Formula sets

70 of 70 named groups. A set is not just a list — each one carries the rule for choosing between its members, which is the part a list can never give you.

Motion & mechanics (7)Waves, light & the very small (8)Electricity (6)Heat, fluids & HVAC (10)Chemistry (10)Water & environment (9)Materials, ground & site (13)Mathematics (7)

Motion & mechanics 7

The kinematic equations

5 formulasThe five equations of motion under constant acceleration, and the trick for choosing between them: pick the one missing the quantity you neither have nor want.

also called: SUVAT equations · equations of motion · big five kinematics

The projectile motion equations

6 formulasRange, maximum height, time of flight and the two velocity components — the standard results for a projectile launched into still air.

also called: projectile equations · range formula · time of flight formula · trajectory equations · cannonball problem

Circular and centripetal motion

7 formulasCentripetal acceleration and force in both linear and angular form, plus the curve-speed results that follow when friction or a bank supplies them.

also called: centripetal force formula · uniform circular motion · centrifugal force · banked curve formula · a = v squared over r

Simple harmonic motion

7 formulasDisplacement, maximum velocity and maximum acceleration in an oscillation, with the two periods and the restoring force that generate them.

also called: SHM equations · oscillation formulas · spring period · pendulum period · mass on a spring

Momentum, impulse and collisions

7 formulasMomentum and impulse, the conservation law that links two bodies, and the elastic, inelastic and restitution results for what happens after they meet.

also called: conservation of momentum · impulse momentum theorem · elastic and inelastic collisions · coefficient of restitution

Work, energy and power

8 formulasWork, the two stores of mechanical energy, the theorem that connects them to speed, and the two ways of writing power.

also called: work energy theorem · conservation of energy formulas · kinetic and potential energy · power formulas

The rotational equations of motion

13 formulasThe angular twins of the linear equations — θ, ω and α in place of d, v and a, and torque, moment of inertia and Iω in place of F, m and p.

also called: rotational kinematics · angular motion formulas · torque and angular momentum · rotational dynamics · moment of inertia formulas

Waves, light & the very small 8

Gravitation and orbital mechanics

8 formulasNewton's inverse-square law and what falls out of it in orbit — field strength, orbital speed and period, Kepler's third law, and escape velocity.

also called: Newton's law of gravitation · Kepler's third law · orbital velocity formula · escape velocity formula · satellite equations

The special relativity equations

4 formulasThe Lorentz factor and the three consequences that follow from it: time dilation, length contraction and mass-energy equivalence.

also called: Lorentz factor · time dilation formula · length contraction · E = mc2 · relativistic equations

Photon and quantum relations

7 formulasThe small family of relations built on Planck's constant — photon energy and momentum, matter waves, the photoelectric effect and the Bohr levels.

also called: E = hf · Planck relation · de Broglie wavelength · photoelectric equation · quantum formulas

The wave equations and harmonics

7 formulasWave speed, period and frequency, the speed of a wave on a string, and the harmonic series for strings and pipes that decides what note you hear.

also called: v = f lambda · wave speed formula · harmonic series · standing waves · beat frequency

Lens and mirror equations

5 formulasThe thin lens and mirror equations with the two magnification relations and lens power — everything needed to place an image and say how big it is.

also called: thin lens equation · mirror equation · magnification formula · 1/f = 1/do + 1/di · diopters

Refraction and total internal reflection

5 formulasSnell's law and the refractive index, with the critical angle, Brewster's angle and apparent depth that follow from bending light at a boundary.

also called: Snell's law · critical angle formula · index of refraction · TIR · Brewster's angle

Sound intensity and decibels

4 formulasSound power spread over area, how it falls with distance, and why the ear's response forces a logarithmic scale.

also called: dB · sound level · inverse square law sound · loudness

Interference and diffraction

4 formulasWhere light waves reinforce and cancel — two slits, many slits, and the thin films that colour soap bubbles and oil.

also called: double slit · Young's experiment · diffraction grating · thin film interference · oil slick colours

Electricity 6

The Ohm's law wheel

4 formulasOhm's law and the three power equations, arranged so that each one omits exactly one of voltage, current, resistance and power.

also called: Ohm's law · power triangle · V = IR · P = VI · watts law · ohms law pie chart

Reactance, resonance and time constants

7 formulasHow capacitors and inductors oppose alternating current, the frequency at which they cancel, and the RC and RL constants that set switching speed.

also called: capacitive reactance · inductive reactance · RC time constant · resonant frequency formula · RMS voltage

Three-phase power and power factor

8 formulasReal, reactive and apparent power, power factor, phase angle and correction kvar — the power triangle as an electrician uses it.

also called: power triangle · kW kVA kVAR · power factor correction · 1.732 formula · apparent power

Motor calculations

5 formulasFull-load current, synchronous speed, slip, efficiency and input power — reading a motor nameplate and checking what it actually draws.

also called: full load amps · FLA · motor slip · synchronous speed · motor efficiency · nameplate

Voltage drop

4 formulasSingle-phase and three-phase voltage drop, percent drop and conductor resistance at temperature — sizing a conductor for a long run.

also called: 3 percent rule · wire sizing · long run · conductor sizing · percent voltage drop

Series and parallel networks

4 formulasCombining resistors and capacitors two at a time — and the reason the two components follow exactly opposite rules.

also called: resistors in series · resistors in parallel · capacitors in series · combining components

Heat, fluids & HVAC 10

The gas laws

5 formulasBoyle, Charles, Gay-Lussac, the combined law and the ideal gas law — each holding one property fixed, and how they collapse into PV = nRT.

also called: Boyle's law · Charles's law · combined gas law · ideal gas law

The pump and fan affinity laws

7 formulasHow flow, head and power scale with impeller speed and diameter — the first, second and third power relationships behind every VFD retrofit.

also called: pump laws · fan laws · similarity laws

The effectiveness-NTU method

5 formulasSizing or rating a heat exchanger without knowing the outlet temperatures — capacity rates, NTU, effectiveness and the maximum possible duty.

also called: NTU method · heat exchanger effectiveness · epsilon-NTU

The HVAC heat transfer constants

6 formulasThe 500, 1.08, 0.68 and 4.5 rules for water and air heat transfer — where each constant comes from and when it stops being true.

also called: 500 rule · 1.08 rule · 0.68 rule · 4.5 rule · sensible and latent heat · BTU formulas

Refrigeration capacity and efficiency

6 formulasTons, COP, EER and kW per ton — the four ways the trade states the same chiller performance, and how to convert between them.

also called: tons of refrigeration · COP · EER · kW per ton · chiller efficiency · gpm per ton

Duct sizing and airflow

5 formulasDuct velocity, equivalent round diameter, velocity pressure and air changes per hour — sizing ductwork and proving the room turns over.

also called: duct velocity · equivalent round duct · air changes per hour · ACH · velocity pressure · CFM

Pump power and efficiency

7 formulasWater horsepower, brake horsepower, pump efficiency, NPSH available and specific speed — sizing the motor and keeping the impeller wet.

also called: water horsepower · brake horsepower · BHP · pump efficiency · NPSH · 3960 formula

Pipe friction losses

9 formulasDarcy–Weisbach, Hazen–Williams, friction factors, minor losses and equivalent length — every way the trade computes head loss in pipe.

also called: head loss · Darcy-Weisbach · Hazen-Williams · friction factor · minor losses · equivalent length

Heads in a piping system

6 formulasPressure head, velocity head, static fill pressure and total dynamic head — the feet of water a pump and a gauge are each talking about.

also called: pressure head · velocity head · static fill pressure · total dynamic head · TDH · feet of head · 2.31 rule

Valve sizing coefficients

4 formulasCv, Kv, K factors and equivalent length — the four coefficients that turn a valve or fitting into a pressure drop at a given flow.

also called: Cv · Kv · flow coefficient · valve sizing · K factor · equivalent length

Chemistry 10

Stoichiometry basics

5 formulasThe conversions every mass-to-mass calculation runs through — moles from grams, particles from moles, gas volume, composition and yield.

also called: mole conversions · mole map · grams to moles · stoichiometry formulas · percent yield

Ways to express concentration

6 formulasMolarity, molality, mass percent, mole fraction, normality and the dilution equation — six answers to “how much solute is in there?”

also called: molarity vs molality · concentration formulas · dilution equation · M1V1 = M2V2 · mole fraction · normality

Colligative properties

4 formulasBoiling-point elevation, freezing-point depression, osmotic pressure and Raoult's law — the four effects that count particles, not identity.

also called: freezing point depression · boiling point elevation · osmotic pressure · Raoult's law · antifreeze calculation

Acid–base relations

7 formulaspH, pOH, Kw, Ka and Kb and the weak-acid shortcut — the chain that turns a concentration into a pH and back again.

also called: pH formulas · pH and pOH · Ka Kb Kw · weak acid pH · percent ionization · how to calculate pH

The buffer equations

4 formulasHenderson–Hasselbalch in both its acid and base forms, plus the pKa and pKb conversions that feed them — buffer pH from a ratio.

also called: Henderson-Hasselbalch · buffer pH · pKa · buffer calculation · how to make a buffer

Chemical equilibrium constants

6 formulasKc, Kp, the reaction quotient Q, Ksp and the link to Gibbs free energy — every way of asking which side a reaction favours.

also called: Kc and Kp · reaction quotient Q · Ksp · solubility product · law of mass action · ICE table

The integrated rate laws

5 formulasZero-, first- and second-order concentration-versus-time laws and their half-lives — and how to read the order off a straight line.

also called: zero first second order kinetics · reaction order · half-life formulas · rate law · kinetics equations

The Arrhenius relations

3 formulasThe exponential rate-constant law, its two-temperature form and the activation energy read off an Arrhenius plot's slope.

also called: activation energy · Arrhenius equation · Arrhenius plot · temperature dependence of rate constant · Ea from two temperatures

Thermochemistry and spontaneity

5 formulasHess's law both ways, the heat a reaction actually releases, and the Gibbs criterion that decides whether it runs at all.

also called: Hess's law · enthalpy of reaction · Gibbs free energy · delta G delta H delta S · heat of reaction

The electrochemistry equations

3 formulasStandard cell potential from half-cells, the Nernst correction for real conditions, and Faraday's law for plating mass.

also called: Nernst equation · cell potential · Faraday's law of electrolysis · galvanic cell · electroplating calculation

Water & environment 9

The cooling tower water balance

6 formulasEvaporation, blowdown, drift and makeup — the four flows that have to balance on every open recirculating tower, and the cycles that link them.

also called: cycles of concentration · blowdown calculation · makeup water

Scaling and corrosion indices

6 formulasLangelier, Ryznar, Puckorius, Larson–Skold and coupon corrosion rate — the indices that say whether water will scale or eat the pipe.

also called: LSI · Langelier · Ryznar · RSI · Puckorius · PSI · Larson-Skold · saturation index

Water hardness and softening

8 formulasHardness as CaCO₃, grains per gallon, resin volume, salt dose and days between regenerations — sizing and running a softener.

also called: grains per gallon · hardness as CaCO3 · GPG · softener sizing · salt dose · resin capacity

Chemical dosing and feed rates

7 formulasFeed rate, dose from mass added, slug dose and product strength — converting between ppm, pounds per day and gallons of product.

also called: chemical feed rate · ppm dosing · slug dose · 8.34 formula · product strength · lb per day

The boiler water balance

8 formulasBoiler cycles, blowdown percent and rate, condensate return, makeup, flash steam and boiler horsepower — the steam side's water balance.

also called: boiler cycles · boiler blowdown · condensate return · flash steam · boiler horsepower · makeup water

Disinfection and chlorination

5 formulasCT value, dose–demand–residual, breakpoint ratio and hypochlorite product weight — getting the right chlorine on the right contact time.

also called: CT value · chlorine demand · chlorine residual · breakpoint chlorination · hypochlorite dose

Activated sludge process control

7 formulasF/M ratio, sludge age, SVI, RAS rate and organic loading — the five numbers an operator uses to steer an activated sludge plant.

also called: F/M ratio · sludge age · SRT · MCRT · SVI · RAS rate · MLSS

Clarifier and filter loading rates

6 formulasDetention time, surface overflow rate, solids loading, filter rate and backwash water — the loading rates that decide plant capacity.

also called: surface overflow rate · SOR · detention time · filter loading rate · solids loading · backwash

Open channel and weir flow

5 formulasManning's equation, Francis rectangular weir, V-notch weir and Parshall flume — measuring flow in a channel with no meter in it.

also called: Manning's equation · Francis formula · V-notch weir · Parshall flume · channel flow · flume

Materials, ground & site 13

Rankine earth pressure

4 formulasActive, passive and at-rest earth pressure coefficients, and the thrust a retaining wall has to carry — three states set by which way the wall moves.

also called: active earth pressure · passive earth pressure · at-rest pressure

Stress, strain and the elastic constants

9 formulasNormal and shear stress, strain, axial deformation, and the four elastic constants E, G, K and ν that link them.

also called: Hooke's law for materials · Young's modulus · Poisson's ratio · shear modulus · stress and strain formulas · E G K nu

Beam bending and deflection

9 formulasMaximum moment, bending stress by Mc/I or M/S, and the deflection of simply supported and cantilever beams under point and uniform loads.

also called: beam formulas · bending stress · Mc/I · section modulus · beam deflection formulas · simply supported beam

Column buckling and slenderness

5 formulasThe Euler critical load, radius of gyration and slenderness ratio — how a column fails by going sideways rather than crushing.

also called: Euler buckling · critical load · slenderness ratio · KL/r · effective length factor · radius of gyration

Soil phase relations

8 formulasVoid ratio, porosity, saturation, water content and the dry, saturated and submerged unit weights of a three-phase soil.

also called: phase diagram soil · void ratio · porosity · degree of saturation · dry unit weight · soil weight volume relationships

The effective stress principle

4 formulasTotal vertical stress, pore water pressure and Terzaghi's σ′ = σ − u — the single idea the whole of soil mechanics rests on.

also called: Terzaghi effective stress · total stress vs effective stress · pore water pressure · sigma prime

Bearing capacity of shallow foundations

4 formulasThe Terzaghi bearing-capacity equation, its Nc and Nq factors, and the net allowable pressure a footing may actually be designed to.

also called: Terzaghi bearing capacity · allowable bearing pressure · bearing capacity factors · footing design · Nc Nq Ngamma

Torsion of shafts

4 formulasTwisting a round shaft: the polar moment of inertia, the shear stress it produces, and how far the far end rotates under load.

also called: torsional stress · angle of twist · polar moment of inertia · drive shaft design

Consolidation settlement

3 formulasHow far a normally consolidated clay settles under new load, and the time factor that governs how many years it takes.

also called: clay settlement · time factor · primary consolidation · how long will it settle

Darcy's law and seepage

4 formulasGroundwater through soil: hydraulic gradient, Darcy discharge, the faster real velocity in the pores, and layered permeability.

also called: groundwater flow · permeability · hydraulic conductivity · seepage velocity

Horizontal curve layout

6 formulasSetting out a circular road curve: radius from degree of curve, then tangent, curve length, external distance, middle ordinate and long chord.

also called: degree of curve · circular curve · road curve staking · tangent length

Earthwork volumes

5 formulasEstimating dirt: average end area and the prismoidal correction, stockpile volume, and the swell and shrinkage between bank, loose and compacted.

also called: cut and fill · average end area · prismoidal formula · swell and shrinkage · cubic yards of dirt

Survey traverse closure

6 formulasClosing a traverse: latitudes and departures per leg, the misclosure they expose, and the precision ratio that decides whether it passes.

also called: latitude and departure · closure error · precision ratio · back azimuth · traverse adjustment