Real Estate Math Cheat Sheet
Every formula below is here because PSI or Pearson VUE names the topic in its published content outline, and every row says which. Nothing is here because a prep book prints it. That single rule removes about a third of a typical real estate math cheat sheet. It also produces a lopsided result worth seeing: 13 of the 26rows point at something inside PSI's calculations area, while 23point at something inside Pearson VUE's.
One thing to be straight about before you scroll: there is no PDF and no email box to get past. This page is the sheet. If you want it on paper, press Ctrl+P or Cmd+P and print it, or choose Save as PDF in that same dialog, which produces the file a download button would have handed you anyway.
Every formula, with the outline reference for both providers
PSI numbers its calculations area XI. Pearson VUE numbers its math area VIII, and each of its seven lettered sub-areas is worth exactly one scored item. Where a cell says "Not named", that provider does not list the topic in its math area. It may still be examinable somewhere else, which is the point of the last three rows.
| Topic | The relationship | PSI | Pearson VUE |
|---|---|---|---|
| Commission | Sale price × rate = gross commission. The rate applies to the price the property sold for. | Not named | VIII.C |
| Commission split | Gross commission × brokerage share × agent share. Two sequential multiplications, never a sum. | Not named | VIII.C |
| Seller’s net proceeds | Sale price − commission − seller-paid closing costs − loan payoff. | XI.A.1 | VIII.E.3 |
| Net to seller, in reverse | (required net + seller costs) ÷ (1 − commission rate) = sale price. Divide, never add the rate back. | XI.A.1 | VIII.E.3 |
| Buyer funds at closing | Purchase price − loan amount − earnest money + buyer-paid costs and prepaids. | XI.A.2 | VIII.E.1 and VIII.E.4 |
| Area | Length × width for a rectangle; ½ × base × height for a triangle. Decompose irregular shapes, and convert units before multiplying. | Not named | VIII.A.1 |
| Acreage | Square feet ÷ 43,560 = acres. | Not named | VIII.A.2 |
| Capitalization rate | NOI ÷ value = rate. Value = NOI ÷ rate. NOI is after operating expenses and vacancy, before debt service and depreciation. | XI.B.2 | VIII.B.2 and VIII.B.3 |
| Equity | Market value − all liens. Not value minus the original purchase price. | XI.B.1 | VIII.B.4 |
| Loan-to-value | Loan ÷ value, where a lender uses the lower of price and appraised value. Down payment percent = 100% − LTV. | XI.B.3 | VIII.D.2 |
| Discount points | Points × 1% × loan amount. One point is 1% of the loan, never of the sale price. Origination fees are computed the same way on a separate line. | XI.B.4 | VIII.D.4 |
| Per-diem interest | Balance × annual rate ÷ days in the year = daily interest, then × days. Mortgage interest runs in arrears. | Not named | VIII.D.1 |
| Amortized payment | (loan ÷ 1,000) × the payment factor given in the question. The factor is per $1,000 and you are not expected to derive it. | XI.A.5 implies it | VIII.D.4 |
| PITI | Principal + interest + (annual tax ÷ 12) + (annual insurance ÷ 12). Mortgage insurance, where present, is a fifth line and is not in the acronym. | XI.A.5 | VIII.E.2 |
| Proration | Annual amount ÷ days in the year × days owed. Divisor and day count must come from the same convention. | XI.A.3 | VIII.E.5 |
| Ad valorem tax | Assessed value ÷ 1,000 × mill rate. Assessed value after exemptions, not market value. | XI.A.3 | VIII.B.6 |
| Transfer or documentary tax | Taxable consideration ÷ the unit, rounded up to a whole unit, × the rate per unit. | XI.A.4 | VIII.E.7 |
| Debits and credits | A prepaid item used by the buyer credits the seller and debits the buyer. An item in arrears runs the other way. | Implied by XI.A.3 | VIII.E.6 |
| Appreciation | Straight line: original × (1 + n × rate). Compounding: original × (1 + rate) to the power n. Read the question to see which it wants. | Not named | VIII.F.2 |
| Depreciation, straight line | Improvement cost ÷ economic life = annual; × effective age = accrued. Land does not depreciate, so strip the site value out first. | Not named | VIII.F.3 |
| Return on investment | Annual return ÷ amount invested. Where a loan is involved, invested means cash in, not purchase price. | Not named | VIII.F.1 |
| Effective gross income | Potential gross income − vacancy and collection loss. Operating expenses come off after that to reach NOI. | Not named | VIII.G.1 |
| Rent and tenancy calculations | Monthly rent ÷ days in the month for a daily rate; percentage leases add a rate on sales above a stated breakpoint. | Not named | VIII.G.2 |
| Gross rent multiplier | Price ÷ gross monthly rent. Gross income multiplier uses annual gross income instead, so the two differ by a factor of 12. | Not named | Not named for salespeople. Broker math VIII.B; salespeople meet it at III.C.4, under appraisal |
| Profit or loss percentage | (new − old) ÷ old. The denominator is always the earlier figure. | Not named | Not named. Nearest is VIII.F.1 |
| Qualifying ratios | Housing expense ÷ gross monthly income; total fixed payments ÷ gross monthly income. Income is gross, not net. | Not named | Not in the math area at all. VII.B.5, under Financing and Settlement |
The three formulas most likely to be studied for the wrong exam: commission, area and acreageare worth real scored items on Pearson VUE and are not named in PSI's math area at all. If you do not yet know which provider runs your state's exam, PSI real estate exam and Pearson VUE real estate exam both say so, and where do you take the real estate exam covers where you will actually sit it.
The relationships themselves are arithmetic, so they are not sourced the way a figure is. What is sourced is the right-hand side: the outline reference that puts each topic on an exam. Both outlines are reproduced in full on real estate math.
The numbers you actually have to memorize
Pearson VUE publishes a short list under the heading "The following information is NOT available at the test center and SHOULD be memorized". It contains two conversions. That is the entire declared memorization requirement in either provider's math documentation.
| Conversion | Value | Status |
|---|---|---|
| Square feet per acre | 43,560 | Declared must-memorize by Pearson VUE |
| Feet per mile | 5,280 | Declared must-memorize by Pearson VUE |
Commonly taught, not required
These four are on every cheat sheet in the category, and neither provider names any of them, in the math outline or in the math notes. They come from the Bureau of Land Management, which describes the survey system rather than the exam. Learn them anyway, because area questions use the vocabulary. Just do not believe anyone who tells you a provider requires them.
| Figure | Value | Who actually says so |
|---|---|---|
| Acres per section | 640 | Bureau of Land Management, which writes that each section is “usually 640 acres” |
| Sections per township | 36 | Bureau of Land Management: “Each township is broken down into 36 sections” |
| Township dimensions | 6 miles square, 36 square miles | Bureau of Land Management: townships are “for the most part 36 square miles or 6 miles square” |
| Quarter-quarter section | 40 acres | Bureau of Land Management: dividing a section into sixteen gives 40 acres each |
The BLM hedge is worth reading twice. Sections are usually 640 acres, because survey lines do not close perfectly and the correction falls on the edge sections. The exam does not hedge. But a candidate who has seen the hedge understands why area questions hand you the dimensions instead of expecting you to assume them.
Three definitions worth quoting exactly
- One discount point.The Consumer Financial Protection Bureau: "One point equals one percent of the loan amount", worked as $1,000 on a $100,000 loan. Of the loan. Not of the price.
- One mill.Florida's Department of Revenue: "one mill is one dollar per $1,000 of assessed value", and it states the equation as taxable value ÷ 1,000 × millage rate = tax owed.
- Loan-to-value.The CFPB defines it as "a measure comparing the amount you are financing with the appraised value of the property". When a question gives you a price and a lower appraisal, the appraisal is the denominator.
Transfer tax rates are state law and vary, so no rate belongs on a national sheet. Florida is a worked example rather than a benchmark: 70 cents per $100 of consideration on a deed, or a portion thereof, with Miami-Dade instead charging 60 cents per $100 plus a 45-cent surtax that does not apply to single-family homes.
Prorations: the question tells you which convention to use
This is the most useful sentence either provider publishes about math, and almost nobody quotes it. Pearson VUE prints a "Notes on Math Calculations"block after the national content outline, and repeats it in the body of its candidate handbooks: "If a question requires the calculation of prorated amounts, the question will specify whether the calculation should be made on the basis of 360 or 365 days a year; and/or whether the day of closing belongs to the buyer or the seller for purposes of prorations."
Read that again if you have spent an evening trying to decide which convention "the exam uses". Neither, by default. A well-written item hands you the convention as part of the fact pattern. The ambiguity the prep industry teaches candidates to agonize over is resolved by the item writer, in writing, in a published document.
| Convention | Divisor | Month length | When you see it |
|---|---|---|---|
| 360-day statutory year | 360 | Every month counts 30 days | Questions that say "360-day year" |
| 365-day actual year | 365 | Real calendar days, so February counts 28 | Questions that say "365-day year", and nearly every real closing |
Both halves of the convention move together. Under a 365-day year you divide by 365 and count real calendar days. Under a 360-day year you divide by 360 and count every month as 30. Mixing them, a 365 divisor with 30-day months, is the most common arithmetic error in the topic. That is our assessment from writing the question bank, not a provider statement.
Whose day is the closing day
- Day of closing to the seller.The seller is charged through and including the closing date. The seller-side day count includes closing day; the buyer's begins the next day.
- Day of closing to the buyer. The seller is charged up to but not including the closing date. The buyer-side count includes closing day.
It moves the answer by exactly one day, in opposite directions for the two parties. Which is why it matters that the question states it, and why a distractor is usually built one day either side.
An asymmetry worth knowing.The published guarantee above is Pearson VUE's. PSI publishes nothing on prorations beyond naming themat XI.A.3, "Real property tax and other prorations". No PSI bulletin we read contains the strings "360" or "365" or any statement of a proration convention. A PSI candidate has no published promise that the convention will be given, and should read the stem for it rather than assume. Two versions of the Pearson VUE wording also differ slightly: the content outline says "and/or", while the handbook body says "and", which would mean both facts are always given.
Direction is examinable separately from arithmetic. Pearson VUE gives "Debits and credits" its own sub-item at VIII.E.6. Taxes paid in arrears produce a seller debit and a buyer credit; anything prepaid runs the other way. Which items are in arrears is state law rather than national exam content.
Three problems that use the sheet
One legal description, one 365-day proration and one 360-day proration, taken from the 105 math questions in our bank. Notice that both proration questions state their own convention, exactly as Pearson VUE says they will.
How many acres are in the N ½ of the SW ¼ of the SE ¼ of a section?
Answer: 20 acres. 640 × ½ × ¼ × ¼ = 20 acres. Multiply every fraction in the description against the 640-acre section; skipping the N ½ gives 40.
Taxes of $5,475 for the year are unpaid. Closing is 10 March. Using a 365-day year and charging the seller through the day before closing, the seller owes:
Answer: $1,020. $5,475 ÷ 365 = $15 per day. January 31 + February 28 + 9 days of March = 68 days. 68 × $15 = $1,020 debited to the seller.
Annual taxes of $4,380 are paid in arrears. Closing is 15 September. Using a 360-day year with 30-day months, what is the seller’s share?
Answer: $3,102.50. $4,380 ÷ 360 = $12.1667 per day. From 1 January through 15 September is 8 months × 30 = 240 days, plus 15 = 255 days. 255 × $12.1667 = $3,102.50, debited to the seller.
Real estate math (calculations) practice questions has the rest, timed and scored. real estate exam simulator puts them back in proportion inside a full-length run.
What is deliberately not on this sheet
A cheat sheet is judged by what it leaves out as much as by what it contains, so here is the reasoning rather than a silent omission.
- The 28/36 qualifying ratio. We could not find a federal regulator, a provider handbook or a published selling guide that states it. It appears to be a lender rule of thumb with no publisher, and neither provider puts qualifying ratios in the math area anyway.
- FHA's 31/43 ratios as a current figure. The only source we could stand behind is an archived HUD reference guide whose underlying handbook has been superseded, and current maximums vary by credit score and underwriting method. A number we cannot date is worse than an absent one.
- Gross rent multiplier, for salespeople. It is genuinely examinable, but Pearson VUE files it under appraisal at III.C.4 rather than in the salesperson math area. It appears in the math area only on the broker outline.
- "The nine formulas", the T-bar and IRV. None of the three appears in any PSI or Pearson VUE document we read. The underlying relationships are real and both outlines name capitalization rate. The labels are prep-industry vocabulary, and real estate math explains where they probably came from.
- A pass mark for the math section. There is not one. You pass the national portion as a whole, and how many questions are on the real estate exam has the thresholds by state.
Printing it, and what to do the night before
Use your browser's print command. Save as PDF in that dialog if you want a file. We have not built a download, and we are not going to pretend one exists in order to collect an email address: real estate exam cheat sheet works the same way for the non-math material.
Two rules that beat re-reading the sheet, in the last twenty-four hours:
- Learn the two conversions cold, because they are the only figures a provider states you will not be given: 43,560 and 5,280.
- Work problems, not formulas. Pearson VUE classifies every math item as application or analysis and none as knowledge, so recognizing a formula scores nothing on its own. Twenty timed problems on Real estate math (calculations) practice questions tell you more than an hour with this page.
Then check whether you get a calculator at all, because that is set by your state rather than by your provider, and one state on our list bans handheld calculators outright. See can you use a calculator on the real estate exam.
Common questions
What real estate math formulas do I need to memorize?
Fewer than most sheets imply. The topics come from your provider: PSI names nine calculation sub-topics and Pearson VUE names seven sub-areas worth one item each, and the two lists differ. The only figures either provider declares you must memorize are 43,560 square feet per acre and 5,280 feet per mile.
Is there a free real estate math cheat sheet PDF?
This page is the sheet, and there is no separate PDF to download. Print it from your browser, or choose Save as PDF in the print dialog, which gives you the same file without an email signup.
Does the exam use a 360-day or a 365-day year for prorations?
Pearson VUE publishes that the question will specify which, and whether the day of closing belongs to the buyer or the seller. So there is no default to learn. PSI publishes nothing on the subject beyond naming prorations, so a PSI candidate should read the stem carefully for the convention rather than assume one.
Do I need to know that a section is 640 acres?
Neither provider names 640 acres per section or 36 sections per township as required memorization. Those figures come from the Bureau of Land Management, which itself writes that a section is usually 640 acres. Learn them, because legal description questions use the vocabulary, but treat them differently from the two conversions a provider does require.
Is one discount point one percent of the price or of the loan?
Of the loan. The Consumer Financial Protection Bureau states that one point equals one percent of the loan amount, and gives $1,000 on a $100,000 loan as the example. When a question gives you a sale price and a loan-to-value ratio, compute the loan first.
Where to go next
Sources
Every figure on this page was read from the source listed beside it on the date shown. Candidate handbooks are revised without notice, so check yours before you rely on a number.
- Pearson VUE Nevada real estate content outlines (#092901), math area VIII and the Notes on Math Calculations block checked
- Pearson VUE Arizona real estate content outlines (#090301), independent copy of the same outline and notes checked
- Pearson VUE Texas real estate content outlines (#094401), third copy of the memorized-constants list checked
- Pearson VUE Nebraska real estate candidate handbook (#092800), handbook wording of the proration note checked
- Pearson VUE national/general content outline for salespersons and brokers (#099913), broker math area checked
- PSI / Iowa Real Estate Commission licensing information bulletin, area XI Real Estate Calculations checked
- PSI / New Hampshire examination candidate handbook, confirming the same sub-topics checked
- Bureau of Land Management, land legal descriptions (sections, townships and the “usually 640 acres” hedge) checked
- Consumer Financial Protection Bureau, what are discount points and lender credits checked
- Consumer Financial Protection Bureau, what is a loan-to-value ratio checked
- Florida Department of Revenue, a Florida homeowner’s guide to millage checked
- Florida Department of Revenue, documentary stamp tax checked
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