Formula Reference

APR to APY Conversion

$APY = \left(1 + \frac{APR}{n}\right)^n - 1$

BMI (Imperial Units)

$BMI = \frac{w_{lbs}}{h_{in}^2} \times 703$

BMI Prime

$BMI' = \frac{BMI}{25}$

Body Mass Index (BMI) Formula

$BMI = \frac{w_{kg}}{h_m^2}$

Calorie Deficit for Weight Loss

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

Celsius to Fahrenheit

$F = C \times \frac{9}{5} + 32$

Compound Interest Formula

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

Continuous Compounding

$A = Pe^{rt}$

Devine Formula (Ideal Body Weight)

$IBW_{male} = 50 + 2.3 \times (h_{in} - 60)$

EMI (Equated Monthly Installment)

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

Error Percentage

$E\% = \frac{|measured - actual|}{actual} \times 100$

Future Value

$FV = PV \times (1 + r)^n$

Gestational Week

$Week = \lfloor\frac{today - LMP}{7}\rfloor$

GPA Scale Conversion

$GPA_{new} = \frac{GPA_{old}}{Scale_{old}} \times Scale_{new}$

Harris-Benedict Equation (Female)

$BMR = 447.593 + 9.247w + 3.098h - 4.330a$

Harris-Benedict Equation (Male)

$BMR = 88.362 + 13.397w + 4.799h - 5.677a$

Housing Subscription Points

$Points = H_{homeless} + F_{family} + S_{savings} \leq 84$

International Age

$Age = Y_{now} - Y_{birth} - (\text{before birthday} \;?\; 1 : 0)$

Jeonse-Wolse Conversion

$\text{Monthly} = \frac{(\text{Jeonse} - \text{Deposit}) \times Rate}{12}$

Korean Acquisition Tax

$Tax = Price \times Rate + Rural + Education$

Korean Capital Gains Tax

$Tax = (Gain - LTHD - Basic) \times ProgressiveRate$

Korean Counting Age

$Age = Y_{now} - Y_{birth} + 1$

Korean Progressive Income Tax

$Tax = \sum_{i=1}^{8} (B_i \times R_i)$

Korean Realtor Fee

$Fee = Price \times Rate + VAT(10\%)$

Korean Year Age

$Age = Y_{now} - Y_{birth}$

Leap Year Test

$leap = (y \bmod 4 = 0) \land (y \bmod 100 \neq 0 \lor y \bmod 400 = 0)$

Long-Term Holding Deduction

$LTHD = Gain \times Rate(years, residency)$

Markup vs Margin

$Margin = \frac{Markup}{1 + Markup}$

Mifflin-St Jeor Equation (Female)

$BMR = 10w + 6.25h - 5a - 161$

Mifflin-St Jeor Equation (Male)

$BMR = 10w + 6.25h - 5a + 5$

Military Discharge Date

$D_{out} = D_{in} + Duration_{branch} - 1$

Naegele's Rule

$EDD = LMP + 280 \text{ days}$

Percentage Change

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

Percentage Of

$result = value \times \frac{p}{100}$

Percentile to Grade (CSAT)

$Grade = f(percentile), \text{ 9 tiers}$

Present Value

$PV = \frac{FV}{(1 + r)^n}$

Pyeong to Square Meters

$m^2 = pyeong \times \frac{400}{121}$

Pyeong-Tsubo Equivalence

$1 \text{ pyeong} = 1 \text{ tsubo} = \frac{400}{121} m^2$

Real Return (Inflation-Adjusted)

$r_{real} = \frac{1 + r_{nom}}{1 + r_{inf}} - 1$

Remaining Loan Balance

$B_k = P\frac{(1+r)^n - (1+r)^k}{(1+r)^n - 1}$

Rule of 72

$t_{double} \approx \frac{72}{r\%}$

Shaku to Tsubo Derivation

$1 \text{ tsubo} = (6 \times 0.303m)^2 = 3.3058 m^2$

Simple Interest Formula

$I = P \times r \times t$

Square Meters to Square Feet

$sqft = m^2 \times 10.7639$

Tatami to Square Meters (Regional)

$m^2 = tatami \times k_{region}$

Total Daily Energy Expenditure (TDEE)

$TDEE = BMR \times ActivityMultiplier$

Total Interest on a Loan

$I_{total} = (EMI \times n) - P$

Tsubo to Square Meters

$m^2 = tsubo \times 3.3058$

Weighted Average

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

What Percentage

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