling 3 meters, fastest electronic switching |
-7 | high-performance CPU clock cycle |
-6 | RAM memory access time, radar echo |
-5 | modern computer instruction cycle, sound traveling 3.4 meters |
-4 | fastest human reflex, high-speed camera frame, computer memory access |
-3 | computer CPU cycle, camera flash duration, neuron firing |
-2 | fast eye movement, nerve impulse transmission, hummingbird wingbeat |
-1 | camera shutter click, finger snap, lightning flash |
0 | sheartbeat, eye blink, saying a short word |
1 | staking a quick breath, typing a sentence, drinking a glass of water |
2 | 1.7 min, microwaving a meal, brushing teeth thoroughly, waiting in a short line |
3 | 16.7 min, cooking a meal, commuting to work, watching a sitcom episode |
4 | 2.8 hr, watching a movie trilogy, cross-town drive, professional sports game |
5 | 1.2 days, weekend getaway, binge-watching a TV season, transatlantic flight |
6 | 11.6 days, two-week vacation, waiting for a passport, healing from minor surgery |
7 | 3.8 months, college semester, pregnancy trimester, training for a marathon |
8 | 3.2 years, undergraduate degree, Olympic cycle, presidential term |
9 | 31.7 years, mortgage payoff, career span, generational shift |
10 | 317 years, rise and fall of empires, scientific revolutions, industrial age |
11 | 3,170 years, development of world religions, rise and fall of ancient civilizations |
12 | 31,700 years, ice ages, evolution of human language, cave painting to quantum computing |
Frequency (hertz)
-1 | earth rotation cycle, tide changes, circadian rhythm |
0 | human heartbeat, breathing cycle, clock second |
1 | slow typing speed, resting brain alpha waves, hummingbird wings |
2 | lowest musical note perception, fast typing, camera shutter |
3 | telephone voice band, musical middle C (261.6 Hz), bee's wings |
4 | highest musical notes, upper limit of human hearing (young adults) |
5 | bat echolocation, ultrasonic cleaning, medical imaging |
6 | AM radio transmissions, medical ultrasound imaging (1 MHz) |
7 | shortwave radio, MRI scanners, RFID systems |
8 | FM radio broadcast, aerospace communications |
9 | microwave ovens, mobile phones, GPS signals (1 GHz) |
10 | satellite communications, wireless networks, microwave links |
11 | millimeter-wave scanners, automotive radar, 5G communications |
12 | infrared radiation, thermal imaging, fiber optic communications (1 THz) |
Money (dollars)
-2 | penny, small paper clip, individual grain of rice, single cotton ball, one sheet of paper, 1g of soil, single drop of fresh water |
-1 | text message, small candy, plastic pen, rubber band pack, paper napkin, 1kg of sand, 1L of fresh water, handful of topsoil |
0 | candy bar, song download, dollar store item, public transit ride, service tip, 1 cubic meter of air, small bundle of firewood |
1 | fast food meal, movie ticket, paperback book, basic streaming subscription, cocktail, 1 ton of raw limestone, small garden plot (1 sq meter) |
2 | decent pair of shoes, week of groceries, nice dinner for two, monthly utility bill, entry-level headphones, 1 barrel of crude oil, 1 ton of coal, small pine tree |
3 | one month's rent (some areas), budget laptop, domestic flights, basic furniture set, low-end bicycle, 1 acre of rural land, 1 ton of iron ore, small residential solar array |
4 | used car, year of in-state tuition, high-end appliances, budget wedding, luxurious vacation, 1 acre of arable farmland, small woodlot, 1 ton of copper ore |
5 | home down payment, luxury car, four-year degree, small business startup, year's salary for mid-level professional, small local businesses, pre-seed startups, 1 ton of refined copper, small natural gas well, 10 acres of forest land |
6 | house in most cities, retirement fund, small business acquisition, exotic supercars, multiple college educations, seed-stage startups, small local chains, small oil well, 1 ton of silver ore, small quarry operation |
7 | mansion in premium location, medium-sized jet, multi-location business, minor league sports team, significant art collection, early-stage startups, regional businesses, medium mining operation, small wind farm, 1 ton of gold ore |
8 | private island development, large business conglomerate, major market sports franchise, significant venture capital fund, feature film production, series B/C startups, medium-sized private companies, coal-fired power plant, small oil field, moderate hydroelectric dam |
9 | major sports teams, large commercial developments, significant philanthropic foundations, major research initiatives, large company ownership stakes, Instacart, Roblox, Reddit, large diamond mine, major forest reserve, all of a small country's lithium reserves |
10 | national high-speed rail line, global tech platform, major airline group, significant portion of a major city, multiple global pharmaceutical companies, Airbnb, Snap, Uber, PayPal, large oil field, major hydroelectric project, 1% of global rare earth elements |
11 | large country's annual budget, global banking group, major tech ecosystem, comprehensive national infrastructure, international space program, Meta, Tesla, Alphabet, 10% of the world's copper reserves, all of Canada's timber, major river system |
12 | GDP of countries like Indonesia or Mexico, entire U.S. defense budget, ~5% of U.S. economy, nation-scale infrastructure overhaul, ~1/32 of U.S. national debt, Apple, Microsoft, Saudi Aramco, NVIDIA, all the world's extracted gold (~200,000 tons), all the world's copper reserves, Amazon rainforest |
Dollars per day
-1 | passive income from tiny investment, individual blog ad impression |
0 | small app subscription, basic streaming service, candy machine |
1 | entry-level gig work, small creator tips, coffee shop regular |
2 | minimum wage job, side hustle, small rental income |
3 | successful professional, small business, popular creator income |
4 | successful small business, local restaurant, medical practice |
5 | regional retailer, medium business, successful startup |
6 | major franchise, large corporation division, popular e-commerce site |
7 | Fortune 500 company, major sports team, large hospital system |
8 | tech giant, major bank, global retail chain |
9 | global conglomerate, major stock exchange, oil company |
10 | top global corporations combined, large national tax revenue |
11 | major economy GDP, global payment networks, global industry sector |
12 | largest global economies combined, world financial system |
13 | world economy, planetary scale economic activity |
Days per $1000
-4 | seconds | micro-transaction processor fees, penny stock day trading |
-3 | minutes | hourly wage of high-earner, fast food restaurant hourly sales |
-2 | hours | minimum wage day's work, small coffee shop daily revenue |
-1 | days | entry-level weekly salary, independent contractor daily rate |
0 | weeks | average monthly rent payment, typical car payment |
1 | months | budget smartphone lifetime cost, basic appliance over useful life |
2 | years | lifetime utility of basic furniture, depreciation of budget used car |
3 | decades | rural housing in developing regions, subsistence farming annual yield |
4 | centuries | medieval craftsman lifetime earnings, ancient agricultural output |
5 | millennia | early bronze age village production, paleolithic community resources |
Dollars per kilogram
-1 | bulk sand, gravel, raw earth, tap water |
0 | coal, industrial salt, raw agricultural products (wheat, rice) |
1 | bulk steel, basic plastics, flour, cement |
2 | basic electronics components, processed foods, common household goods |
3 | consumer electronics, quality clothing, specialty foods |
4 | high-end smartphones, designer clothing, quality tools |
5 | professional equipment, luxury fashion, fine jewelry |
6 | industrial machinery, medical devices, rare materials |
7 | advanced scientific instruments, satellite components, fine art |
8 | rare earth elements, pharmaceutical APIs, specialized aerospace materials |
9 | medical radioisotopes, cutting-edge semiconductor materials, precious gems |
10 | research-grade antimatter, certain advanced pharmaceuticals, rare isotopes |
11 | artificially produced super-heavy elements, experimental materials |
Kilograms per dollar
-11 | artificially produced super-heavy elements, experimental materials |
-10 | research-grade antimatter, certain advanced pharmaceuticals, rare isotopes |
-9 | medical radioisotopes, cutting-edge semiconductor materials, precious gems |
-8 | rare earth elements, pharmaceutical APIs, specialized aerospace materials |
-7 | advanced scientific instruments, satellite components, fine art |
-6 | industrial machinery, medical devices, rare materials |
-5 | professional equipment, luxury fashion, fine jewelry |
-4 | high-end smartphones, designer clothing, quality tools |
-3 | consumer electronics, quality clothing, specialty foods |
-2 | basic electronics components, processed foods, common household goods |
-1 | bulk steel, basic plastics, flour, cement |
0 | coal, industrial salt, raw agricultural products (wheat, rice) |
1 | bulk sand, gravel, raw earth, tap water |
Energy (Joules)
-18 | energy of a single DNA bond, quantum computing operation |
-14 | energy to flip a transistor in modern CPU |
-10 | energy to transmit one bit wirelessly, single nerve impulse |
-6 | energy of a mosquito flying for one second, mechanical watch tick |
-3 | energy to lift a paperclip 1 cm, honeybee wing flap |
0 | energy to lift an apple one meter, energy in a French fry, smartphone tap |
1 | energy of a slap, burning a match, smart watch charging for one minute |
2 | energy of a strong punch, AA battery, phone screen energy used per hour |
3 | food calories in a bite of apple, bicycle movement for ten seconds, boiling a cup of water |
4 | food calories in a candy bar, car movement for one second, toaster use for one minute |
5 | energy to heat a gallon of water, laptop energy use per day, microwave heating a meal |
6 | daily food intake for an adult, smartphone battery for a year, car moving at highway speed |
7 | energy in 1 liter of gasoline, household electricity for a day, lightning bolt |
8 | energy to launch a small rocket, household electricity for a week, small meteorite impact |
9 | energy in 30 gallons of gasoline, home energy use for a month, small tornado |
10 | energy released in a barrel of oil, residential electricity for a year, small earthquake |
11 | energy in a lightning storm, fuel for a cross-country flight, medium earthquake |
12 | small nuclear bomb, daily electricity for a small city, large hurricane |
13 | moderate nuclear explosion, monthly energy for a small city, major earthquake |
14 | large nuclear explosion, annual energy consumption of a small town, volcanic eruption |
15 | large meteor impact, daily solar energy reaching small country, hydrogen bomb |
Power (Watts)
-18 | single enzyme reaction, quantum tunneling event |
-15 | bacterial flagellar motor, molecular computation |
-12 | single neuron at rest, RFID tag in passive mode |
-9 | electronic watch operation, insect brain, ultra-low-power sensor |
-6 | hearing aid, pacemaker, IoT sensor in sleep mode |
-3 | smart watch in standby, Bluetooth headset, calculator |
0 | smartphone in standby, LED indicator, small electronic device |
1 | smartphone in active use, incandescent light bulb, laptop in sleep mode |
2 | laptop in active use, TV, refrigerator, ceiling fan |
3 | microwave oven, hairdryer, small electric heater, average home |
4 | small office building, electric car at highway speed, industrial machinery |
5 | large commercial building, passenger airplane, small factory |
6 | small power plant, large office building, passenger train |
7 | cruise ship, skyscraper, small town's electricity usage |
8 | medium-sized power plant, small city, large steel mill |
9 | large power plant, medium city, large industrial complex |
10 | nuclear power plant, large city, international airport |
12 | all power plants in a major country, civilization-level energy flow |
15 | worldwide human energy consumption, global electrical infrastructure |
17 | total solar energy intercepted by Earth, large asteroid impact |
26 | total energy output of the Sun, major stellar event |
Kilowatt hours (kWh)
-3 | single LED indicator for an hour, digital watch for a day |
-2 | bluetooth headset standby, hearing aid daily usage |
-1 | smartphone standby mode for a day, fitness tracker weekly use |
0 | laptop use for 5-10 hours, LED bulb for 1-2 days |
1 | average US household daily usage, electric vehicle charge (30-40 miles) |
2 | average US household weekly usage, Tesla Model S battery capacity |
3 | average US household monthly usage, small business monthly consumption |
4 | average US household yearly usage, small factory monthly operation |
5 | medium-sized business yearly usage, small hospital monthly consumption |
6 | large factory monthly usage, small town daily consumption |
7 | small city monthly consumption, large industrial complex annual usage |
8 | medium city monthly usage, average nuclear plant weekly output |
9 | large metropolitan area monthly consumption, nuclear plant monthly output |
10 | small country annual consumption, major hydroelectric dam yearly output |
11 | medium-sized country annual energy consumption |
12 | United States quarterly electricity consumption, global energy industry day |
13 | global annual electricity production, all human energy use for weeks |
Milli-amp hours (mAh)
-1 | hearing aid, bluetooth earbud, single LED for hours |
0 | smartwatch, wireless mouse, fitness tracker weekly use |
1 | entry-level smartphone, wireless keyboard, medical device |
2 | flagship smartphone, tablet, e-reader, 1-2 days mixed use |
3 | ultrabook laptop, portable speaker, 8-16 hours active use |
4 | gaming laptop, professional camera, 2-6 hours heavy use |
5 | electric scooter, small drone, portable power station |
6 | electric bicycle, professional video equipment, small UPS |
7 | electric motorcycle, home backup battery, 4-12 hours essential load |
8 | compact electric car, home energy storage, 100-250 miles range |
9 | luxury electric car, commercial backup, 250-400 miles range |
10 | electric bus/truck, neighborhood microgrid, 100-300 miles |
11 | grid-scale storage, commercial backup, days of power |
Energy Storage Density (Wh/kg)
0 | lead-acid, vehicle starter batteries, UPS systems |
1 | Ni-MH, power tools, early hybrid vehicles |
2 | Li-ion common, smartphones, laptops, most EVs |
3 | next-gen solid-state, emerging tech, future EVs |
4 | theoretical lithium-air, research stage, potential future |
Dollars per kilowatt hour
-3 | wholesale hydroelectric power, excess grid energy during oversupply |
-2 | large industrial electricity contracts, utility-scale solar in optimal locations |
-1 | typical residential electricity rates, grid-scale battery storage discharge |
0 | peak demand charges, small-scale battery storage, emergency backup power |
1 | remote microgrid electricity, power in disaster areas, portable power stations |
2 | helicopter-delivered emergency power, extreme remote locations, military expeditions |
3 | space station power costs, antarctic research stations during winter |
4 | early satellite power systems, specialized military portable power |
5 | first space missions power costs, experimental fusion research energy |
6 | theoretical cost of antimatter energy, earliest space program power supplies |
Kilowatt hours per dollar
-6 | theoretical antimatter energy production, earliest space program power |
-5 | early space mission power systems, experimental fusion research |
-4 | vintage satellite power, specialized military portable power systems |
-3 | space station power, antarctic research station during winter |
-2 | helicopter-delivered emergency power, extreme remote locations |
-1 | remote microgrid electricity, disaster area power, portable power stations |
0 | peak demand electricity, small-scale battery storage, emergency backup generators |
1 | typical residential electricity, standard grid power in developed countries |
2 | large industrial electricity contracts, utility-scale solar in optimal locations |
3 | wholesale hydroelectric power, excess grid energy during oversupply periods |
Information (bits)
0 | binary digit, yes/no answer, single state |
1 | two decimal digits, 3-digit binary number, single ASCII character |
2 | short sentence in ASCII, small icon, QR code with URL |
3 | paragraph of text, small black and white image, musical note |
4 | page of text, low-resolution image, short audio clip |
5 | book chapter, medium-quality image, few seconds of MP3 audio |
6 | entire book, high-quality photo, minute of music |
7 | encyclopedia article, RAW photo, song |
8 | small database, short video clip, software application |
9 | entire encyclopedia, hour of standard video, complex software |
10 | library collection, 4K movie, large dataset |
11 | all books in a large library, 8K video collection, enterprise database |
12 | Library of Congress holdings, year of HD video content |
13 | all words ever spoken by humans, DNA of human population sample |
14 | all music ever recorded, high-resolution brain scan database |
15 | all text/images ever published online, large enterprise data |
16 | global daily internet traffic, astronomical observation data |
17 | all digital content produced in a year, particle physics data |
18 | all human knowledge digitized, complete genomic database |
Throughput (bps)
0 | telegraph, Morse code transmission |
1 | slow teletype, early text terminals |
2 | early dialup modems, basic telemetry |
3 | early home internet, text-only experiences |
4 | basic dialup internet, text with simple images |
5 | fast dialup, early mobile data |
6 | early broadband, basic streaming audio |
7 | standard home broadband, SD video streaming |
8 | fast home internet, HD video streaming |
9 | gigabit internet, 4K video streaming |
10 | enterprise connection, multiple 8K streams |
11 | data center interconnect, major backbone links |
12 | major internet backbone, submarine cable systems |
13 | multi-cable submarine systems, satellite constellations |
14 | global internet infrastructure, combined backbone capacity |
Operations
0 | single CPU instruction, one line of code execution |
1 | simple database query, basic API call, small function execution |
2 | complex database transaction, rendering a web page, image processing routine |
3 | video frame rendering, machine learning prediction, complex search algorithm |
4 | 3D scene rendering, large language model inference, complex sorting of large data |
5 | image recognition pipeline, real-time video processing, large matrix multiplication |
6 | training small machine learning model, full-text search of large corpus |
7 | 3D animation rendering, large-scale data processing job, genome sequence alignment |
8 | climate simulation timestep, protein folding calculation, large ML model training |
9 | complex physics simulation, global weather model update, large video rendering |
10 | astronomical simulation, national-scale logistics optimization |
12 | global climate model, universe simulation timestep, cryptocurrency blockchain |
Operations per second
0 | mechanical calculator, human mental arithmetic |
1 | desktop calculator, early microcontroller |
2 | vintage personal computer, 1980s gaming console |
3 | 1990s desktop computer, early smartphone |
4 | entry-level modern CPU core, embedded system |
5 | high-end desktop processor, game console GPU |
6 | server-grade CPU, high-end graphics card (FLOPS) |
7 | small cluster of servers, specialized AI hardware |
8 | supercomputer, large data center processing capacity |
9 | top 10 supercomputer, major cloud region processing power |
10 | combined processing power of major cloud provider |
11 | estimated global computing infrastructure |
12 | hypothetical exascale supercomputing network |
15 | theoretical quantum computing milestone |
18 | computational capacity to simulate human brain |
Operations per Joule
-9 | mechanical computing, early vacuum tube computers |
-6 | early transistor computers, 1960s mainframe |
-3 | personal computers of the 1980s, early laptops |
0 | desktop computers, game consoles, typical server |
3 | mobile phones, low-power embedded systems |
6 | specialized efficiency hardware, advanced mobile processors |
9 | theoretical thermodynamic limits of conventional computing |
12 | quantum computing theoretical efficiency, reversible computing |
17 | Landauer limit (theoretical maximum computing efficiency) |
Operations per dollar
-3 | mechanical calculators, earliest electronic computers |
0 | 1980s personal computers, vintage game systems |
3 | low-end smartphone, basic cloud computing instance |
6 | high-performance computing, GPU cloud instances |
9 | major cloud provider data centers, enterprise computing |
12 | global computing infrastructure efficiency projection |
15 | theoretical future of computing price-performance |