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81 results for “rate”

Formulae (80)

Unit Rate

\text{unit rate} = \frac{\text{total}}{\text{quantity}}

Cost or amount for a single unit.

CalculusAdvanced

Surface of Revolution

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

Surface area generated by revolving a curve about the x-axis.

CalculusAdvanced

Partial Derivative

\frac{\partial f}{\partial x}

Rate of change with respect to one variable, holding others fixed.

Probability & CombinatoricsAdvanced

Poisson Probability

P(X=k) = \frac{\lambda^k e^{-\lambda}}{k!}

Probability of k events in a fixed interval given average rate λ.

PhysicsBasic

Power

P = \frac{W}{t}

Rate of doing work.

PhysicsBasic

Acceleration

a = \frac{\Delta v}{t}

Rate of change of velocity.

PhysicsBasic

Power from Work

P = \frac{W}{t}

Rate of doing work.

Physics Laws & TheoremsBasic

Newton's Second Law

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

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

Fluid MechanicsBasic

Volumetric Flow Rate

Q = Av

Volume of fluid passing per unit time.

Fluid MechanicsAdvanced

Poiseuille's Law

Q = \frac{\pi r^4 \Delta P}{8\mu L}

Laminar flow rate through a pipe.

Electronics & CircuitsAdvanced

Nyquist Bit Rate

C = 2B\log_2 M

Maximum data rate of a noiseless channel.

Electronics & CircuitsBasic

Current from Charge

I = \frac{Q}{t}

Current as the rate of charge flow.

ChemistryIntermediate

Rate Law

r = k[A]^m[B]^n

Reaction rate as a function of reactant concentrations.

ChemistryAdvanced

Arrhenius Equation

k = A e^{-E_a/RT}

Temperature dependence of the reaction rate constant.

ChemistryAdvanced

Rate Law

rate = k[A]^m[B]^n

Reaction rate as a function of reactant concentrations.

Biology & Life SciencesBasic

Per Capita Growth Rate

r = b - d

Net growth rate from birth and death rates.

Biology & Life SciencesAdvanced

Michaelis-Menten Kinetics

v = \frac{V_{max}[S]}{K_m + [S]}

Rate of an enzyme-catalysed reaction.

Biology & Life SciencesAdvanced

Kleiber's Law

q_0 = 70\,M^{0.75}

Metabolic rate scales with body mass to the ¾ power.

Biology & Life SciencesIntermediate

Enzyme Activity Unit

U = \frac{\mu mol\ product}{min}

One unit converts 1 µmol of substrate per minute.

Biology & Life SciencesIntermediate

Population Growth Rate

r = \frac{B - D}{N}

Per-capita growth from births and deaths.

Health & FitnessIntermediate

BMR (Mifflin, Men)

BMR = 10m + 6.25h - 5a + 5

Basal metabolic rate — daily calories at rest for men.

Health & FitnessIntermediate

BMR (Mifflin, Women)

BMR = 10m + 6.25h - 5a - 161

Basal metabolic rate for women.

Health & FitnessBasic

Max Heart Rate

HR_{max} = 220 - a

Estimated maximum heart rate by age.

Health & FitnessAdvanced

Target Heart Rate (Karvonen)

HR_{target} = (HR_{max} - HR_{rest})\,I + HR_{rest}

Training heart rate at intensity I.

Health & FitnessAdvanced

Corrected QT (Bazett)

QTc = \frac{QT}{\sqrt{RR}}

Heart-rate-corrected QT interval from an ECG.

Health & FitnessIntermediate

RMR (Cunningham)

RMR = 500 + 22\,LBM

Resting metabolic rate favoured for athletes.

Health & FitnessBasic

Max Heart Rate (Tanaka)

HR_{max} = 208 - 0.7\,a

A more accurate maximum heart rate estimate.

Health & FitnessIntermediate

Heart Rate Reserve

HRR = HR_{max} - HR_{rest}

The usable range between rest and maximum heart rate.

Health & FitnessAdvanced

Corrected QT (Fridericia)

QTc = \frac{QT}{\sqrt[3]{RR}}

Heart-rate-corrected QT interval using a cube root.

Nutrition & FoodBasic

Calories from Carbohydrate

E_C = 4C

Energy from carbohydrate at 4 kcal per gram.

Nutrition & FoodIntermediate

Net Carbohydrates

C_{net} = C_{total} - F - \tfrac{A}{2}

Digestible carbs after subtracting fibre and half of sugar alcohols.

EngineeringBasic

Volumetric Flow Rate

Q = Av

Volume of fluid passing per unit time.

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 & AeronauticsIntermediate

Stall Speed vs Load Factor

V_{s,n} = V_s\sqrt{n}

Accelerated stall speed rises with the square root of the load factor.

Aviation & AeronauticsIntermediate

Rate of Turn

\omega = \dfrac{g\tan\phi}{v}

Angular rate of a coordinated turn (radians/s; a standard rate turn is 3°/s).

Aviation & AeronauticsAdvanced

ISA Temperature Lapse

T = 15 - 1.98\left(\dfrac{h}{1000}\right)

Standard atmosphere temperature decreases about 2°C per 1000 ft up to the tropopause.

Aviation & AeronauticsIntermediate

Rate of Climb

ROC = \frac{\text{excess power}}{W}

Vertical speed from excess engine power.

Finance & InterestBasic

Simple Interest

I = P r t

Interest earned on principal at a simple rate.

Finance & InterestAdvanced

CAGR

CAGR = \left(\frac{V_f}{V_i}\right)^{1/n} - 1

Compound annual growth rate of an investment.

Finance & InterestAdvanced

Effective Annual Rate

EAR = \left(1 + \frac{r}{n}\right)^n - 1

True annual rate accounting for compounding.

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 & InterestAdvanced

Real Rate of Return

r = \frac{1+n}{1+i} - 1

Return adjusted for inflation.

AccountingIntermediate

Return on Equity (ROE)

ROE = \dfrac{Net\ Income}{Shareholder\ Equity}

The profit generated for each dollar of shareholders’ equity.

AccountingAdvanced

Double-Declining Balance

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

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

AccountingAdvanced

Double Declining Depreciation

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

Accelerated depreciation of an asset.

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 & 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.

EconomicsAdvanced

Fisher Equation

i \approx r + \pi

Relates nominal interest rates to the real rate plus expected inflation.

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 Conversion

Foreign = Domestic \times Rate

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

Currency & ForexBasic

Inverse Exchange Rate

Rate_{B/A} = \dfrac{1}{Rate_{A/B}}

Flip a quoted rate to express it from the other currency’s point of view.

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

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

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.

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.

Geography & EarthAdvanced

Darcy's Law

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

Rate of groundwater flow through porous rock.

Environmental ScienceIntermediate

Exponential Population Growth

N = N_0 e^{rt}

Growth of a population at a constant rate.

Environmental ScienceIntermediate

Energy Payback Ratio

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

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

Number TheoryBasic

Triangular Number

T_n = \frac{n(n+1)}{2}

Sum of the first n natural numbers.

Number TheoryBasic

Square Number

S_n = n^2

The nth perfect square.

Number TheoryIntermediate

Pentagonal Number

P_n = \frac{n(3n-1)}{2}

The nth pentagonal figurate number.

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 ScienceBasic

Data Transfer Time

t = \frac{S}{R}

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

Computer ScienceAdvanced

Nyquist Sampling Rate

f_s \geq 2f_{max}

Minimum sampling rate to capture a signal without aliasing.

Computer ScienceAdvanced

Nyquist Data Rate

C = 2B\log_2 L

Maximum data rate of a noiseless channel.

Computer ScienceAdvanced

Shannon Channel Capacity

C = B\log_2(1 + SNR)

Maximum error-free data rate of a noisy channel.

Computer ScienceAdvanced

Average Memory Access Time

AMAT = H + M \times P

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

Math Tricks (1)

Rule of 72 (Doubling Money)

Estimate how many years it takes an investment to double: divide 72 by the annual interest rate.

View trick