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Every formula is grouped by official syllabus topic, with the formula in math notation plus a one-line note on when to use it (or a watch-out from CAIA, CFA, or other prep-provider commentary). Coverage is calibrated to the 2026 syllabus and refreshed when the corpus changes.

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Free IRS Enrolled Agent SEE Part 1 Formula Sheet, No Signup (2026)

Preliminary Work and Taxpayer Data 6 items

Dependent's standard deduction

SD_{dep} = \min(\max(\$1{,}350,\ E + \$450),\ SD_{reg})

— E = earned income, SD_reg = regular standard deduction for filing status

Foreign housing exclusion

HE = \min(H - 0.16 \times FEIE,\ 0.14 \times FEIE)

— H = qualified housing costs, FEIE = foreign earned income exclusion cap ($130,000 in 2025)

Kiddie tax on a child's unearned income

T = (U - 2700) \times t_p + 1350 \times t_c

— U = child's unearned income (>$2,700), t_p = parent's marginal rate, t_c = child's rate on the second $1,350; first $1,350 untaxed

Additional child tax credit refundable amount

ACTC = \min(1{,}700n,\ 0.15 \times (EI - 2{,}500))

— n = qualifying children with SSN, EI = earned income

Excess Social Security tax withholding refund (2025)

\text{Excess} = \text{SS withheld} - 10{,}918.20

where ceiling = $176,100 wage base × 6.2%, claimed only when multiple employers over-withheld

Child tax credit after MAGI phaseout

CTC = \max(0,\ 2{,}000n - 50 \cdot \lceil (MAGI - T)/1{,}000 \rceil)

— n = qualifying children under 17 with SSN, T = $200K (S/HoH/MFS) or $400K (MFJ)

Income and Assets 15 items

Installment sale gross profit ratio

GPR = \dfrac{Gross\ profit}{Contract\ price}

— gross profit = sale price − adjusted basis − selling expenses; contract price = total payments due (Form 6252)

Taxable state tax refund under section 111 tax benefit rule

T = \min(R,\ I - S,\ U)

— R = refund received, I = prior-year itemized deducted, S = prior-year standard deduction, U = unrecovered SALT

IRA pro-rata taxable distribution

Taxable = D \times \left(1 - \dfrac{B}{V}\right)

— D = distribution, B = total nondeductible basis (Form 8606), V = aggregate traditional IRA value before distribution

Insolvency exclusion amount for cancellation of debt

\text{Excluded COD} = \min(\text{COD},\ L - \text{FMV})

— L = liabilities, FMV = FMV of assets, both measured immediately before discharge

Recourse foreclosure cancellation of debt income

\text{COD} = \text{Debt canceled} - \text{FMV}

— FMV = property fair market value at foreclosure; property gain/loss = FMV − basis is computed separately

Active participation rental real estate \$25,000 loss allowance

\text{Allowance} = \$25{,}000 - \tfrac{\text{MAGI} - \$100{,}000}{2}

— MAGI = modified AGI; allowance fully phased out at $150,000

Excess IRA contribution excise tax

\text{Excise} = 0.06 \times E

— E = excess contribution remaining at year-end, applied each year until withdrawn or absorbed

Missed RMD excise tax

\text{Excise} = 0.25 \times S

— S = RMD shortfall; rate drops to 10% if corrected within 2 years with Form 5329 explanation

Mandatory withholding on plan-to-participant distribution

W = 0.20 \times G

— G = gross plan distribution; participant must replace W from other funds within 60 days to roll the full gross amount

Substituted basis in a Section 1031 like-kind exchange

B_{new} = B_{old} + \text{boot paid} + G_r - \text{boot received} - L_r

— B = basis, G_r = gain recognized, L_r = loss recognized

Recognized gain in a Section 1031 like-kind exchange

G_r = \min(G_{realized}, \text{boot received})

— G_r = gain recognized, G_realized = realized gain, boot = cash or non-like-kind property received

Realized gain or loss on a property disposition

G = AR - AB

— AR = amount realized (sale proceeds net of selling expenses), AB = adjusted basis (cost plus improvements minus depreciation)

Self-employed health insurance deduction cap

\text{SEHI}_{\max} = \text{Net SE} - \tfrac{1}{2}\text{SE tax} - \text{Retirement deduction}

— excess premiums shift to Schedule A medical

Net self-employment earnings from Schedule C

\text{Net SE} = 0.9235 \times \text{Schedule C net profit}

; 0.9235 = 1 minus employer-equivalent SE tax share; 15.3% SE tax then applies to Net SE

SEP-IRA deduction cap for a self-employed owner

\text{SEP}_{\max} = 0.20 \times (\text{Net SE} - \tfrac{1}{2}\text{SE tax})

— capped at $70,000; 25% of comp for employees

Deductions and Credits 9 items

Investment interest expense deduction

D = \min(I_{inv},\ NII)

— I_inv = investment interest paid, NII = net investment income (interest, non-qualified dividends, short-term gains); excess carries forward indefinitely

Itemized medical expense deduction above the AGI floor

D = \max(0,\ M - 0.075 \times AGI)

— M = qualified unreimbursed medical expenses (including LTC up to age-band cap), AGI = adjusted gross income, 7.5% = statutory floor

Quid pro quo charitable contribution deduction

D = P - \text{FMV}_{benefit}

— P = payment to charity, FMV_benefit = fair market value of goods or services received by the donor (dinner, raffle, auction item)

SSTB includible QBI inside the phase-in window

\text{Includible QBI} = \text{QBI} \times (1 - \text{D\%})

— D% = (TI − threshold) / window; same scaling applies to W-2 wages and UBIA

QBI deduction inside the phase-in range

\text{QBI}_{\text{comp}} = \text{Tent} - (\text{Tent} - \text{WageLim}) \cdot \text{D\%}

— Tent = 20% × QBI; WageLim = W-2/UBIA cap; D% = disallowance percentage

Overall QBI deduction with REIT and PTP income

\text{QBI Ded} = \min(0.20 \cdot \text{QBI} + 0.20 \cdot (\text{REIT}+\text{PTP}),\ 0.20 \cdot (\text{TI} - \text{NCG}))

— TI = taxable income before QBI ded, NCG = net capital gain

Premium tax credit allowed amount

PTC = \min(\text{premium paid},\ SLCSP - \text{expected contribution})

— SLCSP = second-lowest-cost silver plan premium, expected contribution = applicable % × household income

General business credit limitation

\text{Limit} = \text{net income tax} - \max(\text{TMT},\ 0.25 \times (\text{net regular tax} - \$25{,}000))

— TMT = tentative minimum tax

Residential clean energy credit (Section 25D)

\text{Credit} = 0.30 \times \text{qualifying expenditures}

— expenditures = solar, geothermal, wind, biomass, fuel cell costs (fuel cells capped at $500 per half-kW)

Taxation 3 items

Failure-to-file penalty

P_{file} = \min(0.05m, 0.25) \times U

— m = months (or part) late, U = unpaid tax; reduced by concurrent failure-to-pay penalty for the same months

AMT exemption phaseout

E = \max(0, E_0 - 0.25 \times (AMTI - T))

— E = allowed exemption, E₀ = full exemption ($88,100 single / $137,000 MFJ), T = phaseout threshold ($626,350 / $1,252,700)

Additional Medicare tax

\text{AddlMed} = 0.009 \times (\text{Wages} + \text{SE} - T)

— SE = self-employment earnings, T = threshold ($200K single, $250K MFJ, $125K MFS)

Advising the Individual Taxpayer 10 items

Basis of replacement shares after a wash sale

B_{new} = C_{new} + L_{disallowed}

— C_new = cost of replacement shares, L_disallowed = loss disallowed under §1091; holding period tacks

Required minimum distribution (RMD)

RMD = \dfrac{B_{prior}}{F_{ULT}}

— B_prior = prior year-end IRA balance, F_ULT = Uniform Lifetime Table divisor for current age (begins age 73)

Maximum long-term tax on a collectibles gain under Section 408(m)

T = \min(28\%, r_{ord}) \times G

— r_ord = taxpayer's ordinary marginal rate, G = net long-term gain on collectibles

Nonqualified annuity exclusion ratio

\text{Exclusion ratio} = \frac{\text{Investment in contract}}{\text{Expected return}}

— IIC = after-tax basis, expected return = total contract payout; taxable = payment × (1 − ratio)

Section 529 five-year-forward gift exclusion election cap

\text{Max} = 5 \times \text{annual gift exclusion}

— 2025: 5 × $19,000 = $95,000 per donor ($190,000 MFJ split); elected on Form 709

Section 1041 carryover basis on spousal or divorce-incident transfer

B_{recipient} = B_{transferor}

— B = adjusted basis; gain/loss nonrecognition under §1041; holding period also tacks

Injured spouse allocated refund share on Form 8379

R_{IS} = WH_{IS} + C_{IS} - T_{IS}

, capped at joint refund — WH = withholding, C = credits allocated to injured spouse, T = MFS-allocated tax on her income

Capital loss carryover to next year

Carry = NetLoss - \$3{,}000

— NetLoss = net capital loss after offsetting gains; use $1,500 if MFS; ST/LT character preserved

Annualized income installment required payment

Inst_i = AnnTax_i \times p_i

— AnnTax_i = annualized tax for cumulative period i; p_i = 22.5%, 45%, 67.5%, 90% for Q1-Q4

Post-2017 net operating loss deduction limit

NOL_{ded} \leq 0.80 \times TI_{pre}

— NOL_ded = allowable NOL deduction; TI_pre = taxable income computed before the NOL deduction

Specialized Returns for Individuals 9 items

Tentative estate and gift tax above the \$1M base

T = \$345{,}800 + 0.40 \times (B - \$1{,}000{,}000)

— B = tax base (taxable estate + adjusted taxable gifts), 40% is the top unified rate above $1M

Federal estate tax with unified credit

\text{Estate Tax} = T(TE + ATG) - GTP - UC

— TE = taxable estate, ATG = adjusted taxable gifts, GTP = gift tax payable on prior gifts, UC = unified credit ($5,389,800 in 2025)

Deceased Spousal Unused Exclusion amount

DSUE = E_1 - (TE_1 + ATG_1)

— E_1 = first decedent's basic exclusion, TE_1 = first decedent's taxable estate, ATG_1 = first decedent's adjusted taxable gifts

Surviving spouse's total gift and estate exemption with DSUE

E_{surv} = BEA_{own} + DSUE

— BEA_own = survivor's own basic exclusion amount ($13.99M in 2025), DSUE = deceased spousal unused exclusion elected on first spouse's Form 706; does NOT apply to GST

Current-year gift tax under the Form 709 cumulative method

T_{cur} = T(G_{cum}) - T(G_{prior}) - C_{rem}

— T() = tax from §2001 schedule, G_cum = cumulative lifetime taxable gifts including current year, G_prior = prior taxable gifts, C_rem = remaining unified credit

Gift-split taxable gift per spouse on a separate-property gift

T_{spouse} = \frac{G}{2} - E_{ann}

— G = total separate-property gift to one donee, E_ann = annual exclusion per donee per spouse ($19,000 in 2025); both spouses must consent on Form 709

Section 6038(c) foreign tax credit reduction for missing Form 5471 or 8865

R = (10\% + 5\% \times n) \times FT

— n = full 3-month periods of continued failure after IRS notice, FT = available foreign taxes; capped at lesser of $10,000 or FT

Form 8938 maximum failure-to-file penalty

P = \$10{,}000 + \min(\$50{,}000,\ \$10{,}000 \times k)

— k = 30-day periods after IRS notice; add 40% accuracy penalty on related underpayment

Willful FBAR penalty

P = \max(\$165{,}353,\ 0.50 \times B)

— P = penalty, B = account balance at time of violation (2025 inflation-adjusted floor)

Preliminary Work and Taxpayer Data 6 items

CTC is $2,000 per qualifying child under 17, refundable up to $1,700 as ACTC.

2025 HSA contribution limits are $4,300 self-only and $8,550 family, with a $1,000 catch-up at age 55+.

A 2025 qualifying relative must have gross income under $5,200 and receive more than half of support from the taxpayer.

The Form 1116 de minimis exception skips the form when foreign tax shown on 1099s is $300 or less ($600 MFJ).

Kiddie tax applies to a child's unearned income above $2,700 at the parent's marginal rate, filed on Form 8615.

Form 8938 thresholds for a single U.S. resident are $50,000 at year-end or $75,000 at any time during the year.

Income and Assets 15 items

2025 LTCG and qualified-dividend rates are 0% up to $48,350 single / $96,700 MFJ, with the top 20% rate above $533,400/$600,050.

§121 excludes up to $250,000 single / $500,000 MFJ of gain on a principal residence with 2-of-5-year ownership and use tests.

QCDs are available at age 70½, capped at $108,000 per year (2025), and count toward the RMD while excluded from AGI.

Form 5471 is required for U.S. persons owning 10% or more of a foreign corporation, with a $10,000 per-form minimum penalty.

W-2G is issued at $1,200 for slots/bingo, $1,500 for keno, $5,000 for poker, or $600 and 300x the wager.

Qualified principal residence COD exclusion (through 2025) is capped at $750,000 ($375,000 MFS), acquisition debt only.

Qualified plan loans are capped at the lesser of $50,000 or 50% of the vested balance, repaid within 5 years.

Roth IRA contributions phase out from $150,000 to $165,000 single and $236,000 to $246,000 MFJ in 2025.

The 2025 IRA contribution limit is $7,000 with a catch-up to $8,000 at age 50.

ISO favorable treatment requires holding the stock at least 2 years from grant and 1 year from exercise, with the bargain element an AMT preference at exercise.

Section 1031 like-kind exchanges require identification within 45 days and closing within 180 days, and post-2018 apply only to real property.

Section 1245 depreciation is recaptured as ordinary income, while unrecaptured Section 1250 gain on real property is taxed at a maximum rate of 25%.

Traditional IRA active-participant deduction phaseout is $79,000-$89,000 single and $126,000-$146,000 MFJ for 2025.

SEP-IRA contributions are capped at 25% of employee comp or 20% of net SE income for the owner, with an overall cap of $70,000.

Student loan interest deduction is capped at $2,500 with MAGI phaseout $85,000-$100,000 single and $170,000-$200,000 MFJ; MFS disqualified.

Deductions and Credits 9 items

QBI phase-in begins at taxable income of $197,300 single/HoH/MFS and $394,600 MFJ for 2025.

2025 mileage rates are $0.70 business, $0.21 medical, and $0.14 charitable.

Personal casualty losses in a federally declared disaster apply a $100 per-event floor and a 10% of AGI floor on the aggregate.

Nonresident aliens cannot claim the standard deduction except under U.S.-India treaty Article 21(2) for students and business apprentices.

Federally declared disaster casualty losses on 1040-NR Schedule A apply a floor of $100 per event plus 10% of U.S.-source AGI.

The §199A W-2 wage and UBIA limit is the greater of 50% of W-2 wages or 25% of W-2 wages plus 2.5% of UBIA.

The 2025 adoption credit is $17,280 per child, non-refundable with a 5-year carryforward, phasing out from MAGI $259,190 to $299,190.

2025 EITC maximums are $8,046 with 3+ kids and $4,328 with 1 child, with investment income capped at $11,950.

AOTC and LLC both phase out at MAGI $80,000 to $90,000 single/HoH and $160,000 to $180,000 MFJ, with MFS disqualified from both.

Taxation 2 items

When a return is more than 60 days late, the minimum failure-to-file penalty is the lesser of $510 (2025) or 100% of unpaid tax.

Schedule H 2025: cash wages of $2,800 to one household employee triggers FICA; $1,000 in any quarter triggers FUTA on the first $7,000.

Advising the Individual Taxpayer 12 items

2025 gift annual exclusion is $19,000 per donee, with a lifetime gift/estate exemption of $13.99M reported on Form 709; top transfer-tax rate is 40%.

§72(t) 10% early-withdrawal penalty applies before age 59½; first-time homebuyer IRA exception is capped at $10,000 lifetime.

§6654 estimated-tax safe harbor: pay 90% current or 100% prior, rising to 110% if prior AGI exceeds $150,000.

2025 401(k)/403(b)/457(b) elective deferral is $23,500 with an age-50 catch-up of $7,500 and an ages 60-63 super catch-up of $11,250.

SECURE 2.0 allows unused §529 balances to roll to the beneficiary's Roth IRA up to $35,000 lifetime when the account is at least 15 years old.

The §529 5-year-forward election front-loads $95,000 single or $190,000 MFJ in one year via Form 709.

Section 1041 treats property as incident to divorce if transferred within 1 year of marriage ending or pursuant to instrument within 6 years.

Pre-2019 alimony triggers front-loading recapture if payments drop by more than $15,000 between years 1, 2, and 3.

Alimony under instruments executed after 12/31/2018 is not deductible by payer and not taxable to recipient.

Post-2017 NOLs carry forward indefinitely with no carryback and are capped at 80% of taxable income before the NOL deduction.

Charitable contribution carryovers last 5 years (or 15 years for qualified conservation easements), and foreign tax credits carry 1 back, 10 forward by category.

Form 1045 tentative refund for an NOL must be filed within 12 months of the loss year-end, and the IRS must act on it within 90 days.

Specialized Returns for Individuals 8 items

§6166 defers estate tax when a closely held business exceeds 35% of the adjusted gross estate, with 2% interest on the first $1,800,000 deferred.

Form 706-NA is required for a nonresident alien decedent with U.S.-situs property exceeding $60,000, due 9 months after death.

Gift-splitting under §2513 doubles the 2025 annual exclusion to $38,000 per donee, and each spouse must file a separate Form 709.

A GST skip person is at least 2 generations below the transferor, or an unrelated individual more than 37.5 years younger.

The 2025 annual gift limit to a noncitizen spouse is $190,000, while transfers to a U.S. citizen spouse qualify for an unlimited marital deduction.

Form 3520 is triggered by foreign gifts exceeding $100,000 from a nonresident individual or $20,116 from a foreign corporation or partnership in 2025.

Willful FBAR penalty is the greater of $100,000 or 50% of the account balance; non-willful is $10,000 per form per year post-Bittner.

Form 8938 failure-to-file is $10,000 plus $10,000 per 30-day continuation capped at $50,000, plus a 40% accuracy penalty on undisclosed assets.

Free IRS Enrolled Agent SEE Part 1 (Individuals) Formula and Limits Sheet (2026)

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