Tax is complicated. There are loads of different rules that override each other, and different resources will differ on details.
Though I have spoken to accountants during the development
of this calculator, I am not an accountant.
This program was initially created to help me understand how
Salary Sacrifice works (with Income Tax and National Insurance
being a prerequisite).
My aim in releasing this is not to offer a tool for real
calculations, but rather to help people to understand how
tax works.
For all of the values I have tested, my calculations align with this site: https://listentotaxman.com/
(Please raise an issue in the Issues tab if you find an input that gives a different output).
If you are working a job with an annual salary of £100,000, you don't actually see £100,000 in your bank account every year.
Income Tax and National Insurance are deducted from your 'gross' 100k.
Take_Home = Gross_Salary - Income_Tax - Employee_National_Insurance
With a Gross Salary of £100,000 this is about £67,053.00.
Not only that, but your employment will cost your company more than £100,000. This is because companies also have to pay National Insurance, however the company's National Insurance contribution is calculated differently.
Company_Cost = Gross_Salary + Company_National_Insurance
With a Gross Salary of £100,000 this is about £112,544.20.
The first £12,570* of your salary is tax-free*. This is known as your Personal Allowance.
* The £12,570 is actually between £12,570 and £12,579, and isn't the case for everyone (just most people) - more on this in the Tax Bands section.
* If your Gross is over £100,000 per year, this decreases. For every £2 over £100k, your Personal Allowance decreases by £1. Note: if you earn £100,003, your PA decreases by £1, not £1.50 - it is step-based, not ratio-based if this helps.
If you are blind, or partially-sighted, you can receive a Blindness Allowance. I'm not sure how this is calculated, but this seems to be where it applies.
Tax_Free_Allowance = Personal_Allowance + Blindness_Allowance
The government website (https://www.gov.uk/income-tax-rates) suggests the following:
Unfortunately it is nowhere near as simple as this.
These bands are dependent on your Tax Code
(https://www.gov.uk/tax-codes/what-your-tax-code-means).
Your Tax Code is determined by a number of factors; examples:
- If you have multiple sources of income, they will use different Codes.
- If you are married and have a Gross Salary less than
£12,570you can 'donate' excess Personal Allowance to your partner so that they pay less tax - this is done through changes in Tax Code.
The Tax Code that applies to most people is 1257L,
which corresponds to the table above, however it gets more difficult still.
The "1257" refers to the Tax Code's Personal Allowance (£12,570),
but the rather than an actual value (£12,570),
1257L represents the range £12,570 - £12579.
I don't understand why this is, but the implication is that
some of the bands from the table above are shifted.
In order to align the numbers in this calculator with the ListenToTaxman site, I had to use an offset of 9 (I've used £12,579 instead of £12,570).
Even more confusingly, when your Personal Allowance decreases, you pay the newly taxable amount at Higher Rate.
In other words, notice that the Basic Rate band has a range of £37,700 (£50,270 - £12,570). This range stays the same for salaries over £100k.
Let's look at an example:
Gross_Salary = £110,000
PERSONAL_ALLOWANCE_MAX = £12,579
Gross_Over_100k = Gross_Salary - £100,000 (if Gross_Salary > £100,000, otherwise 0)
= £10,000
PA_Loss = round_down(Gross_Over_100k / 2)
= £5,000
Personal_Allowance = PERSONAL_ALLOWANCE_MAX - PA_Loss
= £12,579 - £5,000
= £7,579
Blind_Allowance = 0
Tax_Free_Allowance = Personal_Allowance + Blind_Allowance
= £7,579 + £0
= £7,579
Bands Formula:
£0 - Tax_Free_Allowance at 0%
Tax_Free_Allowance - (50,279 - PA_Loss) at 20%
(50,279 - PA_Loss) - £125,140 at 40%
£125,140+ at 45%
Bands:
£0 - £7,579 at 0%
£7,579 - £45,279 at 20%
£45,279 - £125,140 at 40%
£125,140+ at 45%
(All-caps values mean independent of Gross_Salary).
That's the hard part of Income Tax out of the way, but we still need to add up the numbers.
You may or may not find this intuitive, but I found that this diagram helps.
(not to scale)
We can clearly see from this that we have £7,579 in the 0% band.
0% of £7,579 is £0.
The amount in the 20% band is the Band_Max - Band_Min.
£45,279 - £7,579 = £37,700.
This means that we have £37,700 in this band.
20% of £37,700 is £7,540.
The amount in the 40% band is calculated slightly differently because the Gross_Salary is less than the Band_Max.
We use Gross_Salary - Band_Min.
Or in general min(Gross_Salary, Band_Max) - Band_Min.
£110,000 - £45,279 = £64,721.
So we have £64,721 in the 40% band.
40% of £64,721 is £25,888.40.
Since the Gross_Salary is less than the 45% Band_Min, our general formula from above will give us a negative number (which is not right) - to fix this, we can take the larger of the value and 0.
max(0, min(Gross_Salary, Band_Max) - Band_Min).
We have £0 in the 45% band.
45% of £0 is £0.
Our total Income Tax payment is the sum of these bands:
£0 + £7,540 + £25,888.40 + £0 = £33,428.40.
If you run the calculator program with the input £110,000 you will see the same figures:
On top of Income Tax, employees also have to pay a National Insurance contribution.
National Insurance has Classes/Categories - similar to Income Tax codes.
https://www.gov.uk/national-insurance-rates-letters/category-letters
There are many different NI Categories, but the most common is A.
Not only this, but a few other codes have the same rates as A
(at least for Employee NI), e.g.
- H - Apprentices under 25,
- M - Employees under 21,
- V - Employees whose previous role was in the armed forces.
https://www.gov.uk/national-insurance-rates-letters
These classes pay:
£0 - £12,570 at 0%
£12,570 - £50,270 at 12%
£50,270+ at 2%
Note: the Income Tax offset of 9 that we were using before doesn't apply here even though the base band numbers are the same.
National Income is calculated based on Gross_Salary,
not (Gross_Salary - Income_Tax).
The National Insurance calculation is done in the same way as Income Tax.
Let's continue with the £110,000 Gross Salary example:
Gross_Salary = £110,000
Gross_Salary > £12,570, so we reach the 12% band.
Gross_Salary > £50,270, so we use Band_Max - Band_Min to get the amount in the band.
Twelve_Percent_Band_Amount = £50,270 - £12,570
= £37,700
NI_At_Twelve_Percent = Twelve_Percent_Band_Amount * 0.12
= £4,524
Gross_Salary > £50,270, so we reach the 2% band.
The 2% band is the top band, so we use Gross_Salary - Band_Min to get the amount in the band.
Two_Percent_Band_Amount = £110,000 - £50,270
= £59,730
NI_At_Two_Percent = Two_Percent_Band_Amount * 0.02
= £1,194.60
Again, the total National Insurance Payment is the sum of
the band values.
£4,524 + £1,194.60 = £5,718.60
And if we check this against the program, the numbers once again align.
As mentioned in the Basics, Employers pay a National Insurance contribution on top of Gross_Salary. Since the words "Employee" and "Employer" look so similar, I will use the term "Company" instead of "Employer" from now of, even though this isn't always strictly accurate.
Employer National Insurance relies on the same Categories as
Employee National Insurance however the bands are completely different.
https://www.gov.uk/national-insurance-rates-letters
Luckily, this is much easier to calculate than Income Tax or Employee NI.
For Category A - the most common - company National Insurance contribution is simply 13.8% of earnings over £9,100.
Gross_Salary = £110,000
Amount_Over_9100 = £110,000 - £9,100 = £100,900 Amount_At_Rate = Amount_Over_9100 * 0.138 = £100,900 * 0.138 = £13,924.20
Since there is only once band:
Company_National_Insurance = £13,924.20
Salary Sacrifice is basically where you buy something with your Gross
Salary before tax is applied. This can allow you to pay less in tax,
and effectively bring home more.
Of course - because it's tax - it's not as simple as this; there is
usually tax applied to the Salary Sacrifice benefit in some way,
but it is often still worth it.
Note: you cannot sacrifice enough of your salary to take you below national minimum wage.
Types of Salary Sacrifice include:
- Pension schemes,
- Company Car schemes,
- Private Healthcare schemes,
- Gym Membership schemes.
I am using the term "Subtotal" to mean the post-sacrifice, pre-tax figure.
Subtotal = Gross_Salary - Sacrificed_Amount
This changes the Net Salary formula to:
Take_Home = Subtotal - Income_Tax - National_Insurance
Income Tax is calculated based on the Subtotal.
National Insurance (Employee and Company) should also be calculated
based on the Subtotal, however when I did some testing with the
ListenToTaxman site's Pension Contribution field, the numbers only
seemed to add up when National Insurance was calculated from Gross.
I'm not sure if this is an issue with their calculator,
or if I'm missing something.
You may notice from the contents of the salary_sacrifice.py file
that this has not been implemented in my calculator.
I feel that Income Tax and National Insurance are applicable to
more people. Plus, Salary Sacrifice is applied differently depending
on what type of sacrifice it is (Company Car scheme, etc.)
I don't feel inclined to add this level of complexity for a set of
features that most people aren't interested in. I also don't feel
confident in my knowledge of Salary Sacrifice to provide any
explanation further to what is here.
This may depend on the particular scheme, but it seems to me that you don't pay any tax on sacrifice, however your pension claims are considered a source of income, so you pay Income Tax, and possibly National Insurance contribution them.
Company Car schemes seem to decrease your Gross Salary by the annual P11D (recommended price) value of the car you wish to buy. They invoke a BIK Tax (Benefit in Kind) which is deducted in the same place as Income Tax and National Insurance.
Take_Home = Subtotal - Income_Tax - National_Insurance - BIK_Tax
Every car has a P11D and a BIK percentage
(based off of emmissions for fuel and hybrid cars, or range for electric cars)
These are multiplied together along with your highest income tax band
to determine how much you pay.
https://www.fleetnews.co.uk/fleet-faq/what-are-the-current-bik-bands-/3/
BIK_Tax = P11D * BIK% * Highest_Tax_Band
Since the P11D and BIK% are both dependent on the car,
they may be multiplied together before being presented to you.
i.e. BIK_Tax = Car_Tax_Value * Highest_Tax_Band
This means that someone earning £150,000 will pay more BIK_Tax than someone earning £30,000 for the same car.
It also means that if the annual P11D (the Sacrifice amount) brings you down a tax band, you make a huge saving over buying the car with your Net Salary without the scheme.
I couldn't get my numbers to align properly,
but this site seems quite good if you wish to look into this further.
https://comcar.co.uk/taxtools/salarysacrifice/
I would like to reiterate that I am not an accountant and that this calculator and this method should not be used in a professional setting without the approval of a qualified individual.
I hope this was able to demystify the UK tax system somewhat.
Please let me know via the
Issues tab
if there is any section that is incorrect or unclear,
and I will try to resolve it.