Browse formulae organized by mathematical discipline.
Everyday number sense: fractions, percentages, ratios and averages
Equations, polynomials, identities and algebraic laws
Areas, volumes, angles and trigonometric identities
Trigonometric ratios, identities, laws and angle formulae
Derivatives, integrals, limits and series
Averages, spread, distributions and probability
Counting, permutations, combinations, and core probability laws.
Machine learning metrics, loss functions, and statistical learning formulae.
Vectors, matrices, determinants and transformations
Mechanics, energy, waves, electricity and light
Named laws, principles and theorems that govern the physical universe
Heat, temperature, gas laws and the laws of thermodynamics
Light, lenses, mirrors, sound and wave behaviour
Electric fields, magnetic forces and electromagnetic induction
Pressure, buoyancy, flow and the behaviour of fluids
Relativity, quantum mechanics and nuclear physics
Circuit analysis, components, signals and digital logic formulae
Reactions, solutions, gases and thermodynamics
Genetics, ecology, physiology and cellular biology formulae
Body metrics, nutrition, exercise and wellness formulae
Calories, macros, diet, cooking ratios and culinary maths
Orbits, gravity, stars and cosmology
Stress, fluids, circuits and structures
Structural, construction, and materials-engineering formulae.
Aerodynamics, flight performance, navigation and atmospheric formulas used in aviation
Interest, loans, investments and valuation
Core accounting identities, financial-statement measures and ratios used to read a company’s books
Pricing, sales, inventory and growth metrics used to run and scale a commercial business
Macro and micro relationships: national output, inflation, elasticity and the theory of money
Exchange-rate conversion, cross rates, spreads, pips and purchasing-power measures used in foreign exchange
Practical formulae for daily life: shopping, cooking, travel, and home projects.
Calendar rules, weekday and date algorithms, clock and astronomical timekeeping.
Distances, maps, coordinates and the planet
Sustainability, energy, ecology, and earth-science formulae.
Convert temperature, length, area, volume, mass and more
Primes, divisibility, modular arithmetic
Algorithms, information theory and discrete math
Core algorithms behind machine learning and AI — models, activation functions, loss functions, optimizers, deep learning and reinforcement learning.
Meteorology, climate change and natural hazards — humidity, storms, global warming, floods, tsunamis and seismic activity.
Media, advertising and data-infrastructure metrics — TV ratings, ad performance, data-centre efficiency and IT capacity.
Radio navigation, radar, communications, antennas, GPS and signal-processing formulae behind aircraft electronic systems
Sales, pricing and recurring-revenue metrics used in business and SaaS
The physics of sound: note frequencies, decibels, harmonics, tempo and the Doppler pitch shift
The maths behind the game: projectile range, pace, xG, VO₂ max, Elo and player ratings
Keeping secrets safe: modular arithmetic, RSA, entropy, hashing and error-correcting codes
Light and lenses: exposure, f-stops, depth of field, hyperfocal distance and image resolution
What makes cars go: horsepower, torque, compression, gearing, fuel economy and braking
Ships and the sea: hull speed, buoyancy, draft, knots and great-circle navigation
Turning signals into data: sampling, Nyquist, FFT bins, SNR, filters and quantisation
Clean power maths: solar yield, wind turbines, capacity factor, batteries and LCOE
Pricing risk: premiums, loss ratios, annuities, life expectancy and expected claims
Making machines move: PID control, kinematics, torque, gear reduction and encoders
Farming by numbers: crop yield, seed rate, irrigation, fertiliser, livestock and stocking
The maths of choices: expected value, utility, the Kelly criterion, minimax and Bayes
Property maths: mortgage payments, LTV, cap rate, rental yield, ROI and price per area
Kitchen maths: baker's percentages, hydration, recipe scaling, food cost and dough temperature
Heating, cooling and air: sensible/latent loads, COP, EER, airflow, humidity and refrigeration tons
Inventory and delivery maths: EOQ, reorder points, safety stock, turnover and Little's Law
Oilfield maths: hydrostatic pressure, mud weight, API gravity, buoyancy, ECD and production decline
Measuring the land: slope and grade, coordinate areas, stadia, traverse latitudes and map scale
Signals and data links: Shannon capacity, path loss, throughput, latency, subnets and Erlang traffic
Advertising metrics, social-media analytics and customer-value formulas
Disease-spread models, outbreak metrics and population-health measures
Qubit states, quantum gates, algorithms and information measures for quantum processors
Drug dosing, pharmacokinetics, clearance and IV-drip calculations for clinical practice
Landmark laws of chemistry and physics — conservation, gas laws, electrolysis, diffusion, cooling and more