Advanced Science & Engineering
Rigorous, interactive tools for physics, chemistry, astrodynamics, genetics, economics and engineering — the serious end of the Apexa Pro catalogue, each page with worked theory and references.
Advanced Science & Engineering20 tools
Gravity Simulator — N-Body Lab
Place masses and watch orbits form under Newtonian gravity, Velocity Verlet integration.
Hohmann Transfer Orbit Simulator
The two burns, total delta-v and transfer time of a fuel-optimal Hohmann transfer.
RLC Circuit Simulator
Frequency response of a series RLC circuit: resonant frequency, Q factor and bandwidth.
Chaos Lab — Lorenz Attractor & Double Pendulum
Two classic chaotic systems showing the butterfly effect live.
Crosswind & Headwind Component Calculator
Resolve wind into crosswind and headwind/tailwind components for any runway.
Density Altitude Calculator
Density altitude from elevation, altimeter setting and temperature (ICAO Standard Atmosphere).
Chemical Equation Balancer & Stoichiometry
Balance any equation and run stoichiometry: molar masses, mole ratios, limiting reagent.
Coulomb's Law Calculator & Electric Field
Electrostatic force between point charges and the electric field they create.
Hardy-Weinberg Equilibrium Calculator
Genotype and allele frequencies under Hardy-Weinberg (p² + 2pq + q² = 1), with a chi-square test.
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 common shapes about any axis, with the parallel-axis theorem.
Monte Carlo Risk Simulator
Run a Monte Carlo simulation over uncertain inputs: mean, P10/P50/P90 and risk.
Projectile Motion Calculator
Range, maximum height and time of flight of a projectile, with the trajectory.
Special Relativity Calculator
Lorentz factor, time dilation, length contraction and relativistic energy.
NPV, IRR & Payback Calculator
Net present value, internal rate of return and payback from a stream of cash flows.
Simple Pendulum Calculator
Period and frequency of a simple pendulum from length and gravity.
Supply and Demand Calculator
Market equilibrium price and quantity from supply and demand curves.
Spring-Mass Oscillator Calculator
Period, frequency and energy of a mass on a spring (simple harmonic motion).
Spacetime Curvature Simulator
A visual analogy of how mass curves spacetime in general relativity.
Atomic Structure Simulator
Build an atom and see its protons, neutrons and electron shells (Bohr model).