taylor.town about spam rss

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