Every finance formula on this site

Calculator formulas: 132
Factor formulas: 6
On this page: 138
Worked examples: 1,307

138 formulas, each with what its symbols stand for and a working calculator underneath it. Every one is applied in a worked example whose numbers are recomputed by an independent program before the site can build. Put that calculator on a class page from widgets.

Class and first paycheck

Simple interest calculator and formula
$I = Prt \qquad A = P(1 + rt)$
$P$ is the original principal, $r$ the annual rate as a decimal, and $t$ time in years. $I$ is the interest. $A$ is principal plus interest. Eighteen months is $t = 1.5$ .
Hourly wage to annual salary
$A = h \times w \times n$
$h$ is the hourly wage, $w$ paid hours in a week, and $n$ paid weeks in a year. Weekly pay is $h \times w$ . Monthly pay on this page is $A / 12$ , not four weeks of pay.
Paycheck calculator and FICA split
$\text{Net} = G - 0.062\min(G, B/n) - 0.0145 G - fG - sG$
$G$ is gross pay this check, $n$ the number of checks a year, $B$ the Social Security wage base, $f$ federal withholding as a decimal, and $s$ state withholding as a decimal. The min term spreads the annual Social Security cap evenly across the year's checks.
50/30/20 budget split calculator
$N = 0.50H \quad W = 0.30H \quad S = 0.20H$
$H$ is take-home pay. The three percents are yours to type. 50, 30 and 20 are the usual starting split, not a law. Leftover is $H$ minus the three buckets.
Net worth calculator and formula
$\text{Net worth} = A - D$
$A$ is everything owned at today's prices. $D$ is everything owed at today's payoff balances. The difference can be negative.
Credit utilization calculator
$U = \frac{B}{L}$
$B$ is the reported revolving balance and $L$ the total revolving limit. The page prints $U$ in percentage points: 30, not 0.30. Instalment loans sit outside this ratio.
Emergency fund calculator: size and time
$D = \frac{\left(T - S\left(1 + \frac{r}{12}\right)^{N}\right)\frac{r}{12}}{\left(1 + \frac{r}{12}\right)^{N} - 1}$
$T$ is the target, which is your essential monthly costs times the months of cover you want. $S$ is what is already set aside, $r$ the nominal annual rate as a decimal, before compounding is folded into it, $N$ the number of monthly deposits, and $D$ the deposit at the end of each month.
FDIC insurance calculator
$\text{covered} = \min(B,L)$
$B$ is the combined eligible balance in one category at one insured bank. $L$ is the coverage limit. Uninsured is whatever sits above $L$ .

Saving and growth

Compound interest calculator and formula
$A = P\left(1 + \frac{r}{n}\right)^{nt}$
$A$ is the ending balance, $P$ the starting amount, $r$ the annual rate as a decimal, $n$ how many times a year interest is added, and $t$ the number of years.
Savings goal calculator: monthly deposit
$PMT = \frac{\left(FV - P\left(1 + \frac{r}{n}\right)^{nt}\right)\frac{r}{n}}{\left(1 + \frac{r}{n}\right)^{nt} - 1}$
$FV$ is the target, $P$ what you have already saved, $r$ the annual rate as a decimal, $n$ how many times a year interest is added and money goes in, and $t$ the number of years. $PMT$ is the deposit at the end of each period.
Rule of 72 calculator and doubling time
$t \approx \frac{72}{r} \qquad t = \frac{\ln 2}{\ln(1 + r/100)}$
$r$ is the annual growth rate in percentage points, so 7 rather than 0.07, and $t$ is the number of years the money takes to double. The expression on the left is the shortcut. The one on the right is the exact answer it is standing in for.
Inflation calculator and buying power
$P_t = P_0 (1 + i)^t \qquad B_t = \frac{P_0}{(1 + i)^t}$
$P_0$ is the sum today, $i$ the inflation rate for one year as a decimal, and $t$ the number of years. $P_t$ is what the same basket of goods costs then. $B_t$ is what $P_0$ still buys then, measured in today's money.
Real return after inflation calculator
$r_{\text{real}} = \frac{1 + r_{\text{nominal}}}{1 + i} - 1$
$r_{\text{nominal}}$ is the return you are quoted, $i$ is inflation over the same period, and $r_{\text{real}}$ is what the money actually buys. Both rates go in as decimals, so 7 percent is 0.07.
Future value of an annuity calculator
$FV = PMT \times \frac{(1 + i)^n - 1}{i}$
$FV$ is the value at the end, $PMT$ the payment made every period, $i$ the rate for one period, and $n$ the number of payments.
Present value calculator
$PV = \frac{F}{(1+i)^n} + PMT \times \frac{1 - (1+i)^{-n}}{i}$
$F$ is a lump due after $n$ periods, $PMT$ a level end-of-period payment, and $i$ the rate per period. At a zero rate the present value is just the undiscounted sum, because nothing is being given up by waiting.
CAGR calculator and formula
$\text{CAGR} = \left(\frac{V_t}{V_0}\right)^{\frac{1}{t}} - 1$
$V_0$ is the value at the start, $V_t$ the value at the end, and $t$ the number of years between them. The answer comes out as a decimal, so 0.1029 means 10.29 percent a year.
APR vs APY calculator and formula
$APY = \left(1 + \frac{APR}{n}\right)^{n} - 1$
$APR$ is the nominal annual rate as a decimal and $n$ is how many times a year interest is added. The result is the effective annual rate.
CD interest calculator
$FV = P(1+\text{APY})^{t}$
$P$ is the deposit, APY the annual percentage yield as a decimal, and $t$ the years. APY is used once a year because it is already an annual figure.
Savings rate calculator
$\text{savings rate}=\frac{S}{I}\times 100$
$S$ is the amount saved over a period and $I$ the income over the same period. Both must cover the same months, and both must be measured on the same side of tax.
Coast FIRE calculator
$F=\frac{S}{w},\qquad V=P(1+r)^{t},\qquad \text{gap}=F-V$
$S$ is annual spending and $w$ the withdrawal rate, so $F$ is the FIRE number. $V$ is what current savings $P$ grow to at rate $r$ over $t$ years with nothing added.

Borrowing

Loan payment calculator and formula
$M = P \times \frac{i}{1 - (1 + i)^{-n}}$
$M$ is the payment, $P$ the amount borrowed, $i$ the rate for one period (the annual rate divided by 12 for a monthly loan), and $n$ the total number of payments.
Mortgage affordability calculator and formula
$\text{max loan} = \frac{\left(L \times I - D - T\right)\left(1 - (1 + i)^{-n}\right)}{i}$
$L$ is the lender's debt-to-income limit as a decimal, $I$ gross monthly income, $D$ the other monthly debt payments and $T$ monthly tax and insurance. What survives those subtractions is the budget for principal and interest, and the fraction turns that budget into a loan size at period rate $i$ over $n$ payments.
Mortgage extra payment calculator
$n = \frac{\ln\left(1 - \frac{iB}{p}\right)}{-\ln(1+i)}$
$B$ is the balance, $i$ the monthly rate, and $p$ the total monthly payment including extra principal. $n$ is the number of months until the balance hits zero. If $p$ does not cover the first month's interest, there is no finite $n$ .
Credit card payoff calculator and formula
$n = -\frac{\ln\left(1 - \frac{iB}{M}\right)}{\ln(1 + i)}$
$n$ is the number of monthly payments, $B$ the balance you owe now, $M$ the fixed payment you make each month, and $i$ the monthly rate. A card quotes a nominal annual rate, so $i$ is that rate divided by 12, not the smaller monthly rate that would compound up to it over a year.
Car loan calculator: payment and total cost
$M = P \times \frac{i}{1 - (1 + i)^{-n}}$
$M$ is the monthly payment, $P$ the amount financed, $i$ the monthly rate (the nominal annual rate divided by 12, not an effective annual rate), and $n$ the number of payments, which is the term in years times 12.
Student loan payoff calculator
$n = \frac{-\ln\left(1 - \frac{i B}{M}\right)}{\ln(1 + i)}$
$B$ is the balance, $i$ the monthly rate (the nominal annual rate divided by 12, not an effective annual rate), $M$ the payment you actually make each month, and $n$ the number of months until the balance reaches zero.
Debt-to-income ratio calculator and formula
$\text{DTI} = \frac{\text{total monthly debt payments}}{\text{gross monthly income}} \times 100\%$
Above the line goes every payment you are required to make each month. Below it goes gross pay, before tax and deductions. The division gives a decimal, so multiply by $100$ for the percentage a lender quotes.
Refinance break-even calculator and formula
$\text{months} = \frac{C}{M_{\text{old}} - M_{\text{new}}}$
$C$ is the closing costs, $M_{\text{old}}$ is the payment on the loan you have and $M_{\text{new}}$ the payment on the loan replacing it. Both payments come from the same level-payment formula, so the only things that set them are the balance, the rate and the term on each side.
PMI calculator and formula
$\text{monthly PMI} = \frac{L \times p}{12} \quad \text{until } B_t \le 0.8 \times H$
$L$ is the loan, $p$ the annual PMI rate as a decimal, $H$ the original purchase price, $B_t$ the amortised balance. The 80 percent threshold is the borrower-request cancellation point under US rules; automatic cancellation sits a little later.
Mortgage points calculator
$\text{cost} = B \times p \qquad n_{BE} = \frac{\text{cost}}{M_0 - M_1}$
$B$ is the loan, $p$ points as a decimal (1 percent is 0.01), $M_0$ the payment at the higher rate and $M_1$ at the lower. Break-even $n_{BE}$ is months of payment saving against the cash cost, a cash-flow test, not a present-value test.
HELOC interest-only calculator
$I_m = \dfrac{B \times r}{12}$
$B$ is the drawn balance. $r$ is the annual rate as a decimal. $I_m$ is the interest-only monthly charge if the balance and rate do not move.
Escrow calculator and formula
$E = \dfrac{T + H}{12}$
$T$ is projected annual property tax. $H$ is projected annual homeowners insurance. $E$ is the base monthly impound deposit before a shortage or cushion.
Gift tax exclusion calculator
$\text{remaining}=\max(E-G,0),\quad \text{excess}=\max(G-E,0)$
$E$ is the annual exclusion input and $G$ is the gift to one recipient. Used room is the smaller of $E$ and $G$ .
Margin buying power calculator
$\text{buying power}=\frac{C}{m}$
$C$ is cash and $m$ is the initial margin percentage written as a decimal. Borrowed amount is buying power minus cash.
PITI mortgage payment calculator
$\text{PITI}=\frac{Pi}{1-(1+i)^{-n}}+\frac{T}{12}+\frac{I}{12}$
$P$ is the loan, $i$ the monthly rate, $n$ the number of payments, $T$ the annual property tax and $I$ the annual insurance premium. The first term is the amortising payment; the other two are annual bills spread over 12 months.
Loan to value calculator
$\text{LTV}=\frac{L}{V}\times 100,\qquad E=V-L$
$L$ is the loan balance and $V$ is the property value. Equity $E$ is the part of the value the loan does not cover, so LTV and equity percentage always add to 100.
Biweekly mortgage calculator
$\text{biweekly}=\frac{M}{2},\qquad 26\times\frac{M}{2}=13M \text{ a year}$
$M$ is the standard monthly payment. There are 26 fortnights in a year, so paying half of $M$ each fortnight pays 13 monthly payments rather than 12.
Interest only mortgage calculator
$\text{monthly}=\frac{P\,r}{12}$
$P$ is the outstanding balance and $r$ the annual rate as a decimal. There is no term in the formula, because nothing is being repaid.
Remaining loan balance calculator
$B_k = P(1+i)^k - M\,\frac{(1+i)^k-1}{i}$
$P$ is the original loan, $i$ the monthly rate, $M$ the monthly payment and $k$ the payments made. The first term grows the debt, the second credits the payments and their compounding.
Years to payoff calculator
$n=\frac{-\ln\left(1-\frac{iB}{M}\right)}{\ln(1+i)}$
$B$ is the balance, $i$ the monthly rate and $M$ the monthly payment. The payment must exceed $iB$ , the first month's interest, or the balance never falls.
Down payment calculator
$D = P\times d,\qquad L = P - D$
$P$ is the purchase price, $d$ the deposit percentage as a decimal, $D$ the down payment and $L$ the loan. The two outputs always add back to the price.
Car lease payment calculator
$\text{payment}=\frac{C-R}{n}+(C+R)f$
$C$ is capitalised cost, $R$ the residual value, $n$ the months in the term and $f$ the money factor. The rent charge uses the sum of $C$ and $R$ , not the difference.
Money factor calculator
$f=\frac{\text{APR}}{2400},\qquad \text{APR}=2400f$
$f$ is the money factor and APR is the annual percentage rate in percentage points. The constant 2400 is 1200 for the monthly rate, doubled for the way a lease charges it.

Work and retirement

Employer match calculator
$M = S \times \min(d, c) \times m$
$S$ is salary, $d$ the share of pay you defer, $c$ the cap the match applies to, and $m$ the match rate, all as decimals. Deferring past the cap still raises your own contribution and does not raise the match.
Retirement withdrawal calculator and formula
$B_n = P(1 + i)^n - W \times \frac{(1 + i)^n - 1}{i}$
$B_n$ is what is left after $n$ withdrawals, $P$ the pot you start with, $W$ the amount you take each period, and $i$ the return for one period, which is the nominal annual return divided by 12 when you withdraw monthly, not an effective annual rate.
FIRE number calculator
$F = \frac{S}{w} \qquad (1+r)^t = \frac{F + C/r}{B + C/r}$
$S$ is annual spending, $w$ the withdrawal rate as a decimal (4 percent is 0.04), $B$ what is already saved, $C$ saved each year, $r$ the annual return. $t$ is years to reach $F$ . The 4 percent rule is $w = 0.04$ , which is also $F = 25S$ .
RMD calculator and formula
$R = \dfrac{B}{d}$
$B$ is the prior 31 December balance. $d$ is the life-expectancy factor for the owner's age. $R$ is the minimum that must leave that account.
Social Security PIA calculator
$\mathrm{PIA}_{raw} = 0.90\min(A,b_1) + 0.32\min(\max(A-b_1,0),b_2-b_1) + 0.15\max(A-b_2,0)$
$A$ is average indexed monthly earnings. $b_1$ and $b_2$ are the bend points for the eligibility year. The raw sum is then floored to the next lower dime.
Social Security claiming calculator
$B = \text{PIA} \times f$
$f$ is 1 minus the early-reduction percents, or 1 plus delayed-retirement credits. The first 36 early months take 5/9 of 1 percent each. Further early months take 5/12 of 1 percent. Delayed months take 2/3 of 1 percent each.
Taxable Social Security calculator
$PI=A+E+\tfrac{1}{2}B,\qquad T=\min\left(\tfrac{1}{2}B,\ \tfrac{1}{2}(PI-\text{base})\right)$
$A$ is other income, $E$ tax exempt interest, $B$ the benefits received and $PI$ provisional income. $T$ is the taxable portion of the benefits under the first tier.
Life insurance needs calculator
$N=(I \times y)+D-A-C$
$I$ is annual income to replace, $y$ the years to replace it for, $D$ debts to clear, $A$ assets already available, and $C$ cover already in force.
Roth conversion tax calculator
$\text{tax}=C\times r$
$C$ is the converted amount and $r$ is the entered tax rate written as a decimal.
Effective tax rate calculator
$\text{effective rate}=\frac{\text{total tax}}{\text{income}}$
Divide total tax by income and multiply the decimal by 100 to express the effective rate as a percentage.
Tax bracket calculator
$\text{tax}=\sum_i \text{band}_i\times\text{rate}_i$
Split income across the teaching bands, multiply each band by its own rate, then add the band taxes.
Self-employment tax calculator
$\text{base}=0.9235\times\text{net},\quad \text{tax}=0.153\times\text{base}$
Multiply net earnings by 0.9235 for the tax base, then multiply that base by 0.153. The deductible half is one half of the tax.
QBI deduction calculator
$D=0.20\times\text{QBI}$
$D$ is the teaching deduction and QBI is qualified business income. The entered rate is 20 percent in both examples.
NIIT calculator and formula
$\text{NIIT}=0.038\times\text{NII}$
NII is the supplied net investment income slice. Multiply it by the entered 3.8 percent rate.
Tax-loss harvest calculator
$\text{tax saved}=\text{loss}\times r$
Loss is basis minus proceeds. Multiply that loss by the entered tax rate $r$ written as a decimal.
Capital gains tax calculator
$\text{gain}=\text{proceeds}-\text{basis},\qquad \text{tax}=\text{gain}\times r$
Basis is what the asset cost, adjusted for commissions and improvements. $r$ is the rate that applies to the gain, entered as a percentage.
Home sale exclusion calculator
$G=S-B,\qquad X=\min(G,\text{cap}),\qquad T=G-X$
$S$ is the sale price, $B$ the adjusted basis, $G$ the gain, $X$ the excluded part and $T$ what remains taxable. The exclusion cap is entered rather than assumed.
After tax return calculator
$r_{\text{after}}=r(1-t)$
$r$ is the pre tax return and $t$ the tax rate on it, both as decimals. The drag is $r-r_{\text{after}}$ , measured in percentage points rather than as a percentage.
Additional Medicare tax calculator
$E=\max(W-\text{threshold},\ 0),\qquad \text{tax}=0.009E$
$W$ is wages or self employment income and $E$ the amount above the threshold. Only $E$ is taxed at the extra 0.9 percent rate.

Investing and valuation

Price to earnings calculator
$\text{P/E} = \frac{P}{\text{EPS}} = \frac{\text{Market cap}}{\text{Earnings}}$
$P$ is the share price and EPS is earnings per share. Multiplying both by the share count gives market cap over total earnings, which is the same ratio.
DCF calculator and formula
$V = \sum_{t=1}^{n} \frac{F_t}{(1+r)^t} + \frac{F_n(1+g)}{(r-g)(1+r)^n}$
$F_t$ is free cash flow in year $t$ , $r$ the discount rate (WACC as a decimal), $g$ perpetual growth after year $n$ . The second term is Gordon growth on the year-after-forecast flow, then discounted back $n$ years. $g$ must stay below $r$ .
Dividend discount calculator
$P = \frac{D_0(1+g)}{k-g} = \frac{D_1}{k-g}$
$D_0$ is the dividend just paid, $g$ perpetual growth, $k$ the required return, all as decimals. $D_1 = D_0(1+g)$ is next year's dividend. $k$ must stay above $g$ or the growing perpetuity has no finite price. The implied yield $D_1/P$ equals $k-g$ .
Bond price calculator and current yield
$P = \sum_{t=1}^{n} \frac{C}{(1+i)^t} + \frac{F}{(1+i)^n}$
$P$ is the price, $C$ the coupon paid each period, $F$ the face value repaid at maturity, $i$ the market rate for one period, and $n$ the number of periods left.
Bond duration calculator
$D_{Mac} = \frac{\sum_t t \, PV(CF_t)}{P} \qquad D_{Mod} = \frac{D_{Mac}}{1 + y/k}$
$PV(CF_t)$ is the present value of the cash flow at time $t$ in years, $P$ the price, $y$ the annual yield and $k$ the number of coupon periods a year. DV01 is modified duration times price over 10,000: the dollar change for a one basis point fall in yield.
Cap rate calculator
$\text{cap} = \frac{\text{NOI}}{\text{price}} \qquad V = \frac{\text{NOI}}{\text{cap}}$
NOI is rent minus operating costs, before debt service and tax. The two forms are the same identity run forwards and backwards: a higher cap is a lower price for the same income.
Tax-equivalent yield calculator
$y_{te} = \frac{y_{ex}}{1 - t}$
$y_{ex}$ is the tax-exempt yield and $t$ is the marginal tax rate, both as decimals. The identity is just 'undo the tax': a taxable yield, after tax, should equal the exempt yield.
Expense ratio calculator and fee impact
$A = P\left(1 + \frac{g - f}{n}\right)^{nt}$
$A$ is the ending balance, $P$ what you start with, $g$ the return before costs as a decimal, $f$ the expense ratio as a decimal, $n$ how many times a year the money compounds, which is twelve on this page, and $t$ the number of years.
PEG ratio calculator and formula
$\text{PEG} = \frac{\text{P/E}}{g_{\%}}$
P/E is price over EPS. g_% is expected EPS growth in percentage points: 10 means ten percent. PEG is 20 / 10 = 2, not 20 / 0.10.
Price to book calculator
$\text{P/B} = \frac{P}{\text{BVPS}} = \frac{\text{Market cap}}{\text{Book equity}}$
BVPS is book equity divided by shares. The two routes cancel the share count and have to agree.
Price to sales calculator
$\text{P/S} = \frac{P}{\text{SPS}} = \frac{\text{Market cap}}{\text{Sales}}$
SPS is sales divided by shares. The two routes cancel the share count and have to agree.
Total return calculator
$\text{HPR} = \frac{\text{End} - \text{Begin} + \text{Income}}{\text{Begin}}$
End is the value at the close of the period. Income is dividends, coupon, or rent paid during it. The result is in percentage points: 8, not 0.08.
Sharpe ratio calculator
$S = \dfrac{R_p - R_f}{\sigma_p}$
$R_p$ is the portfolio return. $R_f$ is the matching risk-free rate. $\sigma_p$ is the standard deviation of the portfolio's returns, on the same scale.
CAPM calculator and formula
$E(R_i) = R_f + \beta_i\left(E(R_m) - R_f\right)$
$R_f$ is the risk-free rate. $E(R_m)$ is the expected market return. $\beta_i$ is beta. The term in parentheses is the market risk premium.
Cash-on-cash return calculator
$\text{cash-on-cash} = \dfrac{C}{E}$
$C$ is cash left after operating costs and debt service for one year. $E$ is the equity cheque: down payment plus cash closing costs, minus credits.
I bond composite rate calculator
$c = f + 2i + fi$
$f$ is the annual fixed rate as a decimal. $i$ is the six-month inflation rate as a decimal. $c$ is the annualized composite rate, floored at zero.
TIPS calculator and formula
$P_t = P_0(1+\pi)^t;\quad \text{coupon}=0.01P_t$
$P_0$ is original par, $\pi$ is annual inflation, and $t$ is years. The teaching coupon is 1 percent of adjusted principal $P_t$ .
Treasury bill price calculator
$P=F\left(1-d\frac{t}{360}\right)$
$F$ is face value, $d$ is the bank discount rate, and $t$ is days. The examples use a 360 day basis.
Call option payoff calculator
$\max(S-K,0)-p$
$S$ is spot at expiry, $K$ is strike, and $p$ is premium paid per share.
Put option payoff calculator
$\max(K-S,0)-p$
$K$ is strike, $S$ is spot at expiry, and $p$ is premium paid per share.
Stock split calculator
$\text{new shares}=\text{old shares}\times N,\quad \text{new price}=\frac{\text{old price}}{N}$
$N$ is the number of new shares for each old share. Share count rises by $N$ while price divides by $N$ .
NAV per share calculator
$\text{NAV per share}=\frac{\text{assets}-\text{liabilities}}{\text{shares}}$
Subtract liabilities from assets to get equity, then divide that equity by shares outstanding.
ETF premium calculator
$\text{premium percent}=100\frac{P-\text{NAV}}{\text{NAV}}$
$P$ is market price. Subtract NAV for the dollar gap, then divide by NAV and multiply by 100.
Rental cash flow calculator
$\text{cash flow}=\text{EGI}-\text{operating expenses}-\text{debt service}$
Effective gross income, or EGI, is gross scheduled rent less vacancy. Subtract annual operating expenses and annual debt service.
Gross rent multiplier calculator
$\text{GRM}=\frac{\text{price}}{\text{annual gross rent}}$
Divide property price by annual gross rent. GRM is a multiple, not a percentage.
DSCR calculator
$\text{DSCR}=\frac{\text{NOI}}{\text{annual debt service}}$
NOI is income after operating costs and before the loan. Annual debt service is twelve monthly payments of principal and interest, not one month and not interest alone.
Net operating income calculator
$\text{NOI}=(\text{gross rent}-\text{vacancy})-\text{operating expenses}$
The bracket is effective gross income, the rent actually collected. Operating expenses are the costs of running the building. The mortgage and income tax are outside both.
One percent rule calculator
$\text{rule}=\frac{\text{monthly rent}}{\text{price}}\times 100$
Monthly rent on top, purchase price on the bottom. The result is a percentage, and the rule of thumb is that it should reach 1.
Yield to maturity calculator
$P=\sum_{t=1}^{n}\frac{C}{(1+y/m)^{t}}+\frac{F}{(1+y/m)^{n}}$
$P$ is the price paid, $C$ is the coupon per period, $F$ is face value, $m$ is payments per year, $n$ is the periods left, and $y$ is the annual yield the solver searches for.
Current yield calculator
$\text{current yield}=\frac{\text{annual coupon}}{\text{price}}$
The numerator is a dollar amount, face value times the coupon rate. The denominator is the price paid, not face value, which is the whole reason the two differ.
Dividend yield calculator
$\text{dividend yield}=\frac{D_{\text{annual}}}{P}$
$D_{\text{annual}}$ is the dividend per share over a full year, not one payment. $P$ is the current share price.
Earnings yield calculator
$\text{earnings yield}=\frac{\text{EPS}}{P}=\frac{1}{P/E}$
EPS is earnings per share for the year and $P$ is the share price. The reciprocal of the same two numbers is the price to earnings ratio.
Graham number calculator
$G=\sqrt{22.5\times\text{EPS}\times\text{BVPS}}$
EPS is earnings per share and BVPS is book value per share. The constant 22.5 is a P/E of 15 multiplied by a price to book of 1.5.
Sortino ratio calculator
$S=\frac{R-T}{\sigma_d}$
$R$ is the portfolio return, $T$ the target or minimum acceptable return, and $\sigma_d$ the downside deviation: the standard deviation of returns below the target only.
Earnings per share calculator
$\text{EPS}=\frac{\text{net income}}{\text{shares outstanding}}$
Net income is profit after tax and after any preferred dividends. Shares outstanding is usually the weighted average over the period rather than the count on the last day.
Market cap calculator
$\text{market cap}=P\times N$
$P$ is the share price and $N$ the shares outstanding. The result is the market value of the equity, which is not the same as the value of the whole business.
Modified duration calculator
$D_{\text{mod}}=\frac{D_{\text{mac}}}{1+\frac{y}{m}}$
$D_{\text{mac}}$ is Macaulay duration in years, $y$ the annual yield as a decimal and $m$ the coupon payments per year. The divisor uses the periodic yield, not the annual one.
Perpetuity calculator
$PV=\frac{C}{r}$
$C$ is the payment each period and $r$ the discount rate for that same period. The stream never ends, and the value is still finite.

Business maths

Enterprise value and EV/EBITDA
$EV = E + D - C$
$E$ is the value of the equity, $D$ interest-bearing debt, and $C$ surplus cash. Net debt is $D - C$ , so $EV = E + \text{net debt}$ . The multiple is $EV$ divided by EBITDA when EBITDA is positive.
Unlevered free cash flow calculator
$FCF = EBIT(1-t) + DA - Capex - \Delta NWC$
$EBIT(1-t)$ is NOPAT. $DA$ is depreciation and amortisation, a non-cash charge added back. $Capex$ is capital expenditure. $\Delta NWC$ is the increase in net working capital. A fall in working capital is a source of cash, so a negative delta raises FCF.
ROIC calculator and NOPAT split
$ROIC = \frac{EBIT(1-t)}{IC}$
$EBIT(1-t)$ is NOPAT. $IC$ is invested capital, the operating capital tied up in the firm. On a teaching sheet that is equity plus interest-bearing debt minus surplus cash. The ratio is in percentage points: 15, not 0.15.
ROE calculator and formula
$ROE = \frac{\text{Net income}}{\text{Equity}}$
Net income is profit after interest and tax. Equity is book equity, not market cap. The ratio is in percentage points: 15, not 0.15.
Cash conversion cycle calculator
$CCC = DSO + DIO - DPO$
DSO is days sales outstanding, DIO days inventory outstanding, and DPO days payable outstanding. The operating cycle is DSO plus DIO. CCC subtracts the payable days from that.
Interest coverage calculator
$\text{Coverage} = \frac{\text{EBIT}}{\text{Interest}}$
EBIT is operating profit before interest and tax. Interest is the period's interest expense. The ratio is a multiple: 8, not 8 percent. A zero interest line is not a coverage ratio.
Unlevered beta calculator
$\beta_U = \frac{\beta_E}{1 + (1 - t)(D/E)}$
$\beta_E$ is the equity beta, $t$ the tax rate as a decimal, and $D/E$ the debt-to-equity ratio. $\beta_U$ is the asset beta, the beta the operations would have if they were all-equity financed. Debt beta is assumed to be zero.
Offer premium calculator
$\text{Premium} = \frac{P_{\text{offer}} - P_{\text{unaffected}}}{P_{\text{unaffected}}}$
The unaffected price is the close before the offer leaked, not the last trade. A negative figure is a discount to that close. The page prints percentage points: 30, not 0.30.
NPV calculator and net present value formula
$NPV = \sum_{t=0}^{n} \frac{CF_t}{(1+r)^t}$
$CF_t$ is the cash flow in year $t$ , $r$ is the discount rate as a decimal, and $n$ is the last year. At $t = 0$ the divisor is 1, so money paid or received today is not discounted.
IRR calculator: internal rate of return
$0 = \sum_{t=0}^{n} \frac{C_t}{(1 + IRR)^t}$
$C_t$ is the cash flow at time $t$ , negative when money goes out and positive when it comes back. $IRR$ is the one rate that makes the whole series sum to zero.
WACC formula and calculator
$\text{WACC} = \frac{E}{V} \times R_e + \frac{D}{V} \times R_d \times (1 - t)$
$E$ is the market value of equity, $D$ the market value of debt, and $V = E + D$ the two added together. $R_e$ is the cost of equity, $R_d$ the cost of debt before tax, and $t$ the marginal tax rate that applies to the company.
Leverage ratio formula and calculator
$\text{D/E} = \frac{D}{E} \qquad \text{D/A} = \frac{D}{A} \qquad \text{EM} = \frac{A}{E}$
$D$ is total debt, $E$ is equity and $A$ is total assets. Equity is assets minus everything the company owes, so one balance sheet fixes all three at once. When the debt line is total liabilities, debt-to-equity plus 1 is the equity multiplier.
Break-even point calculator and formula
$Q = \frac{F}{P - V}$
$Q$ is the number of units you have to sell, $F$ the fixed costs, $P$ the price per unit and $V$ the variable cost per unit. $P - V$ is the contribution margin, the part of each sale left over for the fixed costs.
Payback period calculator and formula
$t = n + \frac{C - \sum_{k=1}^{n} CF_k}{CF_{n+1}}$
$C$ is the cash paid up front, $CF_k$ is the cash the project returns in year $k$ , and $n$ is the last full year at which the running total is still short of $C$ . The fraction finishes the job: what is still owed, over the cash arriving in the next year. When every year pays the same, this collapses to $t = C / CF$ .
Current ratio and gross margin calculator
$\text{CR} = \frac{CA}{CL} \qquad \text{QR} = \frac{CA - I}{CL} \qquad \text{GM} = \frac{R - C}{R}$
$CA$ is current assets, $CL$ current liabilities and $I$ inventory, all three read off the balance sheet. $R$ is revenue and $C$ the cost of goods sold, both off the income statement. Gross margin comes out as a decimal, so multiply by $100$ for the percentage.
ROA calculator and formula
$ROA = \frac{\text{Net income}}{\text{Assets}}$
Net income is profit after interest and tax. Assets are total book assets. The ratio is in percentage points: 5.625, not 0.05625.
DuPont ROE calculator and formula
$ROE = \frac{\text{NI}}{\text{Sales}} \times \frac{\text{Sales}}{\text{Assets}} \times \frac{\text{Assets}}{\text{Equity}}$
Net margin times asset turnover times the equity multiplier. The product is net income over equity, which is ROE. ROA is the first two steps.
EV to sales calculator
$\text{EV/Sales} = \frac{E + D - C}{\text{Sales}}$
E is equity value, D interest-bearing debt, C surplus cash. The numerator is enterprise value. The denominator is sales, not EBITDA.
Operating margin calculator
$\text{Operating margin} = \frac{\text{EBIT}}{\text{Sales}} \qquad \text{EBITDA margin} = \frac{\text{EBIT}+\text{DA}}{\text{Sales}}$
EBIT is operating profit before interest and tax. D&A is added to reach EBITDA. Both ratios are percentage points.
Payout ratio calculator
$\text{payout} = \frac{D}{\text{NI}} \qquad g = \text{ROE} \times (1 - \text{payout})$
D is ordinary dividends. NI is net income. ROE is NI over book equity. g is the sustainable growth rate if those ratios stay put.
FCF yield calculator
$\text{FCF yield} = \frac{\text{Unlevered FCF}}{\text{Market cap}}$
FCF is free cash flow to the firm on the usual teaching bridge. Market cap is the equity market value. The ratio is percentage points: 5, not 0.05.
Cash ratio calculator
$\text{Cash ratio} = \frac{\text{Cash}}{\text{Current liabilities}}$
Cash is cash and cash equivalents. Current liabilities are the bills due within a year. The ratio is a coverage, not a percent.
Current ratio calculator
$\text{current ratio}=\frac{CA}{CL}$
$CA$ is assets expected to turn into cash within a year, $CL$ the bills due within a year. Both come straight from the balance sheet.
Working capital calculator
$WC = CA - CL$
$CA$ is current assets and $CL$ current liabilities, both on the twelve month definition. The result is an amount of money, not a ratio.
Gross margin calculator
$\text{gross margin}=\frac{\text{sales}-\text{COGS}}{\text{sales}}\times 100$
Sales is revenue for the period and COGS the direct cost of what was sold. The numerator is gross profit; dividing by sales makes it comparable across businesses.
NOPAT calculator
$\text{NOPAT}=\text{EBIT}\times(1-t)$
EBIT is earnings before interest and tax, and $t$ is the tax rate as a decimal. Interest never enters, which is what makes the result independent of how the business is financed.
EV to EBITDA calculator
$\text{multiple}=\frac{EV}{\text{EBITDA}}$
Enterprise value is market cap plus debt minus cash. EBITDA is earnings before interest, tax, depreciation and amortisation. Both sides describe the whole business rather than the equity.
Annuity present value calculator
$PV = C\,\frac{1-(1+i)^{-n}}{i}$
$C$ is the payment each period, $i$ the rate per period and $n$ the number of payments. The fraction is the annuity factor: what one unit per period is worth today.
Profitability index calculator
$PI=\frac{PV_{\text{inflows}}}{\text{outlay}},\qquad NPV=PV_{\text{inflows}}-\text{outlay}$
Both use the same two numbers. The index divides them and reports value per dollar invested; NPV subtracts them and reports value in dollars.
Days sales outstanding calculator
$DSO=\frac{\text{receivables}}{\text{sales}}\times \text{days}$
Receivables is the balance owed by customers, sales is credit sales for the period, and days is the length of that period. All three must describe the same window.
Sustainable growth rate calculator
$g=\text{ROE}\times(1-\text{payout})$
ROE is return on equity and the payout ratio is the share of earnings paid as dividends. What is left, the retention rate, is the equity the business adds to itself each year.
Sinking fund calculator
$A=\frac{FV\,i}{(1+i)^{n}-1}$
$FV$ is the target, $i$ the rate per period and $n$ the number of deposits. The fraction is the sinking fund factor: the deposit needed for one unit of target.

Factor formulas

The factors behind the printed tables. Each one turns a single multiplication into an answer, which is why they survived long after calculators replaced the books they came from.

Present value of 1
$PV\text{ factor} = \frac{1}{(1 + r)^{n}}$
Multiply a single future amount by the factor to bring it back to today.
Future value of 1
$FV\text{ factor} = (1 + r)^{n}$
Multiply a single amount today by the factor to carry it forward.
Present value of an annuity of 1
$PVIFA = \frac{1 - (1 + r)^{-n}}{r}$
Multiply a level payment by the factor to value the whole stream today.
Future value of an annuity of 1
$FVIFA = \frac{(1 + r)^{n} - 1}{r}$
Multiply a level payment by the factor to get what the stream is worth at the end.
Loan payment factor
$CRF = \frac{r}{1 - (1 + r)^{-n}}$
Multiply the amount borrowed by the factor to get the payment per period.
Sinking fund factor
$SFF = \frac{r}{(1 + r)^{n} - 1}$
Multiply a target future amount by the factor to get the deposit each period.

Free to use and free to cite. Educational material, not financial advice.