Test Your Engineering Knowledge
116 subjects, 14,900+ questions. Find out what you need to study.
Acoustics & Vibrations
Master acoustics and vibration engineering with this detailed formula sheet covering sound wave equations, decibel calculations, room acoustics, noise control, vibration isolation, structural dynamics, and psychoacoustic parameters.
Additive Manufacturing
Master additive manufacturing with this detailed formula sheet covering process physics, energy density, build parameters, material properties, design guidelines, and quality control for AM engineers and designers.
Aerospace Fundamentals
Master aerospace engineering with this detailed formula sheet covering aerodynamics, flight mechanics, propulsion, orbital mechanics, and aircraft performance.
Agricultural Engineering
Master agricultural engineering with formulas for irrigation, drainage, farm machinery, soil mechanics, and post-harvest processing.
Antenna Theory
Comprehensive antenna theory reference covering radiation mechanisms, antenna parameters (gain, directivity, efficiency), dipoles, monopoles, arrays, aperture antennas, polarization, impedance matching, and link budget calculations for wireless communication and radar systems.
Biochemical Engineering
Master biochemical engineering with this detailed formula sheet covering enzyme kinetics, microbial growth, bioreactor design, oxygen transfer, sterilization, and downstream processing for biopharmaceuticals and industrial biotechnology.
Biomedical Engineering
Master biomedical engineering with formulas covering biomechanics, bioinstrumentation, biomaterials, medical imaging, and physiological systems.
Calculus I - Derivatives & Limits
Test your understanding of limits, derivatives, differentiation rules, and their applications
Calculus II - Integrals
Master integration techniques, applications of integrals, and sequences & series
Calculus III - Multivariable
Explore multivariable calculus including partial derivatives, multiple integrals, and vector calculus
Casting & Metal Forming
Master casting and metal forming with this detailed formula sheet covering solidification, riser design, gating systems, forging, rolling, extrusion, and sheet metal forming for manufacturing engineers.
CFD
Master CFD with formulas covering governing equations, discretization, turbulence modeling, boundary conditions, and numerical methods.
Chemical Process Design
Master chemical process design with formulas for equipment sizing, economics, safety, and process optimization.
Chemical Reaction Engineering
Master chemical reaction engineering with this detailed formula sheet covering reaction kinetics, rate laws, reactor design equations, conversion calculations, selectivity, residence time, and non-ideal reactor analysis.
Chemistry for Engineers
Master engineering chemistry with plain-English explanations of reactions, equilibrium, and material properties
Communication Systems
Master communication systems with formulas covering modulation, channel capacity, digital communications, and wireless systems.
Complex Analysis
Master complex analysis with plain-English explanations of analytic functions, residues, and conformal maps
Composite Materials
Master composite materials with this detailed formula sheet covering laminate theory, micromechanics, failure criteria, ply stacking, hygrothermal effects, and design methods for aerospace and structural engineers.
Computational Mechanics
Master computational mechanics with this detailed formula sheet covering finite differences, boundary element methods, meshless methods, explicit/implicit time integration, coupled analysis, and verification and validation for advanced simulation.
Computer Architecture
Master computer architecture with plain-English explanations of CPU components, memory hierarchy, and performance metrics
Computer Networks
Essential computer networking formulas covering the OSI and TCP/IP models, bandwidth and throughput calculations, latency analysis, error detection (CRC, checksums), routing algorithms (Dijkstra, Bellman-Ford), subnetting and CIDR, flow control, congestion control, and wireless networking fundamentals.
Construction Management
Master construction management with this detailed formula sheet covering estimating, scheduling, productivity, equipment, safety, and contract administration for construction managers and engineers.
Control Systems
Master control systems with plain-English explanations of feedback, stability, and controller design
Corrosion Engineering
Master corrosion engineering with this detailed formula sheet covering electrochemical fundamentals, corrosion rates, galvanic corrosion, cathodic protection, coatings, and materials selection for corrosion prevention and control.
Cybersecurity
Essential cybersecurity formulas covering symmetric and asymmetric encryption, hash functions, digital signatures, PKI, network security protocols, authentication mechanisms, risk assessment, threat modeling, and security metrics for protecting systems and data.
Data Structures & Algorithms
Master DSA with plain-English explanations of data structures, algorithm complexity, and common patterns
Database Systems
Comprehensive database systems reference covering relational algebra, SQL operations, normalization forms (1NF through BCNF), functional dependencies, indexing structures (B+ trees, hashing), query optimization, transaction management, and concurrency control with ACID properties.
Differential Equations
Practice solving ODEs, understanding solution methods, and Laplace transforms
Digital Logic
Master digital logic with plain-English explanations of gates, Boolean algebra, and state machines
Digital Signal Processing
Essential DSP formulas covering discrete-time signals and systems, Z-transform, DFT and FFT algorithms, FIR and IIR filter design, frequency response, windowing techniques, sampling theory, and spectral analysis for audio, communications, and image processing applications.
Discrete Mathematics
Master discrete math with plain-English explanations of sets, counting, graph theory, and proofs
Dynamics
Test kinematics, kinetics, work-energy, and impulse-momentum concepts
Earthquake Engineering
Master earthquake engineering with formulas covering seismology, structural dynamics, seismic design, liquefaction, and base isolation.
Electric Circuits
Test DC/AC circuit analysis, impedance, and circuit theorems
Electric Machines
Comprehensive electric machines reference covering DC motors and generators, AC induction motors, synchronous machines, transformers, power flow analysis, torque-speed characteristics, efficiency calculations, and control principles for power systems and electromechanical applications.
Electromagnetic Fields
Comprehensive electromagnetic field theory reference covering Maxwell's equations in integral and differential forms, electromagnetic wave propagation, transmission lines, boundary conditions, waveguides, radiation, and antenna fundamentals for electrical engineering and physics applications.
Electronics
Master electronics with plain-English explanations of semiconductor devices, amplifier design, and frequency response
Embedded Systems
Comprehensive embedded systems reference covering real-time operating systems (RTOS), task scheduling, power consumption analysis, sensor interfacing, communication protocols, firmware development, debugging techniques, and design considerations for resource-constrained systems.
Engineering Drawing & GD&T
Master engineering drawing and GD&T with this detailed formula sheet covering tolerance stack-up analysis, geometric tolerances, datum reference frames, position calculations, surface finish specifications, and feature control frame interpretation.
Engineering Economics
Test time value of money, NPV, IRR, and economic decision making
Environmental Engineering
Master environmental engineering with this detailed formula sheet covering water treatment, wastewater processes, air pollution control, solid waste management, and environmental remediation for environmental engineers.
Ergonomics & Human Factors
Master ergonomics with this detailed formula sheet covering biomechanics, lifting analysis, workstation design, anthropometry, fatigue assessment, and human reliability for industrial and occupational safety engineering.
Fatigue Analysis
Master fatigue analysis with this detailed formula sheet covering stress-life, strain-life, notch effects, multiaxial fatigue, cumulative damage, and variable amplitude loading for mechanical and structural engineers.
Finite Element Analysis
Master finite element analysis with this detailed formula sheet covering element formulations, shape functions, stiffness matrices, convergence criteria, meshing guidelines, and solution techniques for structural and thermal analysis.
Fire Protection Engineering
Master fire protection engineering with this detailed formula sheet covering fire dynamics, smoke control, sprinkler design, egress analysis, structural fire protection, and detection systems for fire protection engineers.
Fluid Mechanics
Practice fluid statics, Bernoulli equation, and pipe flow problems
Food Engineering
Master food engineering with this detailed formula sheet covering thermal processing, refrigeration, drying, rheology, mass transfer, packaging, and quality kinetics for food manufacturing and preservation.
Fourier Analysis
Comprehensive Fourier analysis reference covering Fourier series for periodic functions, Fourier transforms for aperiodic signals, discrete Fourier transform (DFT), convolution theorems, spectral analysis, and applications in signal processing, differential equations, and physics.
Fracture Mechanics
Master fracture mechanics with this detailed formula sheet covering stress intensity factors, energy release rate, J-integral, crack growth, fracture toughness testing, and design against fracture for structural engineers.
Geotechnical Engineering
Master geotechnical engineering with this detailed formula sheet covering soil classification, effective stress, shear strength, consolidation, bearing capacity, lateral earth pressure, and slope stability for civil engineers.
Heat Transfer
Master heat transfer with plain-English explanations of thermal resistance, convection coefficients, and exchanger design
Hydrology
Master engineering hydrology with this detailed formula sheet covering precipitation analysis, runoff estimation, hydrograph analysis, groundwater flow, flood frequency, reservoir routing, evapotranspiration, and watershed modeling methods.
IC Engines
Comprehensive internal combustion engine reference covering thermodynamic cycles (Otto, Diesel), engine performance parameters, combustion fundamentals, air-fuel ratios, emissions, turbocharging, and engine testing for automotive and mechanical engineering applications.
Instrumentation
Comprehensive instrumentation reference covering sensor types and characteristics, measurement uncertainty analysis, signal conditioning circuits, data acquisition systems, calibration methods, and noise reduction techniques for industrial and laboratory measurement applications.
Lean Manufacturing
Master lean manufacturing with this detailed formula sheet covering takt time, cycle time, OEE, value stream mapping, kanban sizing, SMED, line balancing, and continuous improvement metrics.
Linear Algebra
Test your knowledge of matrices, vectors, eigenvalues, and linear transformations
Machine Design
Master machine design with plain-English explanations of failure theories, fatigue analysis, and mechanical components
Machine Learning
Essential machine learning formulas covering supervised learning (linear regression, logistic regression, SVM, decision trees), unsupervised learning (k-means, PCA), neural networks (backpropagation, activation functions), regularization techniques, evaluation metrics, and optimization algorithms like gradient descent.
Machining
Master machining with this detailed formula sheet covering cutting mechanics, tool geometry, cutting forces, tool life, surface finish, and process parameters for manufacturing engineers and machinists.
Manufacturing Processes
Master manufacturing processes with formulas covering machining, casting, forming, welding, and additive manufacturing.
Marine Engineering
Master marine engineering with this detailed formula sheet covering ship hydrostatics, resistance and propulsion, seakeeping, structural design, and marine systems for naval architects and marine engineers.
Mass Transfer Operations
Master mass transfer with this detailed formula sheet covering diffusion, convective mass transfer, interphase transport, absorption, distillation, extraction, and membrane separations with design equations.
Materials Science
Master materials science with plain-English explanations of atomic structure, phases, and material behavior
Mechanical Vibrations
Master mechanical vibrations with plain-English explanations of natural frequency, damping, and resonance
Mechatronics
Master mechatronics with formulas covering sensors, actuators, control systems, microcontrollers, and system integration.
MEMS
Master MEMS design with this detailed formula sheet covering electrostatic actuation, capacitive sensing, mechanical resonators, thermal actuators, piezoelectric devices, and microfabrication for MEMS engineers and researchers.
Microprocessors
Comprehensive microprocessor reference covering CPU architecture, instruction sets, addressing modes, memory organization, I/O interfacing, interrupts, timing calculations, and assembly programming for embedded systems and computer engineering applications.
Mining Engineering
Master mining engineering with this detailed formula sheet covering ore reserve estimation, rock mechanics, drilling and blasting, ventilation, mine planning, and mineral processing for mining engineers.
Modern Physics
Essential modern physics formulas covering special relativity, quantum mechanics fundamentals, wave-particle duality, atomic structure, nuclear physics, the Schrödinger equation, uncertainty principle, and foundational concepts of 20th-century physics for engineering and science applications.
Nanotechnology
Master nanotechnology with this detailed formula sheet covering quantum confinement, surface effects, nanoparticle properties, self-assembly, characterization techniques, and nanofabrication for nanoscience and nanoengineering courses.
Nondestructive Testing
Master nondestructive testing with this detailed formula sheet covering ultrasonic testing, radiography, magnetic particle, eddy current, liquid penetrant, and visual inspection for quality engineers and inspectors.
Nuclear Engineering
Master nuclear engineering with this detailed formula sheet covering nuclear reactions, radioactive decay, reactor physics, neutron transport, thermal hydraulics, and radiation protection for nuclear engineers.
Numerical Methods
Master numerical methods with plain-English explanations of algorithms for solving equations and approximating solutions
OOP & Design Patterns
Comprehensive object-oriented programming reference covering SOLID principles, creational patterns (Singleton, Factory, Builder), structural patterns (Adapter, Decorator, Composite), behavioral patterns (Observer, Strategy, Command), UML relationships, and software design metrics for clean, maintainable code.
Operating Systems
Master operating system concepts with this comprehensive formula sheet covering process scheduling algorithms (FCFS, SJF, Round Robin, Priority), CPU metrics, memory management techniques, page replacement algorithms, virtual memory, deadlock handling with Banker's algorithm, and disk scheduling strategies.
Operations Research
Master operations research with this detailed formula sheet covering linear programming, network optimization, queuing theory, inventory models, decision analysis, simulation, and game theory for engineering management.
Packaging Engineering
Master packaging engineering with this detailed formula sheet covering cushion design, compression strength, drop testing, vibration analysis, barrier properties, and sustainability metrics for packaging engineers.
Partial Differential Equations
Comprehensive PDE reference covering classification of PDEs (elliptic, parabolic, hyperbolic), the heat equation, wave equation, Laplace equation, separation of variables, Fourier series solutions, boundary value problems, Green's functions, and numerical methods for solving partial differential equations.
Petroleum Engineering
Master petroleum engineering with this detailed formula sheet covering reservoir properties, fluid flow in porous media, well testing, production optimization, drilling calculations, and enhanced oil recovery methods.
Photonics & Optics
Master photonics and optics with this detailed formula sheet covering geometric optics, wave optics, laser physics, fiber optics, optical detection, and optical system design for photonics engineers.
Physics I - Mechanics
Test your understanding of motion, forces, energy, momentum, and rotational dynamics
Physics II - E&M
Master electricity, magnetism, circuits, and electromagnetic waves
Plastics Processing
Master plastics processing with this detailed formula sheet covering injection molding, extrusion, blow molding, thermoforming, and polymer rheology for plastics engineers and manufacturing specialists.
Polymer Engineering
Master polymer engineering with this detailed formula sheet covering molecular weight distributions, polymer rheology, reaction kinetics, mechanical properties, processing equations, and structure-property relationships.
Power Systems
Master power systems with plain-English explanations of AC power, transformers, and grid analysis
Probability & Statistics
Practice probability distributions, hypothesis testing, and regression
Process Control
Master process control with this detailed formula sheet covering Laplace transforms, transfer functions, feedback control, PID tuning, stability analysis, frequency response, and advanced control strategies.
Project Management
Master project management with this detailed formula sheet covering CPM, PERT, earned value management, schedule and cost variance, resource leveling, risk quantification, and critical chain for project engineers and managers.
Quality Control & Six Sigma
Master quality control with this detailed formula sheet covering control charts, process capability, acceptance sampling, measurement system analysis, Six Sigma metrics, design of experiments, and statistical process control.
Refrigeration & HVAC
Comprehensive refrigeration and air conditioning reference covering vapor compression cycles, refrigerant properties, COP calculations, psychrometric analysis, heating and cooling loads, heat pump systems, and HVAC design fundamentals for mechanical engineering applications.
Reinforced Concrete Design
Master reinforced concrete design with this detailed formula sheet covering flexural design, shear and torsion, column design, development length, serviceability, deflection limits, crack control, and footings based on ACI 318 code.
Reliability Engineering
Master reliability engineering with this detailed formula sheet covering failure rate analysis, system reliability, Weibull distribution, fault tree analysis, FMEA, availability calculations, and maintainability for quality and reliability engineers.
Renewable Energy
Master renewable energy with this detailed formula sheet covering solar photovoltaics, wind power, hydropower, bioenergy, geothermal, energy storage, and grid integration for energy engineers and researchers.
Robotics Kinematics
Master robotics kinematics with formulas covering transformations, forward/inverse kinematics, Jacobians, trajectory planning, and dynamics.
Separation Processes
Master separation processes with this detailed formula sheet covering filtration, sedimentation, centrifugation, drying, crystallization, adsorption, ion exchange, and chromatography with equipment design equations.
Signals & Systems
Master signals and systems with plain-English explanations of Fourier, Laplace, and Z-transforms
Software Engineering
Essential software engineering concepts covering software development lifecycles (Waterfall, Agile, Scrum), testing methodologies (unit, integration, system), code metrics (lines of code, function points), effort estimation (COCOMO), version control workflows, and software quality assurance practices.
Statics
Practice equilibrium problems, free body diagrams, and truss analysis
Steel Design
Master structural steel design with this detailed formula sheet covering tension members, compression members, flexural members, beam-columns, connections, and bolted/welded joint design based on AISC 360 specification.
Strength of Materials
Master stress, strain, beam bending, and Mohr's circle
Structural Analysis
Master structural analysis with plain-English explanations of deflections, indeterminate structures, and influence lines
Supply Chain Management
Master supply chain management with this detailed formula sheet covering inventory optimization, demand forecasting, logistics costs, network design, supplier selection, and performance metrics for operations management.
Surveying & Geomatics
Master surveying and geomatics with this detailed formula sheet covering distance measurement, leveling, traverse calculations, coordinate geometry, curve layout, GPS positioning, error analysis, and earthwork volumes.
Tensor Calculus
Master tensor calculus with formulas covering tensor notation, transformations, covariant derivatives, curvature, and applications in physics.
Textile Engineering
Master textile engineering with formulas covering fiber properties, yarn mechanics, fabric structure, dyeing, and finishing processes.
Theory of Computation
Comprehensive theory of computation reference covering finite automata (DFA, NFA), regular expressions and languages, context-free grammars, pushdown automata, Turing machines, decidability, complexity classes (P, NP, NP-complete), and reductions for analyzing computational limits.
Thermodynamics
Master the laws of thermodynamics, cycles, entropy, and heat transfer
Transport Phenomena
Master transport phenomena with formulas covering fluid mechanics, heat transfer, mass transfer, and their analogies.
Transportation Engineering
Master transportation engineering with formulas covering traffic flow, highway design, pavement, intersection design, and transit.
Tribology
Master tribology with this detailed formula sheet covering friction laws, contact mechanics, wear mechanisms, lubrication regimes, bearing design, and surface engineering for mechanical engineers and materials scientists.
Turbomachinery
Master turbomachinery with this detailed formula sheet covering velocity triangles, Euler turbomachine equation, specific speed, cavitation analysis, pump affinity laws, turbine efficiency, compressor performance maps, and cascade aerodynamics.
Vehicle Dynamics
Master vehicle dynamics with this detailed formula sheet covering tire mechanics, suspension, steering, braking, ride and handling, and performance analysis for automotive engineers.
VLSI Design
Master VLSI design with formulas covering MOS transistors, digital circuits, timing, power, and layout.
Water Resources Engineering
Master water resources engineering with this detailed formula sheet covering water demand, pipe hydraulics, pump systems, water distribution networks, wastewater collection, stormwater management, and water treatment processes.
Waves & Oscillations
Master waves and oscillations with formulas covering harmonic motion, wave equations, interference, resonance, and applications.
Welding Engineering
Master welding engineering with this detailed formula sheet covering heat input, thermal cycles, weld metallurgy, residual stress, weld design, and quality control for welding engineers and fabricators.
No tests found
Try adjusting your filters or search term
How It Works
Pick Your Subject
Choose from 116 engineering subjects across all disciplines and levels.
Answer Questions
Take a timed test with exam-style questions. Choose quick, standard, or full mode.
Get Results
See your score, topic breakdown, and personalized study recommendations.
Track Progress
Retake tests to track improvement and compete on the leaderboard.
Ready to Test Your Knowledge?
Pick a subject and find out where you stand in just 15 minutes.
Choose a Subject