Toolkits

Bring the right toolkit to the job. Each one is a bag of formulas typically used together, with the rule for which one to reach for, the part a plain list can never give you. 110 of 110, grouped like the formula categories.

Agriculture & Growing (3)Chemistry & Process (16)Computing & Chips (5)Electricity & Power (8)Health & the Body (5)Heat, Fluids & HVAC (10)Machines & Manufacturing (5)Materials (4)Mathematics (7)Mechanics & Motion (7)Money & Markets (3)Navigation & Position (1)Space, Flight & Modern Physics (5)Structures, Ground & Earth (12)Water, Air & Environment (11)Waves, Light & Sound (8)

Agriculture & Growing 3

Drying and storing a bin of grain

8 formulasFilling, drying and storing a bin: the volume and mass of grain, the water to take out, the fuel it costs, aeration air and safe storage time.

also called: grain bin capacity · grain drying cost · moisture shrink · safe storage time · aeration airflow

Feeding cattle to a target gain

7 formulasBuilding a ration to a target gain: dry matter intake, blending two feeds, the energy supplied, and what a kilo of gain costs in feed.

also called: ration formulation · dry matter intake · feed conversion ratio · cost of gain · Pearson square

Scheduling an irrigation

7 formulasScheduling irrigation: what the soil holds, the depletion you allow, crop water use, the interval between sets and the hours to run.

also called: irrigation scheduling · when to irrigate · available water capacity · crop water use · set run time

Chemistry & Process 16

A brew day

9 formulasStrike temperature to knockout: heating the mash, the gravity a grain bill gives, the colour it makes and the bitterness the hops add.

also called: brewing calculations · homebrew formulas · mash and boil maths · recipe to kettle

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

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

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

Designing a distillation column

9 formulasDesigning a distillation column: the material balance split, minimum reflux, the stages that follow, the operating lines and tray efficiency.

also called: McCabe-Thiele · minimum reflux · number of trays · Underwood and Gilliland · column design

Designing a sacrificial anode system

5 formulasSizing a sacrificial anode system: current demand from coated area, what one anode delivers into the soil, and the mass for the design life.

also called: cathodic protection design · galvanic anode sizing · CP current demand · anode life calculation

Fermenting out and packaging

4 formulasReading a finished fermentation: attenuation and alcohol from two hydrometer numbers, and the priming sugar the bottles then need.

also called: is fermentation finished · ABV from gravity · attenuation · priming sugar · bottling calculations

From a corrosion probe to remaining wall

5 formulasTurning a polarization resistance reading into a corrosion current, a penetration rate in mm per year, and the years of wall left.

also called: LPR measurement · linear polarization resistance · corrosion rate from Icorr · remaining life calculation

Sizing a packed absorber

8 formulasSizing a packed absorber: diffusivity and Schmidt number, the film coefficients, the absorption factor, and the packed height from HTU and NTU.

also called: gas absorption · packed tower height · HTU and NTU · mass transfer coefficient · scrubber sizing

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

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

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

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

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

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

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

Computing & Chips 5

A chip's power and heat budget

6 formulasWhat a CMOS part costs in watts and degrees: the clock its critical path allows, dynamic and leakage power, and the junction temperature.

also called: CMOS power calculation · dynamic and leakage power · junction temperature · thermal budget · why is my chip hot

Information and signals

8 formulasEntropy, compression, error-correcting bits, channel capacity and sampling: what a signal carries and what a channel will pass.

also called: information theory formulas · channel capacity · sampling and quantisation · Shannon and Nyquist

Queueing and capacity

6 formulasUtilisation, queue length, waiting time, blocking and Little's law: how much load a server takes before the line stops moving.

also called: M/M/1 formulas · queue length and waiting time · how many servers · traffic engineering

Reliability and availability

4 formulasMTBF, MTTR, chains, redundancy and the odds of at least one failure: what uptime a system of imperfect parts really delivers.

also called: how many nines · MTBF and MTTR · redundancy maths · uptime calculations

Throughput and bottlenecks

5 formulasAmdahl and Gustafson, cache miss penalty, bandwidth-delay product and transfer time: why a machine never hits its rated speed.

also called: Amdahl's law · why is it slow · cache and network performance · scaling limits

Electricity & Power 8

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

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

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

Siting a wind turbine

7 formulasSiting a wind turbine: shearing the mast wind up to hub height, the power in it, what the rotor takes, and the capacity factor over a year.

also called: wind resource assessment · wind turbine power calculation · hub height wind speed · capacity factor

Sizing a rooftop PV array

6 formulasSizing a rooftop array: sun angle on the tilted plane, peak sun hours, the derate a hot roof costs, and the kilowatt-hours in a year.

also called: solar panel sizing · how many kWh will my solar make · peak sun hours · PV yield estimate

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

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

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

Health & the Body 5

Body and fitness numbers

6 formulasBMI, maximum and target heart rate, body surface area and calories burned — with what each number cannot tell you.

also called: health calculators · BMI and heart rate · fitness formulas

Drug dosing and pharmacokinetics

7 formulasLoading dose, maintenance rate, half-life, surface-area dosing and the two IV rate sums, in the order a prescription is worked out.

also called: loading and maintenance dose · half-life · IV rate calculations · BSA dosing · drip rate

Haemodynamics and oxygen delivery

6 formulasCardiac output, mean arterial pressure, vascular resistance, oxygen content, the Fick principle and minute ventilation as one chain.

also called: cardiac output · MAP and SVR · Fick principle · oxygen content · haemodynamic formulas

Renal function and blood chemistry

5 formulasCreatinine clearance, eGFR, anion gap, corrected calcium and dose rate from clearance: reading a panel and adjusting to it.

also called: creatinine clearance · eGFR · anion gap · corrected calcium · renal dose adjustment

What the weather feels like

4 formulasWind chill, humidex, heat index and dew point — the four numbers that explain why the thermometer lies.

also called: apparent temperature · wind chill and humidex · feels like

Heat, Fluids & HVAC 10

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

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

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

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

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

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 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 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

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

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

Machines & Manufacturing 5

A machine drive train

7 formulasMotor to bearing: torque from power, the gear reduction, tooth load, the shaft diameter torsion demands, key shear and bearing life.

also called: gear drive design · shaft sizing · torque through a gearbox · key and bearing selection

Inventory control

5 formulasEconomic order quantity, reorder point, safety stock and turnover: how much to order, when to order it and what buffer to keep.

also called: EOQ and reorder point · how much stock to hold · stocking policy · safety stock maths

Isolating a machine from the floor

6 formulasChoosing isolators for a machine: the unbalance force, the mount's natural frequency, transmissibility, and the isolation you can claim.

also called: vibration isolation · isolator selection · transmissibility · spring mount sizing · how much vibration gets through

Lean flow and takt

6 formulasTakt time, minimum stations, balance efficiency, work in process, standard time and the learning curve, in design order.

also called: takt time · line balancing · assembly line design · work in process · cycle time

Process capability and control

8 formulasCp, Cpk, control limits, DPMO, rolled throughput yield and OEE: whether a process holds tolerance and what the losses multiply to.

also called: Cp and Cpk · SPC formulas · six sigma maths · is the process capable · OEE

Materials 4

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

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

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

Mathematics 7

Arithmetic and geometric sequences

5 formulasThe nth term and the sum for both arithmetic and geometric progressions, including the infinite sum that converges.

also called: nth term · series sum · geometric series · sum to infinity

Confidence intervals and sample size

8 formulasStandard error, margin of error and the sample size a target precision demands — for both means and proportions.

also called: margin of error · standard error · how many people do I need to survey · 95% confidence

Right-triangle trigonometry

6 formulasThe three ratios for right triangles and the two laws that extend them to any triangle, plus the two-sides-and-an-angle area formula.

also called: SOH CAH TOA · sine cosine tangent · law of sines · law of cosines · solving triangles

The logarithm and exponent rules

7 formulasProduct, quotient and power rules for logarithms, change of base, and the exponent identities they mirror — the toolkit for solving for an exponent.

also called: log rules · laws of logarithms · exponent rules · change of base · solving for an exponent

The quadratic family

8 formulasThe two roots, the discriminant that predicts them, the vertex of the parabola and the sum-and-product shortcuts — all from ax² + bx + c.

also called: quadratic formula · discriminant · Vieta's formulas · vertex formula · completing the square · sum and product of roots

Time value of money

4 formulasSimple interest, periodic and continuous compounding, and discounting a future amount back to what it is worth today.

also called: compound interest · present value · simple vs compound interest · future value

Vector operations

12 formulasMagnitude, direction, components and unit vectors, plus the dot and cross products and the projections and angles they give you.

also called: dot product · cross product · vector components · resultant vector · vector magnitude

Mechanics & Motion 7

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

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

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

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

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

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

Money & Markets 3

Equipment, depreciation and payback

4 formulasStraight-line and declining-balance depreciation plus simple payback — how a purchase looks on paper and in cash.

also called: capital cost formulas · when does it pay for itself · asset write-down

Pricing and profit

5 formulasMarkup, margin, break-even and ROI — the four numbers that decide whether the work is worth doing.

also called: markup vs margin · what to charge · break even formulas

The loan and interest formulas

5 formulasPayment, total interest, effective rate and doubling time — everything that decides what borrowing actually costs.

also called: mortgage maths · borrowing formulas · amortization formulas

Space, Flight & Modern Physics 5

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

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

Sizing a rocket stage

7 formulasSizing a rocket stage from a delta-v budget: exhaust velocity, mass ratio, the propellant load, the thrust to lift it and how long it burns.

also called: rocket equation · delta-v budget · propellant mass calculation · mass ratio · burn time

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

The wing and the drag polar

6 formulasWorking a wing's drag: aspect ratio, the lift coefficient the flight needs, the induced drag it costs, and the lift-to-drag ratio that results.

also called: drag build-up · induced drag · lift and drag coefficients · aspect ratio · L/D ratio

Structures, Ground & Earth 12

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

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

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

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

Laying out a set of stairs

4 formulasRiser count, the 2R plus T comfort rule, total run and stringer length — the full sequence for cutting stairs.

also called: stair maths · rise and run · stringer layout

Materials take-off

7 formulasBoard feet, sheets, studs, paint, concrete bags and truck loads — turning drawings into an order list.

also called: how much material · estimating quantities · ordering formulas

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

Roof pitch and rafters

3 formulasPitch as a ratio and as an angle, common rafter length and roof area from footprint — laying out and covering a roof.

also called: roof maths · rafter layout · pitch to degrees

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

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

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

Water, Air & Environment 11

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

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

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

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

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

Running a stack test

7 formulasRunning a stack test: exit velocity, the isokinetic sampling rate, ppm to mass units, correction to reference oxygen, and the emission rate.

also called: source testing · isokinetic sampling · emission rate calculation · oxygen correction · stack sampling

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

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

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

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

Where the plume lands

8 formulasFrom a stack to the ground-level concentration at the fence: wind at stack height, plume rise, effective height and the Gaussian equation.

also called: Gaussian plume model · plume rise · effective stack height · ground level concentration · dispersion modelling