How the calculation works

Who this is for: Developers and technical payroll staff who want T4127 (Payroll Deductions Formulas) Option 1 in plain language before they read factor symbols.

When you finish: You can walk through the six Chapter 4 steps and reconcile one Ontario weekly paycheque to net_pay 800.79.

Chapter 4 describes Option 1: you project annual income from this pay period, compute annual tax, then divide back to the cheque. Chapters 6 and 7 add CPP and EI for the period.

Six Option 1 steps (Chapter 4)

Annual taxable income (A). Scale this period’s pensionable and taxable earnings to a full year. Subtract CPP additional contribution deductions (F5, F5A, F5B) per Step 1. P is the number of pay periods in the year (52 for weekly).

Federal annual tax (T1). Pick the federal rate R and constant K for A. Compute basic tax T3, then subtract credits K1, K2, K4 (and K3, LCF when they apply). The result is annual federal tax T1.

Federal per-period tax. Divide T1 by P and round to cents. Add any extra tax L the employee requested on TD1.

Provincial annual basic tax (T4). Use provincial rate V and constant KP. Apply the same credit pattern at the provincial level (K1P, K2P, and related factors).

Provincial annual tax (T2). Start from T4. Add Ontario surtax V1 and health premium V2 when they apply. Apply reductions S and Y where relevant. Other provinces skip lines that do not apply.

Tax for the pay period (T). Combine federal and provincial annual tax: round (T1 + T2) / P, then add L. Employee total_tax on the API is often the sum of separately rounded federal and provincial lines (PDOC-style); breakdown.T follows the T4127 Step 6 quotient.

After Chapter 4, the engine computes C (CPP), C2, and EI. Factor C2 is CPP2 (second additional CPP) when pensionable earnings exceed YMPE (Year's Maximum Pensionable Earnings).

net pay = gross pay − total tax − CPP − C2 − EI

Worked example: Ontario, weekly, $1000, claim code 1 on the TD1

Inputs match the first-call vector:

Field	Value
`as_of`	`2026-01-15` (selects rule set `2026-01-01`)
`province`	`ON`
`pay_period`	`52`
`gross_pay`	`1000.00`
`federal_claim_code`	`1`
`provincial_claim_code`	`1`

A claim code (TD1 box) maps personal amounts to TC and TCP. Code 1 is the default basic personal amount for 2026.

Step 1: `A`

The engine annualizes this cheque and lands on A = 51514.84.

Steps 2 and 3: Federal

With R = 0.1400, credits yield annual T1 = 4243.87. Per period federal income tax rounds to 81.61.

Steps 4 and 5: Provincial

Ontario adds health premium V2 in the annual provincial stack. Annual T2 = 2381.51, which rounds to 45.80 per week.

Step 6: Tax total

Employee total_tax = 127.41 (81.61 + 45.80). breakdown.T matches the Step 6 combined quotient (127.41 here).

CPP and EI

For this cheque: C (CPP) = 55.50, C2 = 0.00, EI = 16.30.

Net pay

total_deductions = 199.21
net_pay = 800.79

That is 1000.00 − 199.21. The same request through the API or the Ontario calculator returns these cents as strings.

For symbol definitions, see glossary.md.

Last reviewed: 2026-09-20
Engine: 0.1.0

Source: docs/how-the-calculation-works.md in the Takehome repository, rendered as written.