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.
Roadmap Classifications: Every calculator below remains fully functional and usable today. The labels indicate our migration roadmap for the platform:
- Core Will remain standalone core tools.
- Rebuild planned Slated for major functional upgrades.
- Consolidate Will be merged into broader workbenches.
- Legacy Maintained for reference but no active development.
Mathematics
Symbol Explorer
Every symbol and Greek letter, searchable, with pronunciation, engineering usage, and live editable examples.
Prime Toolkit
Primality with the witness shown, factor trees drawn live, the sieve to 20 000, and the n-th prime.
Equation Solver
Linear, quadratic with discriminant analysis and parabola plot, cubic with complex roots, and 2×2 systems by Cramer.
Complex Number Studio
Full arithmetic, polar and exponential form, DeMoivre powers, and all n-th roots drawn on the Argand plane.
Expansion & Factoring Pro Steps
Binomial theorem to n = 12 with Pascal's triangle drawn, special products, and the aⁿ ± bⁿ factorizations verified.
Matrix Laboratory
Operations to 5×5, determinants with expansion steps, Gauss–Jordan inverses with every row operation, systems solved three ways.
Triangle Solvers
Right triangles from any two knowns; general triangles by SSS, SAS, ASA, AAS, and the ambiguous SSA — drawn to scale.
Trigonometry Studio Pro Steps
Unit-circle evaluator with exact values flagged, fifteen identities verified live, inverse functions and general solutions.
Analytic Geometry
Lines from two points in every form, parallel/perpendicular tests, circles from three points, line–circle intersection.
Function & Limit Explorer Pro Steps
Grapher with composition, three-condition continuity check, and both-sided limit approach tables.
Derivative Engine Pro Steps
Symbolic differentiation of any expression, to fourth order, with point evaluation and the tangent line on the graph.
Definite Integral Pro Steps
Adaptive numeric integration with a convergence table and the signed area shaded under the curve.
Integral Table Explorer
The classic antiderivative catalogue, parameterized to your constants — every row numerically self-verified.
Partial Fractions & Laplace
Heaviside cover-up decomposition with verification, and the transform table parameterized in both directions.
Multiple Integrals & ODEs Pro Steps
Double and triple integrals over boxes; integrating-factor solutions, RK4 solution families, characteristic-equation cases.
Sequence & Series Suite Pro Steps
Arithmetic and geometric terms and sums, convergence with the |r| < 1 test, and the power-sum formulas.
Convergence Test Advisor Pro Steps
Guided test selection — nth-term, p-series, geometric, ratio, alternating — with the full logic and numeric evidence.
Taylor & Fourier Studio Pro Steps
Animated partial sums converging to true functions; square, sawtooth and triangle waves with the Gibbs overshoot measured.
Descriptive Statistics Pro Steps
Paste raw data: the complete summary, sample vs population measures, covariance, histogram, and box plot.
Statistical Tables
z, t, χ², and F computed in both directions for any df and any probability — with shaded-tail density curves.
CLT Simulator
Any population shape → watch the sampling distribution of the mean become a bell, matched against σ/√n theory.
Distribution Calculators
Binomial and Poisson PMF/CDF with expectation and variance, the queried region highlighted on the bars.
Combinatorics & Probability Pro Steps
nPr and nCr with the factorial substitution, and two-event probability rules on a live-shaded Venn diagram.
Inference Suite Pro Steps
Confidence intervals, required sample size, and hypothesis tests with the rejection region shaded on the curve.
Regression & Correlation Lab Pro Steps
Least-squares fit with the full derivation, Pearson r and r², scatter with the line, prediction with extrapolation warnings.
Engineering Statistics & Probability
Descriptive statistics on measured data, binomial trials, event rules, and conditional probability with the Bayes tree drawn.
Engineering Data & Units
Physical Constants
Searchable CODATA/SI constants with precision control, exactness status, imperial equivalents, and one-click copy.
Unit Converter
Nine categories through SI base routing, the factor and chain shown, plus a full table for every value.
Units, Prefixes & Conversions
SI ↔ US customary across eleven quantities, affine temperature, the prefix ladder, and defined units unpacked to base SI.
Geometry & Sections
Geometry & Section Workbench
Our upcoming unified visual environment for geometric and section analysis. Start with the Geometry Suite for foundational shapes and volumes, and Section Properties for composite inertia and centroid calculations. Over time, related reference libraries will consolidate here.
Geometry Suite
Ten shapes — areas, perimeters, volumes, surface areas — solvable forward or inverse, with live labeled diagrams.
Section Properties Studio
Composite-section builder: stack shapes and holes, get the centroid and parallel-axis Ixx, drawn to scale.
Vector Workbench
2D/3D dot and cross products, angle between, projections — parallelogram rule and isometric views drawn live.
Geometry for Engineers
Plane figures through regular polygons and ellipses, plus the solids — area, perimeter, volume, surface, sketched.
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.
Solid 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.
Mechanics & Machine Design
Statics & Mechanics Workbench
Forces, moments, two-force equilibrium with FBD, the full kinematics suite, projectile trajectories, torque.
Beam & Truss Analyzer
Four simply-supported cases with reactions, M_max, and deflection — closed form cross-checked by numerical double integration.
Simple Machines Toolkit
IMA, AMA and efficiency across levers, planes, wedges, screws, pulleys, and compound gear trains.
Energy, Work & Power Suite
Work with the force angle, rotational power from rpm, efficiency, and the three energies compared on one chart.
Thermal & Fluids
Fluid Mechanics Lab
Pressure and gauge/absolute, gas laws solved for any variable, continuity through a drawn contraction, fluid power.
Heat Transfer & Thermo Station
Conduction with a conductivity dataset, R-value wall stacks drawn layer by layer, whole-wall heat loads, net radiation.
Materials & Manufacturing
Stress–Strain Lab
Stress, strain, modulus and elongation with the operating point plotted on the elastic line and the factor of safety judged.
Manufacturing Station
Spindle speed and feed rates, a searchable G- and M-code reference, and the robot end-effector roll angle.
Electrical & Controls
Circuit Solver
Ohm's wheel from any two knowns, series/parallel networks drawn live, Kirchhoff current and voltage balances.
Digital Electronics Bench
555 astable timing, a Boolean truth-table prover, resistor color bands rendered live, capacitor codes.
Engineering Economics
NPV & Cash-Flow Pro Steps
Project evaluation, IRR solver, payback period, profitability index — with cash-flow timeline visualization.
Percentage & Rate Toolkit
Percentage operations, nominal ↔ effective conversion across compounding bases, and payment-count solving.
Time Value of Money Pro Steps
FV and PV suites — annuities ordinary and due, loan payments, continuous compounding, growing annuities — with cash-flow timelines.
Specialized & Legacy
Aerospace & Environment Lab
Lift, drag and Reynolds, Bernoulli between stations, the standard atmosphere plotted, propulsion, orbits, and sustainability formulas.
Civil & Water Systems
Rational-method runoff with composite C, Hazen-Williams losses with fitting equivalent lengths, traffic flow.
USCS Soil Classifier
The classification flowchart as a guided algorithm — group symbol plus the full reasoning path and plasticity chart.
Design Codes: Steel & Footing
ASD shear and moment checks with utilization gauges, spread-footing sizing, and worst-case vs RSS tolerance stacks.