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232 results for “time”

Formulae (231)

Percentage

\% = \frac{\text{part}}{\text{whole}} \times 100

What fraction of a whole a part represents, out of 100.

Arithmetic & BasicsBasic

Percent of a Number

\text{value} = \frac{p}{100} \times N

Find p percent of a number N.

Arithmetic & BasicsBasic

Percentage Change

\% \text{change} = \frac{\text{new} - \text{old}}{\text{old}} \times 100

Increase or decrease of a value as a percentage.

Arithmetic & BasicsBasic

Multiplying Fractions

\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}

Multiply numerators and denominators straight across.

Arithmetic & BasicsBasic

Dividing Fractions

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

Divide by multiplying by the reciprocal (flip and multiply).

Arithmetic & BasicsBasic

Speed = Distance ÷ Time

s = \frac{d}{t}

How fast something moves.

Arithmetic & BasicsBasic

Distance = Speed × Time

d = s \times t

How far something travels.

Arithmetic & BasicsBasic

Place Value

N = \sum d_i \times 10^{i}

Each digit’s value depends on its position.

Arithmetic & BasicsBasic

Tip Amount

\text{tip} = \frac{p}{100} \times \text{bill}

Gratuity as a percentage of the bill.

Arithmetic & BasicsBasic

Square of a Number

n^2 = n\times n

A number multiplied by itself.

Arithmetic & BasicsBasic

Cube of a Number

n^3 = n\times n\times n

A number multiplied by itself three times.

AlgebraIntermediate

Logarithm Power Rule

\log_b(x^n) = n \cdot \log_b(x)

The logarithm of a power equals the exponent times the logarithm.

AlgebraIntermediate

Exponential Growth / Decay

A = A_0 e^{kt}

Growth (k>0) or decay (k<0) over time.

Geometry & TrigonometryBasic

Area of a Rectangle

A = l \times w

Area of a rectangle.

Geometry & TrigonometryBasic

Sum of Interior Angles

S = (n - 2)\times 180^\circ

Total of interior angles of an n-sided polygon.

Geometry & TrigonometryIntermediate

Interior Angle (Regular Polygon)

\theta = \frac{(n-2)\times 180^\circ}{n}

Measure of each interior angle of a regular polygon.

Geometry & TrigonometryBasic

Interior Angle Sum

S = (n-2)\times 180\degree

Sum of interior angles of an n-sided polygon.

Geometry & TrigonometryIntermediate

Each Interior Angle (Regular)

\theta = \frac{(n-2)\times 180\degree}{n}

Measure of one interior angle of a regular polygon.

TrigonometryBasic

Degrees to Radians

\text{rad} = \text{deg} \times \frac{\pi}{180}

Convert an angle from degrees to radians.

TrigonometryBasic

Radians to Degrees

\text{deg} = \text{rad} \times \frac{180}{\pi}

Convert an angle from radians to degrees.

Statistics & ProbabilityBasic

Factorial

n! = n\times(n-1)\times\cdots\times 2\times 1

Product of all positive integers up to n.

Statistics & ProbabilityIntermediate

Coefficient of Variation

CV = \frac{\sigma}{\bar{x}}\times 100\%

Relative variability as a percentage of the mean.

Statistics & ProbabilityIntermediate

Coefficient of Variation

CV = \frac{\sigma}{\mu}\times 100

Relative variability as a percentage of the mean.

Statistics & ProbabilityBasic

Percentile Rank

PR = \frac{\text{below}}{n}\times 100

Percentage of values below a given score.

Statistics & ProbabilityAdvanced

Odds Form of Bayes

O(A|B) = O(A)\times \frac{P(B|A)}{P(B|\neg A)}

Updates odds using a likelihood ratio.

Probability & CombinatoricsBasic

Factorial

n! = n \times (n-1) \times \cdots \times 2 \times 1

Product of all positive integers up to n.

Data Science & MLIntermediate

TF-IDF Weight

w_{t,d} = tf_{t,d} \times \log\frac{N}{df_t}

Term importance: frequency in a document scaled by rarity across documents.

Linear AlgebraAdvanced

Cross Product Magnitude

|\vec{a}\times\vec{b}| = |a||b|\sin\theta

Magnitude of the vector perpendicular to two vectors.

Linear AlgebraAdvanced

Scalar Triple Product

\mathbf{a}\cdot(\mathbf{b}\times\mathbf{c})

Volume of the parallelepiped spanned by three vectors.

PhysicsBasic

Newton's Second Law

F = ma

Force equals mass times acceleration.

PhysicsIntermediate

Impulse

J = F\Delta t = \Delta p

Change in momentum from a force over time.

PhysicsBasic

Ohm's Law

V = IR

Voltage equals current times resistance.

PhysicsBasic

Speed

v = \frac{d}{t}

Speed equals distance divided by time.

PhysicsIntermediate

Impulse

J = F\Delta t = \Delta p

Change in momentum from a force over time.

Physics Laws & TheoremsBasic

Newton's Second Law

F = ma = \frac{dp}{dt}

Net force equals mass times acceleration (rate of change of momentum).

Physics Laws & TheoremsAdvanced

Kepler's Second Law

\frac{dA}{dt} = \text{const}

A line from a planet to the Sun sweeps equal areas in equal times.

Physics Laws & TheoremsBasic

Ohm's Law

V = IR

Voltage across a resistor equals current times resistance.

Thermodynamics & HeatAdvanced

Heat Conduction (Fourier)

Q = \frac{kA\Delta T\,t}{d}

Heat conducted through a slab over time.

Optics & WavesBasic

Wave Period

T = \frac{1}{f}

Time for one complete oscillation.

Fluid MechanicsBasic

Volumetric Flow Rate

Q = Av

Volume of fluid passing per unit time.

Modern & Quantum PhysicsAdvanced

Time Dilation

\Delta t = \frac{\Delta t_0}{\sqrt{1 - v^2/c^2}}

Moving clocks run slow.

Modern & Quantum PhysicsIntermediate

Radioactive Decay

N = N_0 e^{-\lambda t}

Number of nuclei remaining over time.

Modern & Quantum PhysicsIntermediate

Half-Life

t_{1/2} = \frac{\ln 2}{\lambda}

Time for half a sample to decay.

Modern & Quantum PhysicsAdvanced

Schrödinger (Time-Independent)

\hat{H}\psi = E\psi

Fundamental equation of quantum mechanics.

Electronics & CircuitsBasic

Ohm's Law

V = IR

Voltage equals current times resistance.

Electronics & CircuitsIntermediate

RC Time Constant

\tau = RC

Time to charge a capacitor to ~63%.

Electronics & CircuitsIntermediate

RL Time Constant

\tau = \frac{L}{R}

Time constant of an inductor-resistor circuit.

ChemistryIntermediate

Percent Yield

\% = \frac{\text{actual}}{\text{theoretical}} \times 100

Efficiency of a chemical reaction.

ChemistryBasic

Avogadro's Number

N = n \times N_A

Number of particles from moles.

ChemistryBasic

Percent Composition

\% = \frac{\text{mass of element}}{\text{molar mass}} \times 100

Mass percentage of an element in a compound.

ChemistryBasic

Avogadro Number

N_A = 6.022\times 10^{23}

Number of particles in one mole.

ChemistryBasic

Number of Particles

N = n\times N_A

Particles from moles and Avogadro number.

ChemistryBasic

Mass Percent

\% = \frac{m_{solute}}{m_{solution}}\times 100

Concentration as a percentage by mass.

Biology & Life SciencesIntermediate

Exponential Population Growth

N_t = N_0 e^{rt}

Unlimited growth of a population over time.

Biology & Life SciencesIntermediate

Population Doubling Time

t_d = \frac{\ln 2}{r}

Time for a population to double.

Biology & Life SciencesIntermediate

GC Content

\%GC = \frac{G + C}{A + T + G + C} \times 100

Proportion of G and C bases in DNA.

Biology & Life SciencesIntermediate

Lincoln-Petersen Estimate

N = \frac{M \times C}{R}

Population size from mark-and-recapture sampling.

Biology & Life SciencesIntermediate

Cardiac Output

CO = HR \times SV

Blood pumped by the heart per minute.

Biology & Life SciencesAdvanced

Hemocytometer Cell Count

C = \bar{n} \times DF \times 10^4

Cells per mL from a counting-chamber average.

Biology & Life SciencesBasic

Bacterial Growth Count

N_t = N_0 \times 2^n

Cell count after n binary fissions.

Biology & Life SciencesIntermediate

Osmolarity

\text{Osm} = n \times C

Solute particle concentration in solution.

Biology & Life SciencesAdvanced

Recombination Frequency

RF = \frac{\text{recombinants}}{\text{total offspring}} \times 100

Genetic map distance in centimorgans.

Biology & Life SciencesIntermediate

Ecological Efficiency

E = \frac{\text{energy at level } n+1}{\text{energy at level } n} \times 100

Energy transfer between trophic levels (~10%).

Biology & Life SciencesBasic

Total Magnification

M = M_{obj}\times M_{eye}

Total magnification of a compound microscope.

Biology & Life SciencesIntermediate

Bacterial Doubling

N = N_0\times 2^{t/g}

Exponential bacterial growth by generations.

Health & FitnessBasic

BMI (Imperial)

BMI = 703 \times \frac{m}{h^2}

BMI using pounds and inches.

Health & FitnessIntermediate

Total Daily Energy (TDEE)

TDEE = BMR \times \text{activity factor}

Daily calories burned including activity.

Health & FitnessIntermediate

Calories Burned (MET)

C = MET \times m \times t

Energy used during exercise.

Health & FitnessBasic

Daily Water Intake

W = 0.033 \times m

Rough daily water need in litres.

Health & FitnessBasic

Protein from Calories

g = \frac{0.30 \times C}{4}

Grams of protein for a 30% protein diet (4 kcal/g).

Health & FitnessBasic

Running Pace

\text{pace} = \frac{t}{d}

Time taken to cover one unit of distance.

Health & FitnessBasic

Step Length from Height

L \approx 0.415 \times h

Estimated walking step length from height.

Health & FitnessAdvanced

Creatinine Clearance (Cockcroft-Gault)

CrCl = \frac{(140 - a)\,m}{72 \times S_{cr}}

Kidney function estimate (men; ×0.85 for women).

Health & FitnessIntermediate

Body Surface Area (Mosteller)

BSA = \sqrt{\frac{h \times m}{3600}}

Total skin surface area of the body.

Health & FitnessIntermediate

One-Rep Max (Brzycki)

1RM = w \times \frac{36}{37 - r}

Estimated one-rep max, an alternative to Epley.

Health & FitnessBasic

Fat Mass

FM = m \times \frac{BF\%}{100}

Total mass of body fat.

Health & FitnessIntermediate

MET to Oxygen Uptake

VO_2 = 3.5 \times MET

Oxygen consumption from a MET activity level.

Health & FitnessBasic

Daily Protein Target

P = 1.6 \times m

Grams of protein per day to build muscle.

Nutrition & FoodBasic

Kilocalories to Kilojoules

kJ = kcal \times 4.184

Convert dietary Calories to the SI energy unit used on many food labels.

Nutrition & FoodBasic

Macro % of Calories

\%_M = \frac{E_M}{E_{total}} \times 100

Share of total energy coming from a given macronutrient.

Nutrition & FoodBasic

Protein Requirement (RDA)

P = 0.8 \times m

Recommended daily protein for a healthy adult (grams).

Nutrition & FoodBasic

Protein Grams from Calories

g = \frac{r \times C}{4}

Grams of protein for a target protein ratio of the diet.

Nutrition & FoodAdvanced

Glycemic Load

GL = \frac{GI \times C}{100}

Impact of a food portion on blood sugar, combining quality (GI) and quantity.

Nutrition & FoodBasic

Percent Daily Value (%DV)

\%DV = \frac{a}{r} \times 100

How much a nutrient in a serving contributes to daily needs.

Nutrition & FoodIntermediate

Baker's Percentage

\%_i = \frac{m_i}{m_{flour}} \times 100

Every ingredient expressed relative to flour weight — the backbone of bread recipes.

Nutrition & FoodIntermediate

Dough Hydration

H = \frac{m_{water}}{m_{flour}} \times 100

Water as a percentage of flour — controls how wet and open a dough is.

Nutrition & FoodBasic

Recipe Scaling Factor

m_{new} = m_{old} \times \frac{n_{want}}{n_{have}}

Rescale each ingredient for a different number of servings.

Nutrition & FoodIntermediate

Brine Salinity

S = \frac{m_{salt}}{m_{salt}+m_{water}} \times 100

Salt concentration of a brine or curing solution by mass.

Nutrition & FoodIntermediate

Yield Percentage

Y = \frac{m_{EP}}{m_{AP}} \times 100

Edible portion left after trimming, relative to the amount purchased.

Nutrition & FoodIntermediate

Food Cost Percentage

FC = \frac{c_{ingredients}}{p_{selling}} \times 100

Ingredient cost as a share of menu price — a core restaurant metric.

Nutrition & FoodAdvanced

Alcohol by Volume (ABV)

ABV = (OG - FG) \times 131.25

Estimated alcohol content of beer or wine from gravity readings.

Astronomy & SpaceBasic

Light-Year

d = c \times t

Distance light travels in a given time.

Astronomy & SpaceIntermediate

Synodic Period

\frac{1}{S} = \left|\frac{1}{P_1} - \frac{1}{P_2}\right|

Time between repeated alignments of two orbiting bodies.

EngineeringBasic

Efficiency

\eta = \frac{P_{out}}{P_{in}} \times 100\%

Ratio of useful output to input power.

EngineeringBasic

Efficiency

\eta = \frac{P_{out}}{P_{in}}\times 100

Ratio of useful output to input power.

EngineeringBasic

Volumetric Flow Rate

Q = Av

Volume of fluid passing per unit time.

EngineeringIntermediate

RC Time Constant

\tau = RC

Charging time constant of a resistor-capacitor circuit.

Aviation & AeronauticsBasic

True Airspeed (rule of thumb)

TAS \approx IAS + (IAS \times 0.02 \times \tfrac{alt}{1000})

Quick estimate: true airspeed increases about 2% per 1000 ft of altitude above indicated airspeed.

Aviation & AeronauticsBasic

Flight Time

t = \dfrac{d}{GS}

Time en route equals distance divided by ground speed.

Aviation & AeronauticsBasic

Fuel Required

F = \dot{f} \times t

Total fuel needed is the fuel-burn rate multiplied by flight time.

Aviation & AeronauticsBasic

Rate of Climb

ROC = \dfrac{\Delta h}{t}

Vertical speed is the altitude gained per unit time (ft per minute).

Aviation & AeronauticsBasic

3-Degree Descent Rate

ROD \approx GS \times 5

On a standard 3° glide path, required descent rate (fpm) is roughly ground speed (kt) times 5.

Aviation & AeronauticsBasic

Pressure Altitude

PA = (29.92 - QNH)\times 1000 + h

Altitude referenced to standard pressure; correct field elevation for the altimeter setting.

Aviation & AeronauticsAdvanced

Maximum Endurance (jet)

E = \dfrac{1}{c}\dfrac{L}{D}\ln\dfrac{W_i}{W_f}

Longest time aloft for a jet, maximized at maximum L/D.

Aviation & AeronauticsBasic

Endurance

E = \frac{\text{fuel}}{\text{fuel flow}}

Time an aircraft can stay airborne.

Finance & InterestBasic

Compound Interest

A = P\left(1 + \frac{r}{n}\right)^{nt}

Value of principal compounded n times per year.

Finance & InterestBasic

Return on Investment

ROI = \frac{V_f - V_i}{V_i} \times 100\%

Percentage gain or loss on an investment.

Finance & InterestBasic

Profit Margin

\text{Margin} = \frac{\text{Profit}}{\text{Revenue}} \times 100\%

Profit as a percentage of revenue.

Finance & InterestBasic

Markup

\text{Markup} = \frac{\text{Price} - \text{Cost}}{\text{Cost}} \times 100\%

Increase over cost as a percentage.

Finance & InterestBasic

Dividend Yield

Y = \frac{\text{Dividend}}{\text{Price}}\times 100

Annual dividend as a percentage of share price.

Finance & InterestBasic

Gross Margin

GM = \frac{Revenue - COGS}{Revenue}\times 100

Percentage of revenue left after cost of goods.

Finance & InterestIntermediate

Return on Equity

ROE = \frac{\text{Net Income}}{\text{Equity}}\times 100

Profit generated per dollar of equity.

Finance & InterestIntermediate

Return on Assets

ROA = \frac{\text{Net Income}}{\text{Total Assets}}\times 100

Profit generated per dollar of assets.

Finance & InterestBasic

Payback Period

PP = \frac{\text{Initial Investment}}{\text{Annual Cash Flow}}

Time to recover an investment.

AccountingIntermediate

Inventory Turnover

IT = \dfrac{COGS}{Average\ Inventory}

How many times inventory is sold and replaced over a period.

AccountingIntermediate

Net Profit Margin

NPM = \dfrac{Net\ Income}{Revenue}\times 100\%

The percentage of revenue that survives as profit after all costs.

AccountingAdvanced

Double-Declining Balance

D = \dfrac{2}{n}\times Book\ Value

An accelerated depreciation method charging more expense in an asset’s early years.

AccountingIntermediate

Inventory Turnover

IT = \frac{COGS}{\text{Avg Inventory}}

How many times inventory is sold per period.

AccountingAdvanced

Double Declining Depreciation

D = \frac{2}{n}\times BV

Accelerated depreciation of an asset.

AccountingIntermediate

Operating Margin

OM = \frac{\text{Operating Income}}{Revenue}\times 100

Profit from core operations as a percent of revenue.

Business & CommerceBasic

Selling Price from Markup

SP = Cost \times (1 + m)

The price to charge after adding a percentage markup to unit cost.

Business & CommerceBasic

Discounted Price

P = List \times (1 - d)

The final price after applying a percentage discount to the list price.

Business & CommerceBasic

Sales Tax

Total = Price \times (1 + t)

The amount payable once a sales-tax or VAT rate is added to the price.

Business & CommerceBasic

Revenue

Revenue = Price \times Quantity

Total income from sales before any costs are deducted.

Business & CommerceIntermediate

Margin of Safety

MoS = \dfrac{Sales - Break\text{-}even}{Sales}\times 100\%

How far sales can fall before the business hits its break-even point.

Business & CommerceIntermediate

Customer Lifetime Value (CLV)

CLV = \dfrac{ARPU \times Gross\ Margin}{Churn\ Rate}

The total profit expected from a customer over the whole relationship.

Business & CommerceIntermediate

Churn Rate

Churn = \dfrac{Customers\ Lost}{Customers\ at\ Start}\times 100\%

The percentage of customers who stop buying over a period.

Business & CommerceIntermediate

Conversion Rate

CR = \dfrac{Conversions}{Visitors}\times 100\%

The share of visitors or leads that take the desired action.

EconomicsBasic

GDP Growth Rate

g = \dfrac{GDP_1 - GDP_0}{GDP_0}\times 100\%

The percentage change in real output between two periods.

EconomicsBasic

Inflation Rate

\pi = \dfrac{CPI_1 - CPI_0}{CPI_0}\times 100\%

The rate at which the general price level rises over time.

EconomicsBasic

Unemployment Rate

u = \dfrac{Unemployed}{Labor\ Force}\times 100\%

The share of the labor force that is jobless and actively seeking work.

EconomicsIntermediate

Real GDP

Real\ GDP = \dfrac{Nominal\ GDP}{Deflator}\times 100

Output adjusted for inflation, so growth reflects real production, not rising prices.

EconomicsIntermediate

GDP Deflator

Deflator = \dfrac{Nominal\ GDP}{Real\ GDP}\times 100

A broad price index covering all goods in GDP, not just a consumer basket.

EconomicsAdvanced

Quantity Theory of Money

M \times V = P \times Q

Links the money supply and its velocity to the price level and real output.

EconomicsAdvanced

Consumer Surplus

CS = \tfrac{1}{2}\times \Delta P \times \Delta Q

The benefit consumers gain when they pay less than the maximum they were willing to pay.

EconomicsIntermediate

Consumer Price Index

CPI = \frac{\text{Basket now}}{\text{Basket base}}\times 100

Measures price levels relative to a base year.

EconomicsBasic

Inflation Rate

\pi = \frac{CPI_1 - CPI_0}{CPI_0}\times 100

Percentage change in the price index.

EconomicsBasic

Unemployment Rate

u = \frac{\text{Unemployed}}{\text{Labor Force}}\times 100

Fraction of the labor force without work.

EconomicsIntermediate

Real GDP

Real = \frac{Nominal}{Deflator}\times 100

GDP adjusted for inflation.

Currency & ForexBasic

Currency Conversion

Foreign = Domestic \times Rate

Convert an amount from one currency to another using the quoted exchange rate.

Currency & ForexBasic

Currency % Change

\%\Delta = \dfrac{Rate_1 - Rate_0}{Rate_0}\times 100\%

The percentage move in an exchange rate between two points in time.

Currency & ForexIntermediate

Cross Rate

Rate_{A/C} = Rate_{A/B} \times Rate_{B/C}

Derive the exchange rate between two currencies via a common third currency.

Currency & ForexIntermediate

Spread Percentage

Spread\% = \dfrac{Ask - Bid}{Ask}\times 100\%

The bid-ask spread expressed as a percentage of the ask price.

Currency & ForexIntermediate

Pip Value

Pip\ Value = \dfrac{Pip\ Size}{Rate}\times Lot

The monetary value of a one-pip move for a given trade size.

Currency & ForexIntermediate

Appreciation / Depreciation

App\% = \dfrac{Rate_1 - Rate_0}{Rate_0}\times 100\%

The percentage by which a currency strengthens (positive) or weakens (negative).

Currency & ForexAdvanced

Real Exchange Rate

RER = S \times \dfrac{P_{foreign}}{P_{domestic}}

The nominal rate adjusted for price levels, measuring relative purchasing power.

Currency & ForexAdvanced

Forward Exchange Rate

F = S \times \dfrac{1 + i_d}{1 + i_f}

The agreed future exchange rate implied by interest-rate differentials (covered interest parity).

Currency & ForexAdvanced

Triangular Arbitrage

Profit = \left(\dfrac{1}{R_{AB}} \times R_{AC} \times R_{CB}\right) - 1

A riskless profit captured when three currencies’ cross rates are momentarily inconsistent.

Everyday MathBasic

Tip Amount

\text{Tip} = B \times r

Gratuity based on a bill amount.

Everyday MathBasic

Trip Fuel Cost

\text{Cost} = \frac{D}{E} \times p

Total fuel cost for a trip.

Everyday MathBasic

Average Speed

v = \frac{d}{t}

Distance covered per unit time.

Everyday MathBasic

Travel Time

t = \frac{d}{v}

Time needed to cover a distance at a given speed.

Everyday MathBasic

Recipe Scaling

Q_{new} = Q_{old} \times \frac{S_{new}}{S_{old}}

Adjust ingredient quantities for a different number of servings.

Everyday MathBasic

Room Area

A = l \times w

Floor area of a rectangular room.

Everyday MathBasic

Percentage Change

\%\Delta = \frac{new - old}{old}\times 100

Relative change between two values.

Everyday MathIntermediate

Weight Loss Estimate

\Delta w = \frac{\text{deficit} \times days}{7700}

Approximate body-mass loss from a calorie deficit (kg).

Everyday MathBasic

Aspect Ratio Scaling

h = w \times \frac{r_h}{r_w}

Find a height that preserves an aspect ratio.

Time & CalendarBasic

Leap Year Rule

\text{leap} \iff (y \bmod 4 = 0 \;\wedge\; y \bmod 100 \neq 0) \;\vee\; (y \bmod 400 = 0)

Tests whether a Gregorian year has 366 days.

Time & CalendarBasic

Clock Hand Angle

\theta = |30H - 5.5M|

Angle between the hour and minute hands of an analog clock.

Time & CalendarAdvanced

Zeller's Congruence

h = \left(q + \left\lfloor\tfrac{13(m+1)}{5}\right\rfloor + K + \left\lfloor\tfrac{K}{4}\right\rfloor + \left\lfloor\tfrac{J}{4}\right\rfloor + 5J\right) \bmod 7

Finds the day of the week for any Gregorian date.

Time & CalendarIntermediate

Day of the Week from a Birthdate

W = \left(d + \left\lfloor 2.6m - 0.2 \right\rfloor + y + \left\lfloor\tfrac{y}{4}\right\rfloor + \left\lfloor\tfrac{c}{4}\right\rfloor - 2c\right) \bmod 7

Gauss's weekday formula — find which day of the week any birthdate fell on.

Time & CalendarAdvanced

Julian Day Number

JDN = \left\lfloor 365.25(Y+4716) \right\rfloor + \left\lfloor 30.6001(M+1) \right\rfloor + D + B - 1524

Continuous day count used by astronomers to compare dates.

Time & CalendarIntermediate

Days Between Two Dates

\Delta = JDN_2 - JDN_1

Number of days separating two calendar dates.

Time & CalendarBasic

Age in Years

A = \left\lfloor \dfrac{JDN_{today} - JDN_{birth}}{365.2425} \right\rfloor

Whole years elapsed since a birth date.

Time & CalendarIntermediate

Unix Timestamp

t = 86400\,d + 3600h + 60m + s

Seconds elapsed since 1970-01-01 00:00:00 UTC (the epoch).

Time & CalendarAdvanced

Sidereal Day

T_{sid} = \dfrac{T_{sol}}{1 + T_{sol}/T_{yr}}

Earth's rotation period measured against the stars, not the Sun.

Time & CalendarAdvanced

ISO Week Number

W = \left\lfloor \dfrac{d_o - w_d + 10}{7} \right\rfloor

ISO-8601 week of the year (weeks start on Monday).

Time & CalendarBasic

Local Time from UTC

t_{local} = t_{UTC} + \Delta

Convert Coordinated Universal Time to a local zone.

Time & CalendarAdvanced

Equation of Time

E \approx 9.87\sin 2B - 7.53\cos B - 1.5\sin B

Difference between sundial (apparent) and clock (mean) time.

Time & CalendarBasic

Period & Frequency

T = \dfrac{1}{f}

A repeating event's period is the reciprocal of its frequency.

Time & CalendarIntermediate

Ordinal Day of Year

N = \left\lfloor \dfrac{275M}{9} \right\rfloor - k\left\lfloor \dfrac{M+9}{12} \right\rfloor + D - 30

Day-of-year number (1–366) for a given date.

Time & CalendarAdvanced

Easter Date (Computus)

d = (19a + b) \bmod 30,\quad a = y \bmod 19

Core step of the Gregorian algorithm locating the Paschal full moon.

Geography & EarthBasic

Slope / Gradient

\text{gradient} = \frac{\text{rise}}{\text{run}} \times 100\%

Steepness of terrain as a percentage.

Geography & EarthBasic

Time Zone Difference

\Delta t = \frac{\Delta \text{longitude}}{15^\circ}

Each 15 degrees of longitude equals one hour.

Environmental ScienceBasic

Carbon Footprint

CO_2 = E \times f

Emissions from energy use and an emission factor.

Environmental ScienceIntermediate

Solar Panel Output

P = A \times r \times H \times PR

Energy output of a photovoltaic array.

Environmental ScienceBasic

Energy Consumption

E = P \times t

Electrical energy used over time.

Environmental ScienceIntermediate

Energy Payback Ratio

EPR = \frac{E_{generated}}{E_{invested}}

Energy produced over a lifetime divided by energy to build it.

Unit ConversionsBasic

Celsius to Fahrenheit

°F = °C \times \frac{9}{5} + 32

Convert a temperature from Celsius to Fahrenheit.

Unit ConversionsBasic

Fahrenheit to Celsius

°C = (°F - 32) \times \frac{5}{9}

Convert a temperature from Fahrenheit to Celsius.

Unit ConversionsBasic

Kilometers to Miles

\text{mi} = \text{km} \times 0.621371

Convert kilometers to miles.

Unit ConversionsBasic

Miles to Kilometers

\text{km} = \text{mi} \times 1.60934

Convert miles to kilometers.

Unit ConversionsBasic

Meters to Feet

\text{ft} = \text{m} \times 3.28084

Convert meters to feet.

Unit ConversionsBasic

Feet to Meters

\text{m} = \text{ft} \times 0.3048

Convert feet to meters.

Unit ConversionsBasic

Inches to Centimeters

\text{cm} = \text{in} \times 2.54

Convert inches to centimeters.

Unit ConversionsBasic

Nautical Miles to Kilometers

\text{km} = \text{nmi} \times 1.852

Convert nautical miles to kilometers.

Unit ConversionsBasic

Square Meters to Square Feet

\text{ft}^2 = \text{m}^2 \times 10.7639

Convert area from square meters to square feet.

Unit ConversionsBasic

Acres to Square Meters

\text{m}^2 = \text{acre} \times 4046.86

Convert acres to square meters.

Unit ConversionsBasic

Hectares to Acres

\text{acre} = \text{ha} \times 2.47105

Convert hectares to acres.

Unit ConversionsBasic

Square Km to Square Miles

\text{mi}^2 = \text{km}^2 \times 0.386102

Convert area from square kilometers to square miles.

Unit ConversionsBasic

Liters to US Gallons

\text{gal} = \text{L} \times 0.264172

Convert liters to US gallons.

Unit ConversionsBasic

US Gallons to Liters

\text{L} = \text{gal} \times 3.78541

Convert US gallons to liters.

Unit ConversionsBasic

Cubic Meters to Cubic Feet

\text{ft}^3 = \text{m}^3 \times 35.3147

Convert volume from cubic meters to cubic feet.

Unit ConversionsBasic

Milliliters to Fluid Ounces

\text{fl oz} = \text{mL} \times 0.033814

Convert milliliters to US fluid ounces.

Unit ConversionsBasic

Kilograms to Pounds

\text{lb} = \text{kg} \times 2.20462

Convert kilograms to pounds.

Unit ConversionsBasic

Pounds to Kilograms

\text{kg} = \text{lb} \times 0.453592

Convert pounds to kilograms.

Unit ConversionsBasic

Grams to Ounces

\text{oz} = \text{g} \times 0.035274

Convert grams to ounces.

Unit ConversionsBasic

Metric Tonnes to Pounds

\text{lb} = \text{t} \times 2204.62

Convert metric tonnes to pounds.

Unit ConversionsBasic

km/h to mph

\text{mph} = \text{km/h} \times 0.621371

Convert speed from km/h to mph.

Unit ConversionsBasic

m/s to km/h

\text{km/h} = \text{m/s} \times 3.6

Convert speed from meters per second to km/h.

Unit ConversionsBasic

Calories to Joules

\text{J} = \text{cal} \times 4.184

Convert calories to joules.

Unit ConversionsBasic

kWh to Joules

\text{J} = \text{kWh} \times 3.6\times10^6

Convert kilowatt-hours to joules.

Unit ConversionsBasic

Atmospheres to Pascals

\text{Pa} = \text{atm} \times 101325

Convert atmospheres to pascals.

Unit ConversionsBasic

Bar to PSI

\text{psi} = \text{bar} \times 14.5038

Convert bar to pounds per square inch.

Unit ConversionsBasic

Degrees to Radians

\text{rad} = \text{deg} \times \frac{\pi}{180}

Convert an angle from degrees to radians.

Unit ConversionsBasic

Radians to Degrees

\text{deg} = \text{rad} \times \frac{180}{\pi}

Convert an angle from radians to degrees.

Unit ConversionsBasic

Gigabytes to Megabytes

\text{MB} = \text{GB} \times 1024

Convert gigabytes to megabytes (binary).

Unit ConversionsBasic

Kilometers to Miles

\text{mi} = km \times 0.6214

Convert kilometers to miles.

Unit ConversionsBasic

Miles to Kilometers

km = mi \times 1.6093

Convert miles to kilometers.

Unit ConversionsBasic

Kilograms to Pounds

lb = kg \times 2.2046

Convert kilograms to pounds.

Unit ConversionsBasic

Pounds to Kilograms

kg = lb \times 0.4536

Convert pounds to kilograms.

Unit ConversionsBasic

Inches to Centimeters

cm = in \times 2.54

Convert inches to centimeters.

Unit ConversionsBasic

Liters to US Gallons

gal = L \times 0.2642

Convert liters to US gallons.

Unit ConversionsBasic

MPH to KM/H

km/h = mph \times 1.6093

Convert miles per hour to kilometers per hour.

Unit ConversionsBasic

Calories to Joules

J = cal \times 4.184

Convert calories to joules.

Unit ConversionsBasic

Atmospheres to Pascals

Pa = atm \times 101325

Convert atmospheres to pascals.

Unit ConversionsBasic

Horsepower to Watts

W = hp \times 745.7

Convert horsepower to watts.

Unit ConversionsBasic

Bytes to Bits

bits = bytes \times 8

Convert bytes to bits.

Unit ConversionsBasic

Radians to Degrees

\deg = rad \times \frac{180}{\pi}

Convert radians to degrees.

Unit ConversionsBasic

Acres to Square Meters

m^2 = acre \times 4046.9

Convert acres to square meters.

Unit ConversionsBasic

Feet to Meters

m = ft \times 0.3048

Convert feet to meters.

Computer ScienceAdvanced

Master Theorem (form)

T(n) = aT(n/b) + f(n)

Analyzes running time of divide-and-conquer algorithms.

Computer ScienceIntermediate

Common Time Complexities

O(1) < O(\log n) < O(n) < O(n\log n) < O(n^2) < O(2^n)

Ordering of common algorithmic growth rates.

Computer ScienceIntermediate

Logarithmic Time

O(\log n)

Runtime that grows logarithmically with input size.

Computer ScienceIntermediate

Linearithmic Time

O(n\log n)

Runtime of efficient comparison sorts.

Computer ScienceBasic

Quadratic Time

O(n^2)

Runtime that grows with the square of input size.

Computer ScienceAdvanced

Exponential Time

O(2^n)

Runtime that doubles with each added element.

Computer ScienceBasic

Data Transfer Time

t = \frac{S}{R}

Time to transfer data of a given size at a rate.

Computer ScienceBasic

Hexadecimal to Decimal

d = \sum h_i \times 16^i

Convert a hex number to decimal by positional weights.

Computer ScienceAdvanced

Average Memory Access Time

AMAT = H + M \times P

Effective access time from hit time, miss rate, and penalty.

Computer ScienceBasic

Throughput

X = \frac{N}{T}

Number of operations completed per unit time.

Math Tricks (1)

Multiply by 4 and 8 by Doubling

Multiplying by 4 is doubling twice; by 8 is doubling three times. No memorised tables needed.

View trick