Conversion Tables & Formulas

Length, Mass, Volume, and Time

Measurement	Conversion
Length	\(1\,\mathrm{ft}=12\,\mathrm{in}\); \(1\,\mathrm{yd}=3\,\mathrm{ft}\); \(1\,\mathrm{mi}=5280\,\mathrm{ft}\)
Metric length	\(1\,\mathrm{km}=1000\,\mathrm{m}\); \(1\,\mathrm{m}=100\,\mathrm{cm}\)
Length across systems	\(1\,\mathrm{in}=2.54\,\mathrm{cm}\) (exact); \(1\,\mathrm{mi}=1.609344\,\mathrm{km}\)
Weight/mass	\(1\,\mathrm{lb}=16\,\mathrm{oz}\); \(1\,\mathrm{lb}\approx0.45359237\,\mathrm{kg}\); \(1\,\mathrm{kg}\approx2.20462262\,\mathrm{lb}\)
US customary volume	\(1\,\mathrm{gal}=4\,\mathrm{qt} =8\,\mathrm{pt}=16\,\mathrm{cups}\)
Metric volume	\(1\,\mathrm{L}=1000\,\mathrm{mL}\)
Time	\(1\,\mathrm{hr}=60\,\mathrm{min} =3600\,\mathrm{s}\); \(1\,\mathrm{day}=24\,\mathrm{hr}\)
Area	\(1\,\mathrm{yd}^2=9\,\mathrm{ft}^2\); \(1\,\mathrm{ft}^2=144\,\mathrm{in}^2\)

For squared units, square the linear conversion factor. For example, \(1\,\mathrm{yd}^2=(3\,\mathrm{ft})^2 =9\,\mathrm{ft}^2\).

Temperature: Fahrenheit and Celsius Only

C=\frac{5}{9}(F-32)

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

For a temperature change, use \(\Delta F=\frac95\Delta C\) and \(\Delta C=\frac59\Delta F\). Do not add or subtract 32 for a temperature difference.

Examples: \(68^\circ\mathrm{F}=20^\circ\mathrm{C}\); \(-10^\circ\mathrm{C}=14^\circ\mathrm{F}\); an increase of \(10^\circ\mathrm{C}\) corresponds to an increase of \(18^\circ\mathrm{F}\).

Unit Rates and Dimensional Analysis

\text{Unit rate} = \frac{\text{total quantity}} {\text{number of units}}

Multiply by conversion fractions so the unwanted units cancel. For speed, \(1\,\mathrm{mph} =\frac{5280\,\mathrm{ft}}{3600\,\mathrm{s}} \approx1.46667\,\mathrm{ft/s}\).

Percentages and Budgeting

\text{Percentage} = \frac{\text{part}}{\text{whole}}\times100\%

\text{Percent change} = \frac{\text{new}-\text{old}} {\text{old}}\times100\%

For a percentage increase of \(p\%\):

\text{New amount} = \text{original} \left(1+\frac{p}{100}\right)

For a percentage decrease of \(p\%\):

\text{New amount} = \text{original} \left(1-\frac{p}{100}\right)

For successive changes, multiply the factors. A \(10\%\) increase followed by another \(10\%\) increase produces a total increase of \(21\%\), not \(20\%\).

\text{Savings} = \text{income}-\text{expenses}

\text{Sector angle} = \frac{\text{category amount}}{\text{total}} \times360^\circ

\text{Profit margin} = \frac{\text{selling price}-\text{cost}} {\text{selling price}} \times100\%

Markup percentage instead uses cost as the denominator.

Simple Interest

\[ I=Prt \]

\[ A=I+P=P(1+rt) \]

Here \(P\) is the principal, \(I\) is the interest, \(A\) is the final amount, \(r\) is the annual interest rate as a decimal, and \(t\) is the term in years.

Compound Interest

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

\[ I=A-P \]

To solve for the time \(t\):

t= \frac{\ln(A/P)} {n\ln(1+r/n)}

Here \(P\) is the principal, \(I\) is the interest, \(A\) is the final amount, \(r\) is the annual interest rate as a decimal, \(t\) is time in years, and \(n\) is the number of compounding periods per year.

Common values: annually \(n=1\), quarterly \(n=4\), monthly \(n=12\), weekly \(n=52\), and daily \(n=365\).

Annuities

The future amount \(A\) of an ordinary annuity with recurring periodic payments \(R\), annual interest rate \(r\), \(n\) payments per year, and term \(t\) years is:

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

This formula assumes payments are made at the end of each period, with interest compounded at the same frequency as the payments.

Loans, Amortization and Mortgages

For a loan with total amount owed \(A\), paid in \(N\) equal installments, the payment \(M\) is:

M=\frac{A}{N}

For an amortized loan with principal \(P\), annual interest rate \(r\), \(n\) payments per year, and fixed term \(t\) years, the periodic payment \(M\) is:

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

For monthly payments, use \(n=12\). The formula assumes a fixed interest rate, equal payments, and interest compounded at the same frequency as the payments.

The total amount paid \(A\) and the total interest \(I\) are:

A=MN,\qquad I=A-P

Here \(N=nt\) is the total number of payments. These formulas assume no additional fees.

For a purchase financed with a down payment, the amount financed is:

P=\text{Price}-\text{Down payment}