Engineering formulas
1428 formulas across 20 disciplines, every one solvable for any variable it contains, in any units, with the working shown. The disciplines overlap on purpose: a mechanical engineer and a chemical engineer both want heat transfer, so it appears under both.
Mechanical 392 formulas
Statics and dynamics, stress and deflection, conduction and convection, and the pump and pipe work that moves fluid around a building. The deepest area of the site after water.
Mechanics (160)Heat Transfer (63)Fluid Mechanics (129)Strength of Materials (97)
Worked sets: The kinematic equations · The effectiveness-NTU method · The projectile motion equations · Circular and centripetal motion
Chemical & Process 252 formulas
Equilibria, kinetics and stoichiometry alongside the process side: Bernoulli, Antoine, Van der Waals, the orifice and Venturi meters, and the Rankine, Otto and Brayton cycles.
Chemistry (136)Thermodynamics (137)
Worked sets: The gas laws · Stoichiometry basics · Ways to express concentration · Colligative properties
Civil & Structural 190 formulas
Surveying and highway geometry, effective stress and bearing capacity, and structural design from the parallel axis theorem through Mohr's circle to code load combinations.
Civil & Surveying (83)Soil Mechanics (49)Strength of Materials (97)
Worked sets: Rankine earth pressure · Stress, strain and the elastic constants · Beam bending and deflection · Column buckling and slenderness
Environmental & Water 207 formulas
Treatment plant loading, disinfection, sludge and biology, plus cooling tower and boiler chemistry, and the stormwater hydrology that sizes what carries it away.
Water & Wastewater (79)Erosion & Sediment (11)Water Treatment (148)
Worked sets: The cooling tower water balance · Scaling and corrosion indices · Water hardness and softening · Chemical dosing and feed rates
Electrical 103 formulas
Circuit theory from Kirchhoff to Thevenin, and the utility side of the trade: per-unit impedance, available fault current, voltage drop, motors and filter corners.
Electricity & Magnetism (93)Electrical Trade (61)
Worked sets: The Ohm's law wheel · Reactance, resonance and time constants · Three-phase power and power factor · Motor calculations
Building Services 107 formulas
The sensible and latent air rules, duct and coil sizing, refrigeration performance, expansion tanks, and the hydronic balance that decides whether a system actually heats.
Worked sets: The pump and fan affinity laws · The HVAC heat transfer constants · Refrigeration capacity and efficiency · Duct sizing and airflow
Industrial 20 formulas
Inventory and flow, quality and capability, and the engineering economy that decides which project gets funded: EOQ, takt time, OEE, Cp and Cpk, NPV and equivalent annual cost.
Worked sets: Inventory control · Lean flow and takt · Process capability and control
Computer & Software 37 formulas
Parallel speedup, channel capacity and sampling, queueing and blocking, cache access time, reliability and availability. The arithmetic behind how fast a system can possibly go.
Computer Science (26)Cryptography & Key Sizing (11)
Worked sets: Queueing and capacity · Information and signals · Throughput and bottlenecks · Reliability and availability
Biomedical & Clinical 38 formulas
Cardiac output and haemodynamics, renal function, and the diagnostic-accuracy arithmetic — sensitivity, predictive value, likelihood ratios. Estimates with known limits, and the prose says where each one fails.
Biomedical & Clinical (21)Epidemiology & Diagnostic Accuracy (17)
Worked sets: Drug dosing and pharmacokinetics · Haemodynamics and oxygen delivery · Renal function and blood chemistry
Manufacturing & Production 108 formulas
Feeds and speeds, tool life, press work and flat patterns, weld heat input and carbon equivalent, and the component sizing underneath: shafts, keys, bearings, springs and gears.
Machining & Turning (15)Welding & Joining (9)Additive Manufacturing (12)Machine Design (43)Industrial Engineering (20)Packaging & Box Strength (9)
Worked sets: Inventory control · Lean flow and takt · Process capability and control · A machine drive train
Materials 168 formulas
Stress and deflection, fracture toughness and crack growth, composite bounds, grain size and creep and phase fraction, brittle strength as a Weibull distribution, and the electrochemistry of losing metal.
Ceramics & Glass (11)Concrete (11)Strength of Materials (97)Metallurgy & Heat Treatment (13)Polymers & Plastics Processing (12)Textiles & Fabric (12)Corrosion & Protection (12)
Worked sets: Stress, strain and the elastic constants · Beam bending and deflection · Column buckling and slenderness · Torsion of shafts
Aerospace 76 formulas
Lift and drag, the standard atmosphere, the rocket equation and staging, orbital mechanics, and the navigation that gets an aircraft or a vessel from one waypoint to the next over a sphere.
Aerospace & Flight (33)Navigation & Position (18)Photogrammetry & Remote Sensing (12)Astronomy & Gravitation (13)
Worked sets: Gravitation and orbital mechanics · The wing and the drag polar · Sizing a rocket stage · Planning a leg
Energy & Power 244 formulas
Wind turbines and the Betz limit, solar array sizing and tilt geometry, the power cycles underneath, and the electrical side that turns any of it into something a grid will accept.
Solar & Wind Power (14)Thermodynamics (137)Electricity & Magnetism (93)
Worked sets: The gas laws · The Ohm's law wheel · Reactance, resonance and time constants · Series and parallel networks
Agricultural & Bioresource 105 formulas
Sprayer calibration, fertiliser and soil fertility, irrigation and evapotranspiration, grain drying and storage, ration balancing, controlled-environment light and air, and quantitative breeding.
Crop Production (51)Farm Operations (24)Livestock & Feed (12)Indoor & Greenhouse (11)Plant Breeding & Genetics (11)
Worked sets: Drying and storing a bin of grain · Scheduling an irrigation · Feeding cattle to a target gain
Transportation 48 formulas
Moving people and goods: what traffic does to a road, what a signal can clear, and what it costs to carry a load.
Traffic Flow & Signals (10)Axle Loads & Pavement (10)Freight & Shipping (10)Navigation & Position (18)
Worked sets: Planning a leg
Marine & Coastal 159 formulas
Wave height, period and celerity, shoaling and breaking, the wave power a metre of crest carries, and the great-circle and rhumb-line work that a passage plan is actually built from.
Coastal & Ocean Waves (12)Fluid Mechanics (129)Navigation & Position (18)
Worked sets: Heads in a piping system · Planning a leg
Geotechnical & Earth 183 formulas
Effective stress and bearing capacity, rock mass rating and pillar design, seismic moment and magnitude, site response and liquefaction, and the survey work that sites all of it.
Soil Mechanics (49)Rock Mechanics (37)Seismology (11)Civil & Surveying (83)Concrete (11)
Worked sets: Rankine earth pressure · Soil phase relations · The effective stress principle · Bearing capacity of shallow foundations
Acoustics & Noise 18 formulas
Reverberation time and absorption, transmission loss through a partition, sound power to sound pressure, distance attenuation, and the exposure limits a worker is protected by.
Worked sets: Treating a room for reverberation · Noise from a machine to the property line
Semiconductors 13 formulas
Device physics and chip design — switching and leakage power, gate delay, die yield, the scaling rules, and the thermal path that decides whether any of it survives its own heat.
Worked sets: A chip's power and heat budget
Air Quality & Process Safety 84 formulas
Plume rise and dispersion, stack emissions and correction to reference oxygen, the unit operations behind them — reactors, columns, mass transfer — and the fire science that bounds what happens when a process gets away.
Air Quality & Dispersion (31)Chemical Engineering (43)Fire Protection & Fire Dynamics (10)
Worked sets: Where the plume lands · Running a stack test · Designing a distillation column · Sizing a packed absorber
Not what you were after? Every solver, A–Z · every unit, defined · physical constants