The Complete
Computation Suite
Every result computed live. Every method shown step by step. Every printed table replaced by an algorithm. From arithmetic to orbital mechanics — fully symbolic and numeric.
How the Toolkit works
Interactive engineering-mathematics calculators — every result computed live, every method shown step by step, every printed table replaced by an algorithm. Each module runs a self-test suite on load and cross-checks its answers by an independent method — Sarrus against cofactors, central differences against symbolic derivatives, fixed-grid Simpson against adaptive, three solvers against each other. Free accounts get every answer instantly. Pro accounts unlock the full step-by-step derivation panel for every calculation.
Flagship Modules — Phase 1
Geometry Suite
Ten shapes — areas, perimeters, volumes, surface areas — solvable forward or inverse, with live labeled diagrams.
M12 · AlgebraEquation Solver
Linear, quadratic with discriminant analysis and parabola plot, cubic with complex roots, and 2×2 systems by Cramer.
M14 · AlgebraComplex Number Studio
Full arithmetic, polar and exponential form, DeMoivre powers, and all n-th roots drawn on the Argand plane.
M15 · Linear AlgebraMatrix Laboratory
Operations to 5×5, determinants with expansion steps, Gauss–Jordan inverses with every row operation, systems solved three ways.
M16–17 · TrigonometryTriangle Solvers
Right triangles from any two knowns; general triangles by SSS, SAS, ASA, AAS, and the ambiguous SSA — drawn to scale.
M25 · CalculusDerivative Engine Pro Steps
Symbolic differentiation of any expression, to fourth order, with point evaluation and the tangent line on the graph.
M27 · CalculusDefinite Integral Pro Steps
Adaptive numeric integration with a convergence table and the signed area shaded under the curve.
M35 · StatisticsDescriptive Statistics Pro Steps
Paste raw data: the complete summary, sample vs population measures, covariance, histogram, and box plot.
M42 · StatisticsStatistical Tables
z, t, χ², and F computed in both directions for any df and any probability — with shaded-tail density curves.
M46 · EconomicsNPV & Cash-Flow Pro Steps
Project evaluation, IRR solver, payback period, profitability index — with cash-flow timeline visualization.
Core Modules — Phase 2
Symbol Explorer
Every symbol and Greek letter, searchable, with pronunciation, engineering usage, and live editable examples.
M03 · FoundationsPrime Toolkit
Primality with the witness shown, factor trees drawn live, the sieve to 20 000, and the n-th prime.
M04 · FoundationsPhysical Constants
Searchable CODATA/SI constants with precision control, exactness status, imperial equivalents, and one-click copy.
M05 · FoundationsUnit Converter
Nine categories through SI base routing, the factor and chain shown, plus a full table for every value.
M07 · AlgebraNumber Classifier
Any number or expression placed in ℕ ⊂ ℤ ⊂ ℚ ⊂ ℝ ⊂ ℂ with nested-set diagram and number line.
M08–09 · AlgebraPowers, Radicals & Logs
Exponent laws applied live, radicals reduced with extraction steps, any-base logs expanded and condensed.
M11 · AlgebraExpansion & Factoring Pro Steps
Binomial theorem to n = 12 with Pascal's triangle drawn, special products, and the aⁿ ± bⁿ factorizations verified.
M18–20 · TrigonometryTrigonometry Studio Pro Steps
Unit-circle evaluator with exact values flagged, fifteen identities verified live, inverse functions and general solutions.
M21 · GeometryAnalytic Geometry
Lines from two points in every form, parallel/perpendicular tests, circles from three points, line–circle intersection.
M23–24 · CalculusFunction & Limit Explorer Pro Steps
Grapher with composition, three-condition continuity check, and both-sided limit approach tables.
M28 + M34 · CalculusPartial Fractions & Laplace
Heaviside cover-up decomposition with verification, and the transform table parameterized in both directions.
M29 · CalculusSequence & Series Suite Pro Steps
Arithmetic and geometric terms and sums, convergence with the |r| < 1 test, and the power-sum formulas.
M37–38 · StatisticsCombinatorics & Probability Pro Steps
nPr and nCr with the factorial substitution, and two-event probability rules on a live-shaded Venn diagram.
M43 · EconomicsPercentage & Rate Toolkit
Percentage operations, nominal ↔ effective conversion across compounding bases, and payment-count solving.
Supporting Modules — Phase 3
Number Utilities
Roman numerals decomposed, exact big-integer factorials with Stirling error, and interval ↔ inequality ↔ number-line conversion.
M22 · VectorsVector Workbench
2D/3D dot and cross products, angle between, projections — parallelogram rule and isometric views drawn live.
M26 · CalculusIntegral Table Explorer
The classic antiderivative catalogue, parameterized to your constants — every row numerically self-verified.
M30 · SeriesConvergence Test Advisor Pro Steps
Guided test selection — nth-term, p-series, geometric, ratio, alternating — with the full logic and numeric evidence.
M31 · SeriesTaylor & Fourier Studio Pro Steps
Animated partial sums converging to true functions; square, sawtooth and triangle waves with the Gibbs overshoot measured.
M32 · M33Multiple Integrals & ODEs Pro Steps
Double and triple integrals over boxes; integrating-factor solutions, RK4 solution families, characteristic-equation cases.
M36 · StatisticsCLT Simulator
Any population shape → watch the sampling distribution of the mean become a bell, matched against σ/√n theory.
M39 · StatisticsDistribution Calculators
Binomial and Poisson PMF/CDF with expectation and variance, the queried region highlighted on the bars.
M40 · StatisticsInference Suite Pro Steps
Confidence intervals, required sample size, and hypothesis tests with the rejection region shaded on the curve.
M41 · StatisticsRegression & Correlation Lab Pro Steps
Least-squares fit with the full derivation, Pearson r and r², scatter with the line, prediction with extrapolation warnings.
M44 · M45Time Value of Money Pro Steps
FV and PV suites — annuities ordinary and due, loan payments, continuous compounding, growing annuities — with cash-flow timelines.
Applied Engineering Suite
Statics, fluids, circuits, structures, soil, heat, machines, digital logic, aerospace, and manufacturing — each one cross-checking against first principles.
Engineering Pillar — Flagships (Phase E1)
Statics & Mechanics Workbench
Forces, moments, two-force equilibrium with FBD, the full kinematics suite, projectile trajectories, torque.
E06 · FluidsFluid Mechanics Lab
Pressure and gauge/absolute, gas laws solved for any variable, continuity through a drawn contraction, fluid power.
E07 · ElectricityCircuit Solver
Ohm's wheel from any two knowns, series/parallel networks drawn live, Kirchhoff current and voltage balances.
E09 · StructuresSection Properties Studio
Composite-section builder: stack shapes and holes, get the centroid and parallel-axis Ixx, drawn to scale.
E11 · StructuresBeam & Truss Analyzer
Four simply-supported cases with reactions, M_max, and deflection — closed form cross-checked by numerical double integration.
E14 · CivilCivil & Water Systems
Rational-method runoff with composite C, Hazen-Williams losses with fitting equivalent lengths, traffic flow.
E15 · DigitalDigital Electronics Bench
555 astable timing, a Boolean truth-table prover, resistor color bands rendered live, capacitor codes.
E18 · GeotechUSCS Soil Classifier
The classification flowchart as a guided algorithm — group symbol plus the full reasoning path and plasticity chart.
Engineering Pillar — Core (Phase E2)
Engineering Statistics & Probability
Descriptive statistics on measured data, binomial trials, event rules, and conditional probability with the Bayes tree drawn.
E02 · GeometryGeometry for Engineers
Plane figures through regular polygons and ellipses, plus the solids — area, perimeter, volume, surface, sketched.
E03 · UnitsUnits, Prefixes & Conversions
SI ↔ US customary across eleven quantities, affine temperature, the prefix ladder, and defined units unpacked to base SI.
E05 · EnergyEnergy, Work & Power Suite
Work with the force angle, rotational power from rpm, efficiency, and the three energies compared on one chart.
E08 · ThermalHeat Transfer & Thermo Station
Conduction with a conductivity dataset, R-value wall stacks drawn layer by layer, whole-wall heat loads, net radiation.
E10 · MaterialsStress–Strain Lab
Stress, strain, modulus and elongation with the operating point plotted on the elastic line and the factor of safety judged.
E12 · MachinesSimple Machines Toolkit
IMA, AMA and efficiency across levers, planes, wedges, screws, pulleys, and compound gear trains.
E13 · DesignDesign Codes: Steel & Footing
ASD shear and moment checks with utilization gauges, spread-footing sizing, and worst-case vs RSS tolerance stacks.
Engineering Pillar — Supporting (Phase E3)
Manufacturing Station
Spindle speed and feed rates, a searchable G- and M-code reference, and the robot end-effector roll angle.
E17 · AerospaceAerospace & Environment Lab
Lift, drag and Reynolds, Bernoulli between stations, the standard atmosphere plotted, propulsion, orbits, and sustainability formulas.
Engineering Pillar — Geometric Property Libraries (E19–E20)
Area & Line Elements Library
Every area and arc element with centroid and moments about edge and centroidal axes, under any orientation — each value verified by numeric integration on the spot.
E20 · ReferenceSolid Mass Properties Library
CG and mass moments for the homogeneous solids: choose the symmetry axis, get the full inertia set through the centroid plus base, end, apex and rim axes.