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196 results for “rc”

Formulae (193)

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

Discount Price

\text{price} = N \left(1 - \frac{p}{100}\right)

Final price after a percentage discount.

Arithmetic & BasicsBasic

Sales Tax Total

\text{total} = N \left(1 + \frac{t}{100}\right)

Price after adding a percentage tax.

Arithmetic & BasicsBasic

Tip Amount

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

Gratuity as a percentage of the bill.

Arithmetic & BasicsBasic

Percent Increase

new = old(1 + p)

Value after a percentage increase.

Arithmetic & BasicsBasic

Percent Decrease

new = old(1 - p)

Value after a percentage decrease.

Arithmetic & BasicsBasic

Percent to Fraction

p\% = \frac{p}{100}

Convert a percentage to a fraction.

AlgebraBasic

Slope-Intercept Form

y = mx + b

Equation of a straight line.

Geometry & TrigonometryBasic

Area of a Circle

A = \pi r^2

The area enclosed by a circle.

Geometry & TrigonometryBasic

Circumference of a Circle

C = 2\pi r

The perimeter (boundary length) of a circle.

Geometry & TrigonometryBasic

Arc Length

s = r\theta

Length of a circular arc (θ in radians).

Geometry & TrigonometryBasic

Area of a Sector

A = \frac{1}{2} r^2 \theta

Area of a circular sector (θ in radians).

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 & TrigonometryAdvanced

Circumradius

R = \frac{abc}{4K}

Radius of a triangle circumscribed circle.

Geometry & TrigonometryAdvanced

Inradius

r = \frac{K}{s}

Radius of a triangle inscribed circle.

Geometry & TrigonometryBasic

Arc Length (Radians)

s = r\theta

Arc length from radius and central angle in radians.

Geometry & TrigonometryIntermediate

Sector Area (Radians)

A = \frac{1}{2}r^2\theta

Area of a circular sector with angle in radians.

TrigonometryBasic

Pythagorean Identity

\sin^2\theta + \cos^2\theta = 1

The fundamental trig identity from the unit circle.

CalculusAdvanced

Arc Length (Integral)

L = \int_a^b \sqrt{1 + (f'(x))^2}\,dx

Length of a curve y = f(x) from a to b.

CalculusAdvanced

Arc Length

L = \int_a^b \sqrt{1 + [f'(x)]^2}\,dx

Length of a curve between two points.

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.

Probability & CombinatoricsIntermediate

Pigeonhole Principle

\lceil n/k \rceil

If n items go into k containers, some container holds at least this many.

PhysicsBasic

Newton's Second Law

F = ma

Force equals mass times acceleration.

PhysicsBasic

Work Done

W = F d \cos\theta

Work done by a force over a distance.

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.

PhysicsAdvanced

Coulomb's Law

F = k\frac{q_1 q_2}{r^2}

Electrostatic force between two charges.

PhysicsIntermediate

Newton's Gravitation

F = G\frac{m_1 m_2}{r^2}

Attractive force between two masses.

PhysicsIntermediate

Hooke's Law

F = -kx

Restoring force of a spring.

PhysicsAdvanced

Centripetal Force

F = \frac{mv^2}{r}

Force needed to keep an object in circular motion.

PhysicsBasic

Pressure

P = \frac{F}{A}

Force per unit area.

PhysicsBasic

Weight

W = mg

The gravitational force on a mass.

PhysicsBasic

Mechanical Advantage

MA = \frac{F_{out}}{F_{in}}

Force amplification of a simple machine.

PhysicsBasic

Weight

W = mg

Gravitational force on a mass near Earth.

PhysicsBasic

Hooke Law

F = -kx

Restoring force of a spring proportional to displacement.

PhysicsIntermediate

Impulse

J = F\Delta t = \Delta p

Change in momentum from a force over time.

PhysicsIntermediate

Torque

\tau = rF\sin\theta

Rotational effect of a force about a pivot.

PhysicsAdvanced

Orbital Velocity

v = \sqrt{\frac{GM}{r}}

Speed needed for a circular orbit.

PhysicsBasic

Friction Force

f = \mu N

Resistive force between surfaces.

PhysicsIntermediate

Centripetal Force

F = \frac{mv^2}{r}

Inward force needed for circular motion.

Physics Laws & TheoremsBasic

Newton's First Law (Inertia)

\sum F = 0 \Rightarrow v = \text{const}

An object stays at rest or in uniform motion unless acted on by a net force.

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 & TheoremsIntermediate

Archimedes' Principle

F_b = \rho g V

Buoyant force equals the weight of fluid displaced.

Physics Laws & TheoremsBasic

Hooke's Law

F = -kx

The restoring force of a spring is proportional to its extension.

Physics Laws & TheoremsBasic

Ohm's Law

V = IR

Voltage across a resistor equals current times resistance.

Physics Laws & TheoremsIntermediate

Coulomb's Law

F = k\frac{q_1 q_2}{r^2}

Electrostatic force between two point charges.

Physics Laws & TheoremsAdvanced

Faraday's Law of Induction

\varepsilon = -\frac{d\Phi_B}{dt}

A changing magnetic flux induces an electromotive force.

Physics Laws & TheoremsAdvanced

Ampère's Law

\oint \vec{B} \cdot d\vec{l} = \mu_0 I

A magnetic field circulates around an electric current.

Physics Laws & TheoremsIntermediate

Kirchhoff's Current Law

\sum I_{in} = \sum I_{out}

Current into a junction equals current out of it (charge conservation).

Physics Laws & TheoremsIntermediate

Kirchhoff's Voltage Law

\sum V = 0

The sum of voltages around any closed loop is zero.

Physics Laws & TheoremsIntermediate

Mass–Energy Equivalence

E = mc^2

Mass and energy are equivalent and interconvertible.

Physics Laws & TheoremsIntermediate

Conservation of Momentum

\sum p_i = \sum p_f

Total momentum is conserved without external forces.

Physics Laws & TheoremsBasic

Hooke Law

F = -kx

Elastic restoring force is proportional to displacement.

Physics Laws & TheoremsIntermediate

Archimedes Principle

F_b = \rho V g

Buoyant force equals the weight of displaced fluid.

Electricity & MagnetismIntermediate

Coulomb's Law

F = k\frac{q_1 q_2}{r^2}

Force between two point charges.

Electricity & MagnetismBasic

Electric Field

E = \frac{F}{q}

Force per unit charge at a point.

Electricity & MagnetismIntermediate

Magnetic Force on a Charge

F = qvB\sin\theta

Force on a moving charge in a magnetic field.

Electricity & MagnetismIntermediate

Force on a Current Wire

F = BIL\sin\theta

Force on a current-carrying conductor.

Fluid MechanicsBasic

Pressure

P = \frac{F}{A}

Force per unit area.

Fluid MechanicsIntermediate

Archimedes' Principle

F_b = \rho g V

Buoyant force equals weight of displaced fluid.

Fluid MechanicsIntermediate

Surface Tension

\gamma = \frac{F}{L}

Force per unit length along a liquid surface.

Fluid MechanicsAdvanced

Drag Force

F_D = \tfrac{1}{2}\rho v^2 C_D A

Aerodynamic drag on a moving body.

Electronics & CircuitsBasic

Ohm's Law

V = IR

Voltage equals current times resistance.

Electronics & CircuitsBasic

Electrical Power (VI)

P = VI

Power dissipated by a component.

Electronics & CircuitsBasic

Power (I²R)

P = I^2 R

Power lost as heat in a resistor.

Electronics & CircuitsBasic

Power (V²/R)

P = \frac{V^2}{R}

Power from voltage and resistance.

Electronics & CircuitsBasic

Resistors in Series

R_{eq} = R_1 + R_2 + \cdots

Series resistances add directly.

Electronics & CircuitsIntermediate

Resistors in Parallel

\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \cdots

Reciprocals of parallel resistances add.

Electronics & CircuitsIntermediate

Capacitors in Parallel

C_{eq} = C_1 + C_2 + \cdots

Parallel capacitances add.

Electronics & CircuitsIntermediate

Capacitors in Series

\frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + \cdots

Reciprocals of series capacitances add.

Electronics & CircuitsBasic

Capacitance

C = \frac{Q}{V}

Charge stored per unit voltage.

Electronics & CircuitsIntermediate

Capacitor Energy

E = \tfrac{1}{2}CV^2

Energy stored in a capacitor.

Electronics & CircuitsIntermediate

Inductor Energy

E = \tfrac{1}{2}LI^2

Energy stored in a magnetic field.

Electronics & CircuitsAdvanced

Capacitive Reactance

X_C = \frac{1}{2\pi f C}

Opposition of a capacitor to AC.

Electronics & CircuitsAdvanced

Inductive Reactance

X_L = 2\pi f L

Opposition of an inductor to AC.

Electronics & CircuitsAdvanced

Impedance (RLC)

Z = \sqrt{R^2 + (X_L - X_C)^2}

Total opposition in an AC circuit.

Electronics & CircuitsAdvanced

Resonant Frequency

f_0 = \frac{1}{2\pi\sqrt{LC}}

Frequency at which an LC circuit resonates.

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.

Electronics & CircuitsIntermediate

Voltage Divider

V_{out} = V_{in}\frac{R_2}{R_1 + R_2}

Output voltage from two series resistors.

Electronics & CircuitsAdvanced

Current Divider

I_1 = I\frac{R_2}{R_1 + R_2}

Current split between two parallel resistors.

Electronics & CircuitsIntermediate

Kirchhoff's Voltage Law

\sum V = 0

Voltages around any closed loop sum to zero.

Electronics & CircuitsIntermediate

Kirchhoff's Current Law

\sum I_{in} = \sum I_{out}

Current into a node equals current out.

Electronics & CircuitsIntermediate

RMS Voltage

V_{rms} = \frac{V_{peak}}{\sqrt{2}}

Effective value of a sinusoidal voltage.

Electronics & CircuitsAdvanced

AC Real Power

P = VI\cos\phi

Real power with a phase angle between V and I.

Electronics & CircuitsIntermediate

Decibel (Power)

dB = 10\log_{10}\frac{P_2}{P_1}

Power ratio expressed in decibels.

Electronics & CircuitsIntermediate

Decibel (Voltage)

dB = 20\log_{10}\frac{V_2}{V_1}

Voltage ratio in decibels.

Electronics & CircuitsIntermediate

Transformer Turns Ratio

\frac{V_p}{V_s} = \frac{N_p}{N_s}

Voltage ratio equals turns ratio.

Electronics & CircuitsAdvanced

Inverting Amplifier Gain

A_v = -\frac{R_f}{R_{in}}

Gain of an inverting op-amp.

Electronics & CircuitsAdvanced

Non-Inverting Gain

A_v = 1 + \frac{R_f}{R_{in}}

Gain of a non-inverting op-amp.

Electronics & CircuitsBasic

LED Series Resistor

R = \frac{V_s - V_f}{I}

Resistor to safely drive an LED.

Electronics & CircuitsBasic

Charge from Current

Q = It

Charge transferred by a steady current.

Electronics & CircuitsAdvanced

Drift Velocity

v_d = \frac{I}{nAq}

Average velocity of charge carriers.

Electronics & CircuitsIntermediate

Wire Resistance

R = \frac{\rho L}{A}

Resistance from resistivity, length and area.

Electronics & CircuitsAdvanced

Nyquist Bit Rate

C = 2B\log_2 M

Maximum data rate of a noiseless channel.

Electronics & CircuitsBasic

AND Gate

Y = A \cdot B

Output is 1 only when both inputs are 1.

Electronics & CircuitsBasic

OR Gate

Y = A + B

Output is 1 if either input is 1.

Electronics & CircuitsIntermediate

XOR Gate

Y = A \oplus B

Output is 1 when inputs differ.

Electronics & CircuitsAdvanced

Apparent Power

S = \sqrt{P^2 + Q^2}

Combination of real and reactive power.

Electronics & CircuitsAdvanced

Resonant Frequency

f_0 = \frac{1}{2\pi\sqrt{LC}}

Frequency where an LC circuit resonates.

Electronics & CircuitsAdvanced

Quality Factor

Q = \frac{f_0}{\Delta f}

Sharpness of a resonant peak.

Electronics & CircuitsIntermediate

Capacitor Energy

E = \frac{1}{2}CV^2

Energy stored in a capacitor.

Electronics & CircuitsIntermediate

Inductor Energy

E = \frac{1}{2}LI^2

Energy stored in an inductor magnetic field.

Electronics & CircuitsBasic

Capacitor Charge

Q = CV

Charge stored on a capacitor.

Electronics & CircuitsBasic

Current from Charge

I = \frac{Q}{t}

Current as the rate of charge flow.

Electronics & CircuitsIntermediate

LED Series Resistor

R = \frac{V_s - V_f}{I}

Resistor to safely drive an LED.

Electronics & CircuitsAdvanced

Wheatstone Bridge Balance

\frac{R_1}{R_2} = \frac{R_3}{R_4}

Condition for a balanced measurement bridge.

Electronics & CircuitsBasic

Voltage Divider Output

V_{out} = V_{in}\frac{R_2}{R_1 + R_2}

Output of a two-resistor divider.

ChemistryAdvanced

Nernst Equation

E = E^\circ - \frac{RT}{nF}\ln Q

Cell potential under non-standard conditions.

ChemistryIntermediate

Percent Yield

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

Efficiency of a chemical reaction.

ChemistryBasic

Percent Composition

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

Mass percentage of an element in a compound.

ChemistryBasic

Mass Percent

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

Concentration as a percentage by mass.

Biology & Life SciencesIntermediate

Cardiac Output

CO = HR \times SV

Blood pumped by the heart per minute.

Health & FitnessIntermediate

Calories Burned (MET)

C = MET \times m \times t

Energy used during exercise.

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

MET to Oxygen Uptake

VO_2 = 3.5 \times MET

Oxygen consumption from a MET activity level.

Nutrition & FoodBasic

Macro % of Calories

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

Share of total energy coming from a given macronutrient.

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 & 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.

Astronomy & SpaceIntermediate

Orbital Velocity

v = \sqrt{\frac{GM}{r}}

Speed of a circular orbit.

Astronomy & SpaceAdvanced

Parallax Distance

d = \frac{1}{p}

Distance in parsecs from parallax angle in arcseconds.

Astronomy & SpaceIntermediate

Newton's Law of Gravitation

F = G\frac{m_1 m_2}{r^2}

The attractive force between any two masses.

Astronomy & SpaceAdvanced

Photon Sphere Radius

r_{ph} = \frac{3GM}{c^2}

Radius where gravity bends light into a circular orbit.

Astronomy & SpaceAdvanced

Gravitational Redshift

z \approx \frac{GM}{rc^2}

Fractional stretching of light climbing out of gravity.

EngineeringBasic

Stress

\sigma = \frac{F}{A}

Internal force per unit area in a material.

EngineeringBasic

Electrical Power

P = VI

Power in an electrical circuit.

EngineeringIntermediate

Torque

\tau = r F \sin\theta

Rotational force about a pivot.

EngineeringBasic

Resistors in Series

R_{eq} = R_1 + R_2 + \cdots

Total resistance of resistors in series.

EngineeringIntermediate

Resistors in Parallel

\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \cdots

Total resistance of resistors in parallel.

EngineeringBasic

Mechanical Advantage

MA = \frac{F_{out}}{F_{in}}

Force amplification of a machine.

EngineeringIntermediate

RC Time Constant

\tau = RC

Charging time constant of a resistor-capacitor circuit.

Materials & CivilBasic

Stress

\sigma = \frac{F}{A}

Internal force per unit cross-sectional area.

Aviation & AeronauticsIntermediate

Drag Equation

D = \tfrac{1}{2}\rho v^2 S C_D

Aerodynamic drag force on the aircraft, analogous to lift with a drag coefficient.

Aviation & AeronauticsIntermediate

Load Factor in a Turn

n = \dfrac{1}{\cos\phi}

The g-load in a level, coordinated turn depends only on the bank angle.

Aviation & AeronauticsIntermediate

Crosswind Component

XW = V_w\sin\theta

Crosswind component determines whether landing is within aircraft limits.

Aviation & AeronauticsIntermediate

Point of No Return

PNR = \dfrac{E \cdot GS_{out} \cdot GS_{back}}{GS_{out}+GS_{back}}

Farthest distance an aircraft can fly and still return with available endurance.

Aviation & AeronauticsAdvanced

Reynolds Number

Re = \dfrac{\rho v L}{\mu}

Ratio of inertial to viscous forces; characterises airflow over an airfoil.

Aviation & AeronauticsAdvanced

Breguet Range Equation

R = \dfrac{V}{c}\dfrac{L}{D}\ln\dfrac{W_i}{W_f}

Maximum range of a jet aircraft from speed, efficiency, L/D and fuel fraction.

Aviation & AeronauticsAdvanced

Great Circle Distance

d = R\arccos(\sin\phi_1\sin\phi_2 + \cos\phi_1\cos\phi_2\cos\Delta\lambda)

Shortest distance between two points on the Earth for long-range navigation.

Aviation & AeronauticsIntermediate

Load Factor

n = \frac{L}{W}

Ratio of lift to weight, felt as g-force.

Aviation & AeronauticsIntermediate

Wing Loading

WL = \frac{W}{S}

Aircraft weight per unit wing area.

Aviation & AeronauticsBasic

Endurance

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

Time an aircraft can stay airborne.

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.

AccountingBasic

Cost of Goods Sold

COGS = Opening\ Inventory + Purchases - Closing\ Inventory

The direct cost of the inventory actually sold during a period.

AccountingIntermediate

Net Profit Margin

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

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

AccountingIntermediate

Cost of Goods Sold

COGS = Beginning + Purchases - Ending

Direct cost of goods sold in a period.

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

Contribution Margin

CM = Price - Variable\ Cost

The amount each unit sold contributes toward covering fixed costs and profit.

Business & CommerceIntermediate

Contribution Margin Ratio

CMR = \dfrac{Price - Variable\ Cost}{Price}

Contribution margin expressed as a fraction of the selling price.

Business & CommerceIntermediate

Break-Even (Units)

Q = \dfrac{Fixed\ Costs}{Price - Variable\ Cost}

The number of units that must be sold to exactly cover all costs.

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

Economic Order Quantity (EOQ)

EOQ = \sqrt{\dfrac{2DS}{H}}

The order size that minimizes total inventory ordering and holding costs.

Business & CommerceIntermediate

Customer Acquisition Cost (CAC)

CAC = \dfrac{Sales\ \&\ Marketing\ Cost}{New\ Customers}

The average cost to win one new customer.

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.

Business & CommerceAdvanced

Month-over-Month Growth

g = \left(\dfrac{V_1}{V_0}\right) - 1

The percentage change in a metric from one period to the next.

EconomicsBasic

GDP Growth Rate

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

The percentage change in real output between two periods.

EconomicsBasic

Unemployment Rate

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

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

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.

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

Spread Percentage

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

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

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

Purchasing Power Parity

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

The exchange rate that would equalize the price of an identical basket of goods across countries.

Currency & ForexAdvanced

Real Exchange Rate

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

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

Everyday MathBasic

Discount Price

\text{Final} = P(1 - d)

Price after a percentage discount.

Everyday MathBasic

Tip Amount

\text{Tip} = B \times r

Gratuity based on a bill amount.

Everyday MathBasic

Percentage Change

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

Relative change between two values.

Geography & EarthAdvanced

Haversine Distance

d = 2r\arcsin\sqrt{\sin^2\frac{\Delta\phi}{2} + \cos\phi_1\cos\phi_2\sin^2\frac{\Delta\lambda}{2}}

Great-circle distance between two lat/long points.

Geography & EarthBasic

Slope / Gradient

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

Steepness of terrain as a percentage.

Geography & EarthBasic

Degrees to Distance

1^\circ \text{lat} \approx 111\ \text{km}

Approximate ground distance per degree of latitude.

Geography & EarthBasic

Time Zone Difference

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

Each 15 degrees of longitude equals one hour.

Geography & EarthAdvanced

Darcy's Law

Q = -KA\frac{\Delta h}{L}

Rate of groundwater flow through porous rock.

Computer ScienceAdvanced

Shannon Entropy

H = -\sum_i p_i \log_2 p_i

Average information content of a random source (bits).

Computer ScienceBasic

Bits to Represent n

b = \lceil \log_2(n) \rceil

Minimum number of bits to represent n distinct values.

Computer ScienceAdvanced

Average Memory Access Time

AMAT = H + M \times P

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

Math Tricks (3)

Percentage Flip Trick

x% of y = y% of x. When one direction is hard, flip it! This works because (x/100)×y = (y/100)×x.

View trick

Percentages with Building Blocks

Any percentage can be built from 10%, 5%, and 1% — quick to find and easy to combine.

View trick

Quick Tip Calculation

Find 10% first, then build 15% or 20% from it in your head.

View trick