96 live, computable functions in one portable, fully offline file. The complete AlchemyCalc G2 base (CGB depositions, attributed open-science corpus, instruction editor, AutoPhi math accelerator, Fractal Lab, database loader) plus a 46-instruction Energy pack: Electrical (11) · Generation & Storage (11) · Thermal (9) · Fuel & Motion (10) · Nuclear & Orbital (5).
What the Energy pack computes
series/parallel and divider circuits, RC/LC transients and resonance, transformers, three-phase power, wire drop, power-factor correction, hydro and pumped storage, flywheels, solar-array and battery-bank sizing, Peukert runtime, generator EMF, heat-pump COP, sensible/latent heat, Fourier conduction, Stefan–Boltzmann radiation, degree-days, vehicle road-load, EV range, the Tsiolkovsky rocket equation, escape velocity, Kepler orbits, mass defect and fission energy.
96
live functions — every one attributed
46
Energy instructions in the themed pack
12.2 M/s
log-gamma evaluations — accelerator, measured
10±308
numerical range, honestly displayed
Learn it right — a suggestion. These are professional-grade instructions, and most people need instructional help the first time through. Our suggestion: pair this edition with an AI tutor, such as Claude by Anthropic (claude.ai) — paste an instruction's 📜 origin line, its formula, and your numbers, and ask Claude to walk you through what it means, the units, and how to read the result before you rely on it. The calculator computes; a tutor explains.
Provenance — who and what
Formulas and laws of nature are unpatentable — no one owns them. Every calculation names its origin, in-app and in the shipped ledgers (PROVENANCE.md + PROVENANCE-ENERGY.md). The ten CGB Mathematical Depositions are © Christopher Gabriel Brown; every borrowed formula credits its originator and year.
In the box
- The AlchemyCalc Energy app — one file (186 KB), no install, no internet, phone-ready
- The Proof button — the calculator verifies itself against known values, live on your device
- The Professor button — composes a full lesson prompt for an AI tutor such as Claude (claude.ai)
- Plain-English guide (laymen notes), quick-start, license & IP notice
- Both provenance ledgers and a fictional demo dataset
Engineering estimates — verify against electrical codes, standards, and manufacturer data before any real installation.
Christopher Gabriel Brown — Inventor · Author · Visionary
christopher@cri-one.com · crioneaka@outlook.com · 1341 Wellington Cove, Lawrenceville, GA 30043-5255, USA
© 2010–2026 Christopher Gabriel Brown, CRI-ONE. All rights reserved. Patents issued and pending.
Complete instruction list — all 96 functions
Every instruction in this edition, with its formula and its origin. Mathematical formulas and laws of nature are unpatentable; each borrowed formula credits its originator and year, and the ten CGB Mathematical Depositions are © Christopher Gabriel Brown.
CGB depositions (10)
| Instruction | Formula | Origin — who and what |
|---|---|---|
| 1 · Dimensional Fold | V(n-sphere) = π^(n/2) / Γ(n/2+1) · rⁿ ⟹ peaks at n* = 5, → 0 as n → ∞ | CGB Deposition 1 © Christopher Gabriel Brown — builds on the classical n-sphere volume via Leonhard Euler's Gamma function (18th c.) |
| 2 · Entropic Bridge | S = −k_B Σ pᵢ ln pᵢ ≥ ∮dQ/T (Shannon = Clausius = Helmholtz) | CGB Deposition 2 © Christopher Gabriel Brown — builds on Claude Shannon (1948), Ludwig Boltzmann & Rudolf Clausius (19th c.), Rolf Landauer (1961) |
| 3 · Golden Spiral Convergence | lim F(n+1)/F(n) = φ = (1+√5)/2 ⟹ r_opt = φ⁻² ≈ 0.382 wire/gate area | CGB Deposition 3 © Christopher Gabriel Brown — builds on Leonardo of Pisa “Fibonacci” (1202) and Euclid's extreme-and-mean ratio (~300 BC) |
| 4 · Harmonic Decay | Σ 1/n² = π²/6 ⊗ ∫₀^∞ e^(−λt)cos(ωt)dt = λ/(λ²+ω²) | CGB Deposition 4 © Christopher Gabriel Brown — builds on Leonhard Euler's Basel solution (1734) and Pierre-Simon Laplace's transform (c. 1785) |
| 5 · Photon Chromosome Encoding | C = ⌊log₂(Δλ/δλ)⌋ + ⌊log₂(2π/δθ)⌋ + ⌊log₂(I_max/I_min)⌋ bits/photon | CGB Deposition 5 © Christopher Gabriel Brown — builds on Claude Shannon's information theory (1948) and Max Planck's quantum (1900) |
| 6 · Quantum Counting Paradox | 2ⁿ states ≠ 2ⁿ computations ⟹ P = sin²((2k+1)θ), k* = ⌊(π/4)√N⌋ | CGB Deposition 6 © Christopher Gabriel Brown — builds on Lov Grover's quantum search algorithm (1996) |
| 7 · Recursive Growth Bound | T(n) = a·T(n/b) + n^c ⟹ compare c against log_b(a) | CGB Deposition 7 © Christopher Gabriel Brown — builds on the Master Theorem of Jon Bentley, Dorothea Haken & James B. Saxe (1980) |
| 8 · Thermal Noise Floor | E_bit ≥ k_B·T·ln2 ⟹ FLOPS_max = P_budget / (k_B·T·ln2) | CGB Deposition 8 © Christopher Gabriel Brown — builds on Rolf Landauer's limit (1961) |
| 9 · Voxel Resonance | Ψ(v) = Π[αₖ sin(2πfₖ/Nₖ) + βₖ e^(−γₖd²)] · det(M_seed) | CGB Deposition 9 © Christopher Gabriel Brown — original composite formulation |
| 10 · Zero-Point Fabrication | Σ ½ħω → ∞ ⟹ ζ(−1) = −1/12 ⟹ E_reg = −ħcπ²/(720d³) | CGB Deposition 10 © Christopher Gabriel Brown — builds on Hendrik Casimir (1948) and Euler–Riemann zeta regularization ζ(−1) = −1/12 |
Mathematics (8)
| Instruction | Formula | Origin — who and what |
|---|---|---|
| Quadratic roots | ax² + bx + c = 0 ⟹ x = (−b ± √(b²−4ac)) / 2a | Classical mathematics — Babylonian tablets (~1800 BC); general solution tradition of al-Khwarizmi (c. 820). Unpatentable, public domain |
| Combinations & permutations | C(n,k) = n! / k!(n−k)! · P(n,k) = n!/(n−k)! (log-gamma — no overflow) | Classical combinatorics — Pingala (~200 BC), Blaise Pascal (1654); computed via Cornelius Lanczos's log-gamma approximation (1964). Public domain |
| Bayes' theorem | P(A|B) = P(B|A)·P(A) / [P(B|A)·P(A) + P(B|¬A)·P(¬A)] | Rev. Thomas Bayes (published 1763), generalized by Pierre-Simon Laplace (1774). Public domain |
| Normal distribution | φ(x) = e^(−(x−μ)²/2σ²) / σ√2π · Φ(x) via erf | Abraham de Moivre (1733), Carl Friedrich Gauss (1809); erf approximation from Abramowitz & Stegun's Handbook 7.1.26 (Hastings, 1964, US-Gov public domain) |
| Logistic growth | P(t) = K / (1 + ((K−P₀)/P₀)·e^(−rt)) | Pierre François Verhulst (1838). Public domain |
| Compound & continuous growth | A = P(1 + r/n)^(nt) · A = P·e^(rt) | Classical finance mathematics; continuous compounding via Jacob Bernoulli (1683) and Euler's e. Public domain |
| Shannon channel capacity | C = B · log₂(1 + S/N) | Claude Shannon (1948), with Ralph Hartley (1928) — the Shannon–Hartley theorem. Public domain |
| Prime counting estimate | π(n) ≈ n/ln n · sharper: n/(ln n − 1) | Carl Friedrich Gauss & Adrien-Marie Legendre (1790s); Prime Number Theorem proved by Hadamard & de la Vallée Poussin (1896). Public domain |
Physics & Energy (12)
| Instruction | Formula | Origin — who and what |
|---|---|---|
| Mass–energy E = mc² | E = m·c² | Albert Einstein (1905). A law of nature — unpatentable, public domain |
| Kinetic energy & momentum | KE = ½mv² · p = mv | Classical mechanics — Isaac Newton (1687), Gottfried Leibniz's vis viva; modern ½mv² formalized 19th c. Public domain |
| Ohm's law solver | V = I·R · P = V·I (leave exactly one of V/I/R blank) | Georg Simon Ohm (1827); electrical power after James Prescott Joule. Public domain |
| Coulomb's law | F = k·q₁·q₂ / r² | Charles-Augustin de Coulomb (1785). Public domain |
| Ideal gas PV = nRT | P·V = n·R·T (leave exactly one blank) | Émile Clapeyron (1834), combining Robert Boyle (1662), Jacques Charles, Joseph Gay-Lussac and Amedeo Avogadro. Public domain |
| Carnot efficiency | η = 1 − T_cold / T_hot | Sadi Carnot (1824). Public domain |
| Battery C-rate & runtime | E = Ah·V · I = C·Ah · runtime = 1/C | Standard electrical-engineering C-rate convention (20th c. industry practice). No single originator; unpatentable arithmetic |
| Solar PV yield | E = A · η · H_sun · PR | Standard photovoltaic yield estimation (industry practice, late 20th c.). Unpatentable arithmetic |
| Wind turbine power | P = ½·ρ·A·v³·Cp (Betz limit Cp ≤ 16/27 ≈ 0.593) | Kinetic flux ½ρAv³ (classical); Betz limit — Albert Betz (1919), independently Frederick Lanchester (1915). Public domain |
| Radioactive decay | N(t) = N₀·e^(−λt), λ = ln2 / t½ | Ernest Rutherford & Frederick Soddy (1902). A law of nature — public domain |
| Photon energy E = hc/λ | E = h·c / λ | Max Planck (1900) and Albert Einstein (1905). Public domain |
| Faraday electrolysis | m = Q·M / (z·F), Q = I·t | Michael Faraday's laws of electrolysis (1834). Public domain |
Chemistry & Carbon (10)
| Instruction | Formula | Origin — who and what |
|---|---|---|
| Dilution C₁V₁ = C₂V₂ | C₁·V₁ = C₂·V₂ (leave exactly one blank) | Standard laboratory chemistry (C₁V₁ = C₂V₂ conservation). No single originator; unpatentable arithmetic |
| pH / pOH | pH = −log₁₀[H⁺] · pH + pOH = 14 | Søren Peder Lauritz Sørensen (1909). Public domain |
| Henderson–Hasselbalch | pH = pKa + log₁₀([A⁻]/[HA]) | Lawrence Joseph Henderson (1908) and Karl Albert Hasselbalch (1917). Public domain |
| Arrhenius rate | k = A·e^(−Ea/RT) | Svante Arrhenius (1889). Public domain |
| Gibbs free energy | ΔG = ΔH − T·ΔS · K = e^(−ΔG/RT) | Josiah Willard Gibbs (1873–1878); equilibrium link after Jacobus van 't Hoff. Public domain |
| Nernst equation | E = E° − (RT/zF)·ln Q | Walther Nernst (1889). Public domain |
| Beer–Lambert | A = ε·l·c | Pierre Bouguer (1729), Johann Heinrich Lambert (1760), August Beer (1852). Public domain |
| Hydrocarbon combustion — CO₂ ledger | CₓHᵧ + (x+y/4)O₂ → xCO₂ + (y/2)H₂O | Stoichiometry on Antoine Lavoisier's conservation of mass (1770s–80s). Public domain |
| Carbon-14 dating | t = (t½/ln2)·ln(N₀/N), t½ = 5,730 yr | Willard Libby (1946–49, Nobel 1960); 5,730-yr “Cambridge half-life” (1962). Public domain |
| Percent yield & atom economy | yield% = actual/theoretical · 100 · AE% = M(product)/ΣM(reactants) · 100 | Standard chemistry; atom economy after Barry Trost (1991, concept — the arithmetic is unpatentable). Public domain |
Medicine (10)
| Instruction | Formula | Origin — who and what |
|---|---|---|
| Body mass index | BMI = kg / m² | Adolphe Quetelet (1832); the name “body mass index” after Ancel Keys (1972); WHO bands. Public domain |
| Body surface area (Mosteller) | BSA = √(cm·kg / 3600) | R. D. Mosteller (1987, NEJM). A published clinical formula — unpatentable |
| Creatinine clearance (Cockcroft–Gault) | CrCl = (140−age)·kg·(0.85 if female) / (72·SCr) | Donald Cockcroft & Matthew Gault (1976, Nephron). Public domain |
| Half-life & steady state | t½ = 0.693/k · steady state ≈ 5·t½ | Standard pharmacokinetics, foundational work of Torsten Teorell (1937). Public domain |
| Loading dose | LD = C_target · Vd · kg / F | Standard clinical pharmacokinetics (Rowland & Tozer convention). Unpatentable arithmetic |
| Maintenance dosing | rate = Cl · C_ss / F | Standard clinical pharmacokinetics (Rowland & Tozer convention). Unpatentable arithmetic |
| Clearance ↔ Vd ↔ t½ | Cl = k·Vd · t½ = 0.693·Vd/Cl | Standard pharmacokinetics — clearance/volume/half-life identities. Public domain |
| Mass dose → molar dose | n = dose / M(formula) — molar mass from the built-in engine | Standard chemistry applied to dosing; molar masses from IUPAC values. Unpatentable arithmetic |
| IV drip rate | gtt/min = volume·dropFactor / minutes | Standard clinical/nursing formula. No single originator; unpatentable arithmetic |
| Cardiac output (Fick) | CO = VO₂ / [(CaO₂ − CvO₂) · 10] | Adolf Eugen Fick's principle (1870). Public domain |
Electrical (11)
| Instruction | Formula | Origin — who and what |
|---|---|---|
| Resistors in series & parallel | R_series = ΣR · 1/R_parallel = Σ(1/R) | Circuit laws of Gustav Kirchhoff (1845) on Georg Ohm's law (1827). Public domain |
| Voltage divider | V_out = V_in · R₂/(R₁+R₂) | Standard circuit analysis (Ohm/Kirchhoff lineage). Public domain |
| Capacitor energy & charge | E = ½CV² · Q = CV | Classical electrostatics (Leyden-jar lineage, 18th c.; field energy after Maxwell). Public domain |
| Inductor energy | E = ½LI² | Classical electromagnetism (Faraday/Maxwell lineage, 19th c.). Public domain |
| RC charging curve | V(t) = V₀·(1 − e^(−t/RC)) | Standard first-order transient analysis (19th-c. telegraphy lineage). Public domain |
| LC resonant frequency | f = 1 / (2π·√(LC)) | William Thomson, Lord Kelvin (1853). Public domain |
| Transformer ratios | V_s/V_p = N_s/N_p · I_s/I_p = N_p/N_s | Michael Faraday's induction (1831); practical transformer 1880s. Public domain |
| Three-phase power | P = √3·V_L·I_L·pf | Standard AC power engineering (three-phase after Dolivo-Dobrovolsky & Tesla era, 1880s–90s). Public domain |
| Wire resistance & voltage drop | R = ρL/A · round-trip drop = 2·I·R | Pouillet's law form of Ohm's law (Claude Pouillet, 1837). Public domain |
| Power-factor correction | Q_c = P·(tanφ₁ − tanφ₂) | Standard AC power engineering. Unpatentable arithmetic |
| Ohmic (I²R) heating | P = I²R | Joule's first law — James Prescott Joule (1841). Public domain |
E_GS (11)
| Instruction | Formula | Origin — who and what |
|---|---|---|
| Hydroelectric power | P = ρ·g·Q·H·η | Classical hydraulics (Bernoulli lineage, 18th c.). Public domain |
| Pumped-storage energy | E = ρ·V·g·h·η | Classical mechanics — gravitational potential energy. Public domain |
| Flywheel energy | E = ½·I·ω² | Classical rotational mechanics (Euler lineage). Public domain |
| Capacity factor | CF = actual MWh / (rated MW × 8760) | Standard utility-industry metric. Unpatentable arithmetic |
| Solar array sizing | array kW = daily kWh / (sun-hours × PR) | Standard photovoltaic sizing practice. Unpatentable arithmetic |
| Battery bank sizing | Ah = kWh/day × autonomy days × 1000 / (V × DoD × η) | Standard off-grid sizing practice. Unpatentable arithmetic |
| Peukert battery runtime | t = H·(C/(I·H))^k | Wilhelm Peukert (1897). Public domain |
| Battery pack mass from density | mass = kWh × 1000 / (Wh/kg) | Arithmetic on published energy densities. Unpatentable |
| Generator EMF (Faraday) | EMF_peak = N·B·A·ω | Michael Faraday's law of induction (1831). Public domain |
| Heat-pump COP (Carnot bound) | COP_heat ≤ T_h/(T_h−T_c) · COP_cool ≤ T_c/(T_h−T_c) | Carnot bound — Sadi Carnot (1824). Public domain |
| Fuel mass → electricity | kWh = kg × MJ/kg / 3.6 × η | Standard calorimetry and plant-efficiency arithmetic. Public domain |
E_TH (9)
| Instruction | Formula | Origin — who and what |
|---|---|---|
| Sensible heat Q = mcΔT | Q = m·c·ΔT | Joseph Black's specific heat (18th c.). Public domain |
| Latent heat Q = mL | Q = m·L (water: fusion 334, vaporization 2257 kJ/kg) | Joseph Black's latent heat (1761). Public domain |
| Heat conduction (Fourier) | Q̇ = k·A·ΔT / d | Jean-Baptiste Joseph Fourier (1822). Public domain |
| Radiation (Stefan–Boltzmann) | P = ε·σ·A·T⁴ | Josef Stefan (1879) and Ludwig Boltzmann (1884). Public domain |
| Newton's cooling | T(t) = T_a + (T₀−T_a)·e^(−kt) | Isaac Newton (1701). Public domain |
| Building U-value loss | Q̇ = U·A·ΔT · R = 1/U | Standard building physics (Fourier lineage). Public domain |
| Heating degree-day energy | E = UA·HDD·24 / 1000 | Standard HVAC degree-day method (20th c. practice). Unpatentable arithmetic |
| Thermal expansion | ΔL = α·L·ΔT | Classical thermophysics. Public domain |
| Water-heating time | t = m·c·ΔT / P | Q = mcΔT applied (Joseph Black lineage). Public domain |
E_FM (10)
| Instruction | Formula | Origin — who and what |
|---|---|---|
| Vehicle road-load power | P = C_rr·m·g·v + ½·ρ·C_dA·v³ | Standard vehicle dynamics (rolling + aerodynamic drag, Rayleigh drag lineage). Public domain |
| EV range & charge time | range = kWh×1000 / (Wh/km) | Standard EV engineering arithmetic. Unpatentable |
| Fuel economy conversion & cost | L/100km = 235.215 / mpg(US) | Unit conversion + arithmetic. Unpatentable |
| Stop-and-go energy & regen | E = ½mv² per stop · recovered = E×regen | Classical kinetic energy (Leibniz/Coriolis lineage). Public domain |
| Rocket equation (Tsiolkovsky) | Δv = v_e·ln(m₀/m_f) | Konstantin Tsiolkovsky (1903). Public domain |
| Escape velocity | v_e = √(2GM/r) | Newtonian gravitation (Isaac Newton, 1687). Public domain |
| Orbital period (Kepler) | T = 2π·√(a³/GM) | Johannes Kepler's third law (1619), form via Newton. Public domain |
| Power ↔ torque ↔ rpm | P = τ·ω, ω = rpm·2π/60 | Classical mechanics; horsepower after James Watt (1780s). Public domain |
| Gravity storage E = mgh | E = m·g·h | Classical mechanics — potential energy. Public domain |
| Appliance running cost | cost = W × h/day × 365 × rate / 1000 | Billing arithmetic. Unpatentable |
E_NO (5)
| Instruction | Formula | Origin — who and what |
|---|---|---|
| Binding energy from mass defect | E = Δm·c² · 1 u = 931.494 MeV | Albert Einstein (1905); mass-spectrograph defect work of Francis Aston (1919). Public domain |
| Fission energy per kilogram | E = N_atoms × ~200 MeV | Fission discovered by Hahn & Strassmann, explained by Meitner & Frisch (1938); ~200 MeV/fission standard nuclear engineering. Public domain |
| Radioactivity from mass | A = λN, λ = ln2/t½ | Rutherford & Soddy decay law (1902). Public domain |
| Inverse-square intensity | I = I₀·(r₀/r)² | Classical geometry of radiation (Kepler/Newton lineage). Public domain |
| Photon flux from power | n = P·λ / (h·c) | Max Planck (1900) and Albert Einstein (1905). Public domain |
Image SHA-256 — emb_CRIONE-ALCHEMY-V3-NRG-101_1.png
9ecbf9b2e811b09c65a911928c827da3c1e123d2684ca01b816a261ca89ca554AlchemyCalc Energy V3
$12K
In stock
SKU
CRIONE-ALCHEMY-V3-NRG-101
Leave blank to use the product price.
Themed edition on the AlchemyCalc G2 core: 96 live functions — the G2 base plus a 46-instruction power, storage & thermodynamics pack. Proof & Professor buttons, instruction editor, math accelerator, Fractal Lab. Engineering estimates — verify against codes. Plain-English guide included.
First to market
Publicly online since 2010 · U.S. patent applications since 2012 · inventions offered since 2014. The work of Christopher Gabriel Brown, independently documented.
First posted:
Related Products
Check items to add to the cart or
