Social Arithmetic

Payslips come in a variety of designs. They usually show totals, deductions, and personal information, in addition to the actual pay.

Example

Terminology

Basic Pay = Pay earned during the period without overtime.
Gross Pay = Total income earned during the pay period.
Total Deductions = All money taken off.
Net Pay = Gross pay − Total deductions.
This is what you receive “in hand” or “bottom line”.

Tax Code: This shows how much you may earn before paying tax.
Here, Joe Bloggs can earn £3960 before tax is deducted.

What is Joe Bloggs’ salary?

\[ \text{Salary} = 2133 \times 12 \] \[ = 25596 \]

Joe Bloggs’ annual salary is £25,596.

Basic Pay

\[ \text{Basic pay is the total earned before deductions.} \] \[ \text{Basic Pay} = \text{Hourly Rate} \times \text{Normal Hours} \] \[ \text{or for salaried workers: Basic Pay = Fixed Weekly or Monthly Salary} \]

\[ \textbf{Basic Pay} \] \[ \text{Basic pay is the fixed amount an employee earns for their normal working hours.} \] \[ \text{It does not include overtime, bonuses, commission, or allowances.} \] \[ \text{Basic pay is the starting point for calculating gross pay,} \] \[ \text{and is used when working out tax, NI, and pension deductions.} \] \[ \textbf{Formula:} \]

Gross Pay

\[ \text{Gross Pay} = \text{Basic Pay} + \text{Overtime} + \text{Other Income} \] \[ \text{Gross pay is the total earned before deductions.} \]

Deductions

\[ \text{Deductions include:} \] \[ \text{Income Tax, National Insurance,} \] \[ \text{Pension (Superannuation), Student Loan,} \] \[ \text{Union Fees, Workplace Schemes} \] \[ \text{These are subtracted from gross pay.} \]

Net Pay

\[ \text{Net Pay} = \text{Gross Pay} - \text{Deductions} \] \[ \text{Net pay is the take‑home pay.} \]

Example

Paul works a 35 hour week.
He is paid £5.80 per hour.
What is his weekly wage ?

Basic pay = Number of hours worked x hourly rate = 35 x £5.80 = £203

Overtime Paid = hourly rate x overtime rate x no. of hours worked

Common rates

Overtime Rate	Multiplier	Typical Meaning
Time and a Quarter	1.25 × hourly rate	Often used for early overtime or minor extra hours
Time and a Half	1.5 × hourly rate	Very common for weekday or Saturday overtime
Double Time	2 × hourly rate	Common for Sundays or public holidays
Double Time and a Half	2.5 × hourly rate	Used in some industries for bank holidays or emergency call‑outs
Triple Time	3 × hourly rate	Rare; sometimes used for Christmas Day or extreme conditions

Example

Jack Soap earns £5.78 per hour. He normally works a 37 hour week, but this week worked an extra 8 hours on Saturday, at time and a half, and 5 hours on Sunday at double time.
a) How much overtime did he earn ?
b) What is his gross pay for the week ?

a)

\[ \text{Overtime Pay} = \text{hourly rate} \times \text{overtime rate} \times \text{hours} \] \[ \text{Saturday: } 5.78 \times 1.5 \times 8 = 5.78 \times 12 = £69.36 \] \[ \text{Sunday: } 5.78 \times 2 \times 5 = 5.78 \times 10 = £57.80 \] \[ \text{Total Overtime} = 69.36 + 57.80 = £127.16 \]

b)

\[ \text{Basic Pay} = 5.78 \times 37 = £213.86 \]

\[ \text{Gross Pay} = \text{Basic Pay} + \text{Overtime} \] \[ = 213.86 + 127.16 = £341.02 \]

Commission

\[ \text{Commission is a type of income paid to a worker based on how much they sell.} \] \[ \text{It is usually calculated as a percentage of sales, or a percentage of sales above a certain threshold.} \] \[ \textbf{Common Types of Commission:} \] \[ \text{Straight Percentage: e.g., } 5\% \text{ of all sales} \] \[ \text{Tiered Commission: e.g., } 5\% \text{ on the first £10,000, then } 10\% \text{ on the rest} \] \[ \text{Threshold Commission: e.g., } 12\% \text{ of sales above £15,000} \]

\[ \text{Commission} = \text{Rate} \times \text{Sales (or qualifying sales)} \]

Example

\[ \text{A salesperson earns 12% commission on sales above £15,000.} \] \[ \text{In one month they sell goods worth £23,000.} \] \[ \text{Sales above threshold} = 23000 - 15000 = £8000 \] \[ \text{Commission} = 0.12 \times 8000 = £960 \] \[ \text{The salesperson earns £960 in commission.} \]

Superannuation

Superannuation contributions are payments made towards a pension.

Pension Contribution = Pensionable Pay × Pension Rate

This is often Gross Pay x Pension Rate , but can be basic pay - depending on the pension scheme.

Example

Fred Ash pays 7% of his gross monthly salary towards his pension.
In January his gross pay was £2145.
Calculate his superannuation.

\[ \text{Superannuation (Pension) Contribution} = \text{Gross Pay} \times \text{Percentage Rate} \] \[ = 2145 \times 7\% \] \[ = 2145 \times 0.07 \] \[ = £150.15 \] \[ \text{Fred pays £150.15 per month into his pension.} \]

Example

Joe Bloggs receives a monthly gross pay of £2133.
His superannuation each month is £127.98
What percentage of Joe Bloggs’ monthly salary is paid on superannuation?

\[ \text{Percentage paid on superannuation} \] \[ = \frac{\text{superannuation}}{\text{Gross pay}} \times 100\% \] \[ = \frac{127.98}{2133} \times 100\% \] \[ = 0.06 \times 100\% \] \[ = 6\% \] \[ \text{Superannuation accounts for 6% of his salary} \]

Income Tax

Income tax is payable on all taxable income.

Taxable income = Total income – Personal Allowance – Any other allowances

The rates vary every year, but usually you pay a certain percentage

The following examples compare income tax calculations for Scotland and the rest of the UK during tax year 2020/21.

Source: Tax Bands - Scottish Government

Example

John Doe has a salary of £34,000 and a personal allowance of £12,500. What is the difference in tax paid between Scotland and the rest of the UK?

Scotland

Total Scottish income tax due: £4,367.57

Rest of UK

In the rest of the UK, John pays a flat rate of 20% on all taxable income because £21,500 is below the higher-rate threshold.

Total UK income tax due: £4,300.00

John pays £67.57 more tax in Scotland than in the rest of the UK.

Alternative view

Example

A person earning £25,000 in tax year 2020/21 with a personal allowance of £12,500 would pay £20.85 less in Scotland than in the rest of the UK.

Scotland

Alternative calculation

Rest of UK

Alternative calculation

£2,500 − £2,479.15 = £20.85 less tax in Scotland.

Example

A person earns £40,000 in tax year 2020/21 and pays 10% into a pension (superannuation).

Tax due in Scotland

Or, since pension is tax‑deductible, taxable salary becomes £36,000:

Rest of UK

£4,787.57 − £4,700 = £87.57 more tax in Scotland.

In tax year 2020/21, a salary of £27,243 resulted in equal income tax in Scotland and the rest of the UK.

A salary greater than £27,243 results in more income tax being due in Scotland.
A salary less than £27,243 results in less income tax being due in Scotland.

National Insurance Contributions (NICs) are paid in addition to income tax. The earnings threshold is the amount you can earn before NICs are deducted.

For the tax year 2005/06, the earnings threshold was:

£94 per week
£408 per month

Example

Using the payslip above:
How much Class 1 National Insurance was Joe Bloggs due to pay per month in 2005/06?

Rates for 2020/21

Using these rates, calculate the Class 1 National Insurance due for John Doe from the earlier example.

Source: National Insurance – UK Government

More information on taxation