VAT pricing calculator: inclusive to exclusive and back, at your own rate

The formula

rate fraction            = VAT rate in per cent / 100
adding VAT to a net price:
  VAT per unit           = net x rate fraction
  gross per unit         = net + VAT per unit
taking VAT out of a gross price:
  net per unit           = gross / (1 + rate fraction)
  VAT per unit           = gross - net per unit
shelf rounding (optional) = gross per unit rounded to the nearest step you give; net and VAT re-derived from it
line VAT, per unit       = VAT per unit rounded to 2 decimals, then x quantity
line VAT, rounded once   = VAT on (unit price x quantity), rounded to 2 decimals once
rounding difference      = line VAT per unit - line VAT rounded once
line net, line gross     = the remaining two of net, VAT and gross, carried to the line at the same quantity

How do you add VAT to a net price?

Start from the figure you intend to keep and multiply it by the rate as a fraction. At an illustrative five per cent, a net of 10.00 carries 0.50 of VAT and sells for 10.50; the shortcut is to multiply the net by one plus the fraction, 1.05 in that example, which gives the gross in a single step. This direction suits a venue that settles its margin first and lets the shelf price follow, the approach the session pricing guide takes from cost per child-hour.

How do you take VAT out of a gross price?

Divide, never subtract. A family pays 10.00 for something whose price already includes VAT; at the same illustrative five per cent the net is 10.00 divided by 1.05, which is 9.52, and the VAT is the 0.48 that remains. The usual slip is to knock five per cent off the gross, which gives 9.50 and overstates the tax by 0.02 on every unit sold. Venues that price for walk-in families often work this way round, because the number on the board is the number the parent hands over and the split belongs on the receipt rather than the price list.

Why do per-line and per-total rounding give different answers?

VAT is worked out on exact numbers and paid in coins, so the arithmetic has to be rounded somewhere, and where you round changes the total by a coin or two. Per-line rounding works out the VAT on each line, rounds it to the smallest coin and adds the rounded lines together. Per-total rounding adds up the net of every line first, works out the VAT on that sum and rounds once at the end. Both are defensible; they simply disagree by up to half a coin per line, in either direction, and a Saturday of many small sales can make the gap show on the day's total.

The calculator reproduces the effect inside a single line by treating the quantity two ways: VAT rounded on one unit and multiplied up, against VAT worked out on the whole line and rounded once. PlayAreaOS is on the per-line side of that. Which method a business must follow is a matter for its tax authority and its accountant; what matters at the counter is that the receipt, the daily report and the VAT figures all come from one rule, so that they reconcile.

Which price should go on the board?

When you begin from a net and add VAT, the gross rarely lands on a tidy number, and a price list full of figures like 42.35 reads as accidental. The optional rounding step takes the gross to the nearest 0.50, 1 or 5, whichever suits your price list, then re-derives the net and the VAT from the rounded shelf price so the receipt still adds up. Where the step is used, the VAT on the receipt comes from the rounded shelf price the family actually paid rather than from the net you started with. Once the price is tidy, run it through the break-even calculator to check that it still covers the costs it has to carry.

Where your accountant takes over

Your rate is your own, and PlayAreaOS carries it wherever money moves: a package quoted on the public booking form and the same package rung up at the counter carry identical tax, the receipt prints the total before tax, the VAT and the total with tax, and purchase VAT comes through on the buying side ready for the return. It all lands in finance, and the sales reports export to CSV.