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100 results for “age”

Formulae (96)

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

Average (Mean)

\text{average} = \frac{\text{sum of values}}{\text{number of values}}

Add all values and divide by how many there are.

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.

AlgebraIntermediate

Geometric Mean

GM = \sqrt[n]{x_1 x_2 \cdots x_n}

The nth root of the product of n numbers.

AlgebraAdvanced

Harmonic Mean

HM = \frac{n}{\sum 1/x_i}

Reciprocal of the average of reciprocals.

CalculusAdvanced

Average Value of a Function

f_{avg} = \frac{1}{b-a}\int_a^b f(x)\,dx

The mean value of a continuous function over an interval.

CalculusAdvanced

Mean Value Theorem

f'(c) = \frac{f(b)-f(a)}{b-a}

Guarantees a point where the tangent equals the average slope.

CalculusAdvanced

Average Value of a Function

\bar{f} = \frac{1}{b-a}\int_a^b f(x)\,dx

Mean value of a continuous function over an interval.

Statistics & ProbabilityBasic

Arithmetic Mean

\bar{x} = \frac{1}{n}\sum_{i=1}^{n} x_i

The average of a data set.

Statistics & ProbabilityIntermediate

Variance

\sigma^2 = \frac{1}{n}\sum_{i=1}^{n}(x_i - \bar{x})^2

Average squared deviation from the mean.

Statistics & ProbabilityIntermediate

Expected Value

E[X] = \sum_i x_i\,p_i

The long-run average value of a random variable.

Statistics & ProbabilityBasic

Mode

\text{Mode} = \text{most frequent value}

The value that appears most often in a data set.

Statistics & ProbabilityIntermediate

Geometric Mean

GM = \sqrt[n]{x_1 x_2 \cdots x_n}

The nth root of the product of n values.

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 & ProbabilityIntermediate

Weighted Mean

\bar{x}_w = \frac{\sum w_i x_i}{\sum w_i}

Average where values carry different weights.

Probability & CombinatoricsIntermediate

Expected Value

E[X] = \sum_{i} x_i\, p_i

Long-run average value of a random variable.

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.

Data Science & MLBasic

Mean Squared Error (MSE)

MSE = \frac{1}{n}\sum_{i=1}^{n}(y_i - \hat{y}_i)^2

Average of squared differences between predicted and actual values.

Data Science & MLBasic

Mean Absolute Error (MAE)

MAE = \frac{1}{n}\sum_{i=1}^{n}|y_i - \hat{y}_i|

Average of absolute differences between predictions and actual values.

PhysicsBasic

Ohm's Law

V = IR

Voltage equals current times resistance.

PhysicsBasic

Mechanical Advantage

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

Force amplification of a simple machine.

Physics Laws & TheoremsBasic

Ohm's Law

V = IR

Voltage across a resistor equals current times resistance.

Physics Laws & TheoremsIntermediate

Kirchhoff's Voltage Law

\sum V = 0

The sum of voltages around any closed loop is zero.

Physics Laws & TheoremsIntermediate

Lens Maker's / Thin Lens

\frac{1}{f} = \frac{1}{v} - \frac{1}{u}

Relates focal length to object and image distances for a thin lens.

Thermodynamics & HeatAdvanced

Average KE of a Gas Molecule

\bar{E} = \tfrac{3}{2}k_B T

Mean translational kinetic energy per molecule.

Optics & WavesIntermediate

Thin Lens Equation

\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}

Relates focal length to object and image distances.

Optics & WavesIntermediate

Lens Magnification

M = -\frac{d_i}{d_o}

Image size relative to object size.

Electricity & MagnetismIntermediate

Electric Potential

V = k\frac{q}{r}

Potential due to a point charge.

Electronics & CircuitsBasic

Ohm's Law

V = IR

Voltage equals current times resistance.

Electronics & CircuitsBasic

Power (V²/R)

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

Power from voltage and resistance.

Electronics & CircuitsBasic

Capacitance

C = \frac{Q}{V}

Charge stored per unit voltage.

Electronics & CircuitsIntermediate

Voltage Divider

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

Output voltage from two series resistors.

Electronics & CircuitsIntermediate

Kirchhoff's Voltage Law

\sum V = 0

Voltages around any closed loop sum to zero.

Electronics & CircuitsIntermediate

RMS Voltage

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

Effective value of a sinusoidal voltage.

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

Drift Velocity

v_d = \frac{I}{nAq}

Average velocity of charge carriers.

Electronics & CircuitsBasic

Voltage Divider Output

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

Output of a two-resistor divider.

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 SciencesBasic

Microscope Magnification

M = \frac{\text{image size}}{\text{actual size}}

How much larger an image appears than the object.

Biology & Life SciencesAdvanced

Hemocytometer Cell Count

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

Cells per mL from a counting-chamber average.

Biology & Life SciencesAdvanced

Recombination Frequency

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

Genetic map distance in centimorgans.

Health & FitnessBasic

Max Heart Rate

HR_{max} = 220 - a

Estimated maximum heart rate by age.

Health & FitnessIntermediate

Mean Arterial Pressure

MAP = DBP + \tfrac{1}{3}(SBP - DBP)

Average blood pressure during a cardiac cycle.

Nutrition & FoodBasic

Macro % of Calories

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

Share of total energy coming from a given macronutrient.

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.

Nutrition & FoodBasic

Caffeine Concentration

c = \frac{m_{caffeine}}{V}

Caffeine amount per unit volume of a drink.

Nutrition & FoodAdvanced

Water Activity

a_w = \frac{p}{p_0}

Ratio of a food's vapour pressure to pure water — governs microbial spoilage.

EngineeringBasic

Mechanical Advantage

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

Force amplification of a machine.

EngineeringIntermediate

Transformer Ratio

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

Voltage ratio equals the turns ratio.

Finance & InterestAdvanced

Loan EMI

EMI = \frac{P r (1+r)^n}{(1+r)^n - 1}

Equated monthly installment on a loan.

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

Debt-to-Equity Ratio

D/E = \frac{\text{Total Debt}}{\text{Equity}}

Leverage measure comparing debt to equity.

AccountingIntermediate

Debt-to-Equity Ratio

D/E = \dfrac{Total\ Debt}{Total\ Equity}

Measures financial leverage by comparing borrowed funds to owner-supplied funds.

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.

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 & CommerceIntermediate

Customer Acquisition Cost (CAC)

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

The average cost to win one new customer.

Business & CommerceIntermediate

Churn Rate

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

The percentage of customers who stop buying over a period.

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

Inflation Rate

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

Percentage change in the price index.

EconomicsBasic

GDP per Capita

\frac{GDP}{Population}

Average economic output per person.

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

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

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

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

Average Speed

v = \frac{d}{t}

Distance covered per unit time.

Everyday MathBasic

Percentage Change

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

Relative change between two values.

Time & CalendarBasic

Age in Years

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

Whole years elapsed since a birth date.

Geography & EarthBasic

Slope / Gradient

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

Steepness of terrain as a percentage.

Geography & EarthAdvanced

Radiometric Dating Age

t = \frac{1}{\lambda}\ln\!\left(1 + \frac{D}{P}\right)

Age of a rock from parent and daughter isotopes.

Unit ConversionsBasic

Gigabytes to Megabytes

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

Convert gigabytes to megabytes (binary).

Computer ScienceAdvanced

Shannon Entropy

H = -\sum_i p_i \log_2 p_i

Average information content of a random source (bits).

Computer ScienceAdvanced

Average Memory Access Time

AMAT = H + M \times P

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

Math Tricks (4)

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

Estimate a Square Root

Bracket the number between two perfect squares, then refine with a quick average step.

View trick