Advanced Science & Engineering

Rigorous, interactive tools for physics, chemistry, optics, astrodynamics, genetics, economics and engineering — the serious end of the Apexa Pro catalogue, each page with worked theory and references.

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Advanced Science & Engineering29

Atomic Structure Simulator

Build an atom and see its protons, neutrons and electron shells: the Bohr model and electron configuration.

Chaos Lab — Lorenz Attractor & Double Pendulum

Two classic chaotic systems: the Lorenz attractor and the double pendulum, showing the butterfly effect live.

Chemical Equation Balancer & Stoichiometry Calculator

Balance any chemical equation and run stoichiometry: molar masses, mole ratios and the limiting reagent.

Combined Gas Law Calculator

Leave any one of the six values blank and it solves for that one, converting units and checking the physics as it goes.

Concave & Convex Mirror Simulator

Ray-tracing simulator for concave and convex mirrors, with the mirror equation and magnification.

Coulomb's Law Calculator & Electric Field Simulator

Electrostatic force between point charges and the electric field they create, with the CODATA Coulomb constant.

Crosswind & Headwind Component Calculator

Resolve wind into crosswind and headwind/tailwind components for any runway, with the vector geometry.

Density Altitude Calculator

Density altitude from elevation, altimeter setting and temperature, using the ICAO Standard Atmosphere.

Gravity Simulator — N-Body Lab

An interactive N-body gravity sandbox: place masses, launch them and watch orbits form under Newtonian gravity with Velocity Verlet integration.

Hardy-Weinberg Equilibrium Calculator

Genotype and allele frequencies under Hardy-Weinberg equilibrium (p² + 2pq + q² = 1), with a chi-square test.

Hohmann Transfer Orbit Simulator

The two burns, total delta-v and transfer time of a fuel-optimal Hohmann transfer, from the vis-viva equation.

Ideal Gas Law Calculator (PV = nRT)

Solve PV = nRT for pressure, volume, moles or temperature, with the exact 2019 SI gas constant.

Moment of Inertia Calculator

Moment of inertia of rods, disks, cylinders, spheres and hoops about any axis, with the parallel-axis theorem.

Monte Carlo Risk Simulator

Run a Monte Carlo simulation over uncertain inputs for the full distribution of outcomes: mean, P10/P50/P90 and risk.

NPV, IRR & Payback Calculator

Net present value, internal rate of return, payback and discounted payback from a stream of cash flows.

Prism Light Dispersion Simulator

See a prism split white light into a rainbow: refraction, Snell's law and dispersion.

Projectile Motion Calculator

Range, maximum height and time of flight of a projectile from launch speed and angle, with the trajectory.

Punnett Square Calculator

Enter two parent genotypes and get the square drawn out, with the genotype and phenotype ratios worked through.

RLC Circuit Simulator

Frequency response of a series RLC circuit: resonant frequency, quality factor Q and bandwidth, plotted live.

Rotational Kinetic Energy Calculator

Energy stored in a spinning object, from its moment of inertia and how fast it turns — with common shapes built in.

Simple Pendulum Calculator

Period and frequency of a simple pendulum from length and gravity, with the large-amplitude correction.

Snell's Law Calculator

Find the refracted angle from the incident angle and the two materials — with the critical angle and total internal reflection handled.

Spacetime Curvature Simulator

A visual analogy of how mass curves spacetime in general relativity, with test particles bending along geodesics.

Special Relativity Calculator

Lorentz factor, time dilation, length contraction and relativistic energy for any speed, with the exact speed of light.

Spring-Mass Oscillator Calculator

Period, frequency and energy of a mass on a spring: simple harmonic motion from Hooke's law.

Statistical Significance Calculator

Convert between sigma, p-value and odds of random chance, one-tailed or two-tailed.

Supply and Demand Calculator

Market equilibrium price and quantity from supply and demand curves, with surpluses and shortages.

Torque Calculator

Force, lever length and angle to torque in N·m and lb·ft, with a diagram of the component that actually does the turning.

Wavelength ↔ Frequency Converter

Enter a wavelength or a frequency and get the other from c = λf, with photon energy and the spectrum band shown.