Every calculator on this site rests on either a standard formula, a published physical constant, an engineering/regulatory standard, or a specific real-world data point used for calibration. This page lists the primary source for each, grouped by area. Individual tools also link back to the relevant row here from their own footer.
Referenced across multiple areas rather than tied to one tool.
| Constant / standard | Value used | Source |
|---|---|---|
| Standard gravity, g | 9.80665 m/s² | NIST CODATA — exact by international definition (CGPM, 1901) |
| Gravitational constant, G | 6.674 × 10⁻¹¹ N·m²/kg² | NIST CODATA |
| Universal gas constant, R | 8.314 J/(mol·K) | NIST CODATA |
| Standard atmosphere model | ICAO Standard Atmosphere | ICAO Doc 7488 — the standard reference for pressure/temperature vs. altitude |
| SI unit conversion factors | exact, by definition | NIST SI units guide |
| Claim | Source | Tool |
|---|---|---|
| Psychrometric formulas (Magnus/Arden Buck approximation) | Buck, A.L. (1981), J. Applied Meteorology 20(12) — standard vapour-pressure approximation | Psychrometer |
| Wind chill formula | NWS/Environment Canada 2001 joint formula | Feels Like Temperature |
| Heat index formula | Rothfusz, L.P. (1990), NWS Technical Attachment SR 90-23 | Feels Like Temperature |
| Frostbite time / heat-risk bands | NWS wind chill chart; NWS heat index guidance | Feels Like Temperature |
| Solar position, sunrise/sunset algorithm | Meeus, J., Astronomical Algorithms (2nd ed.) — standard reference for solar/lunar position calculations | Sun & Moon |
| IANA time zone database | IANA tz database, via the browser's Intl API | Time Zone Converter |
| Residential electricity rates by country | Ember / Our World in Data electricity price series — representative national averages, edit to match your own bill | Energy Cost Calculator |
| Grid carbon intensity by country | Ember Yearly Electricity Data | Energy Cost Calculator |
| Typical appliance wattages | U.S. DOE Energy Saver appliance energy guide — starting points, fully editable | Energy Cost Calculator |
| Solar panel output model, standard test conditions | IEC 61215 (1000 W/m², 25°C cell temperature) | Solar PV Estimator |
| Everest / cruising altitude / Titanic / Challenger Deep reference points | National Geographic; NOAA Ocean Exploration (Challenger Deep depth, ~10,935 m) | Altitude & Depth |
| Claim | Source | Tool |
|---|---|---|
| Beam deflection formulas | Roark's Formulas for Stress and Strain; Euler-Bernoulli beam theory | Beam Bench |
| Darcy friction factor (Colebrook / Swamee-Jain) | Swamee, P.K. & Jain, A.K. (1976), J. Hydraulics Division ASCE — explicit approximation of the Colebrook equation | Pipe Flow |
| Bolt torque-tension relationship | Shigley's Mechanical Engineering Design, ch. on threaded fasteners; K-factor method | Bolt Torque |
| Otto/Diesel/Brayton/Carnot cycle efficiency | Cengel & Boles, Thermodynamics: An Engineering Approach — standard air-standard cycle analysis | PV Diagram |
| ISO 281 bearing life (L10) | ISO 281:2007 — rolling bearing dynamic load ratings and rating life | Bearing Calculator |
| O-ring groove dimensions | Parker O-Ring Handbook (ORD 5700); AS568 standard sizes | O-Ring Calculator |
| Circlip / retaining ring dimensions | DIN 471 (external), DIN 472 (internal) standard series | Circlip Calculator |
| ISO limits and fits tolerance grades | ISO 286-1/286-2 | Limits & Fits |
| Thermal expansion coefficients by material | ASM Engineered Materials Reference Book | Limits & Fits |
| Fluid density & viscosity vs. temperature | NIST Webbook (water); Cannon/CRC Handbook of Chemistry and Physics (other fluids) | Fluid Properties |
| Unit conversion factors (imperial/metric) | NIST Handbook 44, appendix C — exact conversion factors | Unit Converter |
| Resistor 4-band colour code | IEC 60062 — colour coding of resistance and capacitance values | Electrical Circuit |
| Wire gauge current-carrying capacity | General-purpose reference figures adapted from NEC (NFPA 70) ampacity tables — not a substitute for a proper electrical code lookup | Electrical Circuit |
| Spring rate & Wahl stress-correction formula | Shigley's Mechanical Engineering Design, ch. on mechanical springs; Wahl, A.M. (1944), Mechanical Springs | Spring Rate Calculator |
| Common spring wire material properties | SAE J1123/J1124; Associated Spring/Barnes Group design handbook | Spring Rate Calculator |
| Euler buckling & Johnson's parabolic formula | Timoshenko, S.P., Theory of Elastic Stability; Shigley's Mechanical Engineering Design, ch. on columns | Column Buckling Calculator |
| Structural material yield strengths | ASTM A36 (steel), ASTM B209 (aluminium) material standards | Column Buckling Calculator |
| Claim | Source | Tool |
|---|---|---|
| Compound interest formula | Standard time-value-of-money mathematics — any introductory finance textbook | Compound Interest |
| Mortgage amortisation formula | Standard fixed-rate amortisation mathematics; matches the method used by CFPB-regulated lenders | Mortgage |
| "4% rule" safe withdrawal rate | Bengen, W.P. (1994), Journal of Financial Planning — the original Trinity-study-adjacent safe withdrawal rate research | FIRE Calculator |
| UK National Living Wage / National Minimum Wage rates | GOV.UK, Low Pay Commission — current as of April 2026 | Salary Converter |
| US federal minimum wage | U.S. Department of Labor — $7.25/hr, unchanged since 2009 | Salary Converter |
| US federal/FICA and UK income tax/NI bands | IRS; GOV.UK income tax rates — simplified, single-filer approximation, not personalised tax advice | Salary Converter |
| Claim | Source | Tool |
|---|---|---|
| PID control theory | Åström & Murray, Feedback Systems (Princeton, freely available) — standard modern reference | PID Control |
| Nyquist-Shannon sampling theorem | Shannon, C.E. (1949), Proc. IRE 37(1), "Communication in the Presence of Noise" | Sampling & Aliasing |
| Ball-and-beam double-integrator dynamics | Standard control-theory teaching example — see Åström & Murray, Feedback Systems, or any undergraduate controls course | Ball and Beam |
| Bode plot construction, gain/phase margin | Nyquist, H. (1932), Bell System Technical Journal; Bode, H.W. (1945), Network Analysis and Feedback Amplifier Design | Bode Plot |
| Claim | Source | Tool |
|---|---|---|
| RAID levels and fault-tolerance mathematics | Patterson, Gibson & Katz (1988), "A Case for Redundant Arrays of Inexpensive Disks (RAID)" — the original paper defining RAID | RAID Calculator |
| IPv4 subnetting (CIDR) | RFC 4632 — Classless Inter-Domain Routing | Subnet Calculator |
| Two's complement, IEEE-754-style bitwise semantics | Standard computer architecture reference — Patterson & Hennessy, Computer Organization and Design | Bit Calculator |
| Binary vs. decimal prefixes (KiB vs. kB) | IEC 60027-2 — the standard defining kibi-, mebi-, gibi- prefixes | Bit Calculator |
| Claim | Source | Tool |
|---|---|---|
| Damped harmonic oscillator equations | Standard 2nd-order ODE result — Halliday & Resnick, Fundamentals of Physics, ch. on oscillations | Mass-Spring-Damper |
| Multi-link pendulum equations of motion (RK4 integration) | Lagrangian mechanics, standard derivation — e.g. Taylor, J.R., Classical Mechanics | Pendulum Simulator |
| Coulomb friction model (static/kinetic) | Standard introductory mechanics result; friction coefficients from Marks' Standard Handbook for Mechanical Engineers | Inclined Plane |
| Newton's law of cooling; convective/radiative heat transfer | Incropera & DeWitt, Fundamentals of Heat and Mass Transfer | Beverage Cooling Simulator |
| Quadratic drag equation, drag coefficients | Hoerner, S.F., Fluid-Dynamic Drag — standard reference for drag coefficient by shape | Galileo Drop Experiment, Projectile Motion |
| Apollo 15 hammer-and-feather drop | NASA Apollo 15 mission transcript/video — Commander David Scott, 2 August 1971 | Galileo Drop Experiment |
| Golf ball flight — Magnus effect, launch conditions | TrackMan/Titleist Performance Institute published launch-condition data; USGA equipment rules for legal driver COR | Projectile Motion & Golf |
| PGA Tour average driving distance | PGA Tour official statistics | Projectile Motion & Golf |
| Kepler's laws, vis-viva equation | Kepler, J. (1609/1619), Astronomia Nova / Harmonices Mundi; modern treatment in Curtis, H.D., Orbital Mechanics for Engineering Students | Orbital Mechanics |
| ISS orbital altitude, period, velocity | NASA ISS Facts and Figures — ~400 km altitude, ~90–93 min period | Orbital Mechanics |
| Standard gravitational parameters (μ) by body | NASA JPL Solar System Dynamics | Orbital Mechanics, Rocket Equation |
| Tsiolkovsky rocket equation | Tsiolkovsky, K.E. (1903), "The Exploration of Cosmic Space by Means of Reaction Devices" | Rocket Equation & Delta-v Budget |
| Falcon 9 / Saturn V / Electron vehicle specifications | SpaceX, NASA (Saturn V Flight Manual SA-503), Rocket Lab public specifications — approximate figures assembled for illustration, not manufacturer data sheets | Rocket Equation & Delta-v Budget |
| Typical mission delta-v budgets (LEO, GTO, TLI, escape) | Curtis, H.D., Orbital Mechanics for Engineering Students — typical, trajectory-dependent published estimates | Rocket Equation & Delta-v Budget |
| Claim | Source | Tool |
|---|---|---|
| RYB subtractive colour mixing model | Gossett, N. & Chen, B. (2004), "Paint Inspired Color Mixing and Compositing for Visualization" — the RYB trilinear interpolation approach this tool is based on | Paint Colour Mixing |