Gross Up

What gross up means

Gross up (grossing up, or a net to gross calculation) starts from the amount that is to reach the employee and works back to the gross amount that has to be paid so that, after deductions, exactly that amount remains. The known figure is the last one in the chain and the unknown figure is the first, which reverses the direction of the ordinary calculation on a payroll statement, where the gross comes first and the net is what is left.

Grossing up applies wherever an agreement states a net figure: a job offer that says “you will receive this much”, or an amount the organisation has committed to deliver to the employee in full, with nothing taken from it. The question it answers is a single arithmetic one: how much has to be paid for the agreed amount to arrive.

The gross up mistake: adding where the formula divides

One mistaken method is to add the deduction to the net. It fails because the deduction is calculated on the gross, not on the net, and the gross is the larger figure, so the amount added always falls short of what is needed.

Take an agreed net of SAR 10,000 and a deduction of 10% of the gross:

• By addition: SAR 10,000 plus 10% of it gives SAR 11,000. The deduction is then calculated on that figure and comes to SAR 1,100, so the employee receives SAR 9,900. The shortfall is SAR 100.
• By division: SAR 10,000 divided by 0.9 gives SAR 11,111.11. The deduction on it is SAR 1,111.11, so the employee receives exactly SAR 10,000.

The two gross figures differ by SAR 111.11 a month, which is more than SAR 1,333 a year for a single employee. The amount is small enough to pass unnoticed, and because it is fixed it does not correct itself over time.

The percentages and the cap used in the examples throughout are assumed figures, chosen to show the method. They are not taken from any regulation, and they are not a reference on which to base a payroll.

The size of the gross up error is predictable

The error can be measured before it happens. The shortfall in the net equals the net multiplied by the square of the deduction rate: SAR 10,000 multiplied by 0.1 squared, that is by 0.01, gives SAR 100, the same figure as in the calculation above.

The square of the rate explains why the mistake can be tolerable at low rates and glaring at high ones. At a rate of 20% instead of 10%, the correct gross is SAR 10,000 divided by 0.8, which is SAR 12,500, while addition gives SAR 12,000. The shortfall in the net is then SAR 400, four times the shortfall in the first case, although the rate has only doubled.

Four rates and four gross up errors

On a net of SAR 10,000, with everything else unchanged, the shortfall that results from adding instead of dividing is as follows:

• At 5%: the correct gross is SAR 10,526.32, and the shortfall in the net is SAR 25.
• At 10%: the correct gross is SAR 11,111.11, and the shortfall is SAR 100.
• At 20%: the correct gross is SAR 12,500, and the shortfall is SAR 400.
• At 30%: the correct gross is SAR 14,285.71, and the shortfall is SAR 900.

Between the first rate and the last, the rate is multiplied by six and the error by 36. That is how the wrong method can survive for years in an organisation whose deductions are light, and then come to light all at once when they grow heavier.

When a deduction has a cap, the gross up rule breaks

The formula above assumes a flat rate on every riyal. A deduction may not work that way: it may be calculated on a base that has an upper limit, so that once the wage passes the limit the deduction stops rising. What enters that base, and how it is set, is a separate question with its own sources; for the social insurance contribution base, it is covered in our guide to the GOSI contribution wage. The definition of grossing up does not decide it.

Suppose the deduction is 10%, charged only on the first SAR 9,000 of the gross. Above that limit the deduction is a fixed SAR 900, however high the wage goes. Then:

• The correct gross for a net of SAR 10,000 is SAR 10,900, reached by adding the fixed deduction, not by dividing.
• Division gives SAR 11,111.11, whose deduction is still SAR 900, so the employee receives SAR 10,211.11, which is SAR 211.11 more than was agreed.

The verdict is reversed. Adding the deduction to the net, wrong in the uncapped case, is right in the capped one, because above the cap the deduction is a fixed sum; and division, right in the uncapped case, is wrong in the capped one. What separates the two is a question answered before any calculation: does the required gross fall above the cap or below it? In this example it falls above the cap whenever the required net is SAR 8,100 or more, because 8,100 divided by 0.9 is exactly 9,000, the point at which the cap begins. Someone who calculates without asking that question is right on one side of the threshold and wrong on the other, and cannot tell which side a case is on until the question is asked.

Grossing up with more than one deduction: the order counts

Suppose there are two deductions: the first is 10% of the gross, and the second is 5%. The question is: 5% of what?

• If the second is calculated on what remains after the first, the gross is SAR 10,000 divided by the product of 0.9 and 0.95, which is SAR 11,695.91.
• If both are calculated on the same gross, together they are 15% of it, and the gross is SAR 10,000 divided by 0.85, which is SAR 11,764.71.

The difference is SAR 68.80, and it comes from the order, not from the rates. A policy that sets the rates without setting the base of each one therefore cannot be applied as written, because it allows two figures. Where deductions are combined, their order is set by the source of each deduction, not by the definition of grossing up.

What a promise of net pay costs under gross up

Promising a net figure moves a burden from the employee to the organisation. Every change in a deduction rate or in the limit of a base changes the gross that has to be paid, while the net stays where it is. The organisation absorbs the effect of the change, which it may not have foreseen when the offer was written.

A second consequence follows. Two colleagues who each receive SAR 10,000 can cost the organisation different amounts, because the deduction base can differ with the components of each one’s pay. Equal net pay is not equal cost, and the cost to the organisation is a separate calculation.

We found no provision in the sources we reviewed that settles whether a wage may be agreed as a net figure. We draw no conclusion in either direction from that silence.

Grossing up an addition to an existing wage

A gross up case need not be the pricing of an offer from scratch; it can be an addition to an existing wage, on the condition that a stated amount of it reaches the employee. The rule then depends on where the existing wage sits against the limit of the base, not on the size of the addition.

If the existing wage is below the limit, the addition enters the base and is calculated by division, as above. If the existing wage is already above the limit, the addition does not increase the deduction at all, and the gross to be paid equals the net requested, with nothing added. Two employees can ask for the same thing at a different cost to the organisation, and the whole difference lies in where each one’s wage sits against a limit that has nothing to do with the amount requested.

Where the addition itself takes the wage across the limit, the calculation has two parts: the portion below the limit by division, and the portion above it by addition. A calculation that handles the case with a single factor is wrong every time the limit falls inside the amount.

How gross up differs from a pay rise, a deduction from wages and net pay

• A pay rise. The gross has gone up, but what reaches the employee has not risen by a single riyal. Presenting it to the employee as an improvement offers them something they will not find in their account.
• A deduction from wages. That is a separate subject, with its own grounds, conditions and ceilings, covered in our guide to wage deductions. Grossing up is a calculation made before payment to set the figure that is paid in the first place. Confusing the two turns an arithmetic question into a legal one, which it is not.
• Net pay on the payroll statement. Net pay there is a result, taken from the calculation once it is done; the net in grossing up is an input on which the calculation is built. The first changes when the deductions change, and the second is the agreed figure, which does not.

What breaks a gross up calculation

• Calculating it once, at hiring. A promise of net pay is a continuing obligation, so the gross is recalculated whenever a rate or the limit of a base changes, not only when the offer is written.
• Including items that do not enter the base. A pay item outside the deduction base inflates the gross for no reason if the deduction is calculated on it. Whether a given item enters a given deduction base is settled where that deduction is defined, and that is what decides which formula applies, division or addition.
• Rounding at every step. Rounding to the nearest riyal in the middle of the calculation and again at the end can leave a small difference, so that the amount paid no longer matches the figure in the offer exactly.
• Copying an earlier case. Two employees whose pay is made up differently do not share the same factor, even when their net pay is equal.

Before a gross up figure goes into a job offer

A figure written into an offer can be consulted years after it was written, so it should carry what makes it clear: whether it is gross or net; if it is net, which deductions are covered; and what happens if one of them changes. An offer that says “you will receive this much” without those details can create a deferred dispute that surfaces only after the first change.

The calculation itself follows one rule: the net is divided by what remains after the rate, not added to. Where the deduction has a cap, division does not hold above the cap, and the position of the figure against the cap is settled before the method is chosen, not after.

This is an explanation of the concept, not legal advice.