A pip calculator returns one figure, to two decimal places, in under a second. Here is the sum it did, and the part that will not sit still. 

Start at the lot, because that is where the money enters 

A pip is the smallest increment a pair is conventionally quoted in: the fourth decimal place on most, 0.0001, and the second on yen pairs, 0.01. That describes a distance the price travelled, and a distance carries no denomination. A pip is not a quantity of money. It is a quantity of price, and becomes money only once something is multiplied by it. 

That something is the position. A standard lot is 100,000 units of the first currency in the pair, a mini lot 10,000, a micro lot 1,000. So the opening multiplication is 100,000 times 0.0001, which comes to 10. Ten of what is the next section’s problem. The shape is fixed: size times increment. 

The currency on the right of the slash decides the rest 

That ten is denominated in the second currency of the pair. A standard lot of EUR/USD gives a pip worth USD 10. A standard lot of GBP/USD also gives USD 10, which catches British traders out, because sterling on the left of the slash feels as though it should produce pounds. The left-hand currency sets what you hold, the right-hand one what the movement is counted in. 

Yen pairs, and the multiplication everybody skips 

Yen pairs run the identical procedure with a different decimal. A standard lot of GBP/JPY is 100,000 pounds, a pip is 0.01, and the product is 1,000 yen. So a second multiplication is waiting, the one everybody skips: divide by the rate between the quote currency and your account currency. Miss it and you have priced the trade for somebody else’s bank account. 

The same ten pip stop, five times over 

Take one instruction, a stop ten pips from entry, and change nothing about it while varying the pair and the size. To make the second multiplication visible, the sums below use GBP/USD at 1.25 and GBP/JPY at 190, round rates chosen so the arithmetic can be followed in your head. Substitute whatever is showing when you do it for real. 

One instruction, a ten pip stop, priced across six setups. The sterling columns are worked at the illustrative rates named above rather than at anything anybody paid. 

Run your eye down the fourth column. One instruction, worded identically each time, costs eighty pence in the third row and a hundred pounds in the fifth, and nothing in the table mentions a different appetite for risk. Rows one and four match to the penny, and one of them is a sterling pair. 

Eighty pence has an exchange rate folded inside it 

Now bring in a measured figure. The EUR/USD spread in the London session, recorded on a funded raw-spread account, was 0.1 pips, or roughly 80p per standard lot. Check it. A tenth of a pip on 100,000 euros is USD 1.00, and if that is being reported as 80p, the rate behind the sentence was 1.25 dollars to the pound. 

Eighty pence is therefore a dollar amount with a conversion already applied, and it appears here rather than in a footnote because The Investors Centre, a UK investing research site that opens and funds live accounts with its own money to test UK trading platforms rather than compiling rankings from providers’ published fee schedules, paid it on a real account. 

What that figure carries that it does not show 

Which makes it strong and, on this narrow point, incomplete: a sterling amount for a dollar-denominated cost carries the day’s rate inside it without showing it as a separate line, so a measurement and a conversion travel as one quantity nobody can pull apart. 

Add the commission, then turn the bill back into pips 

The same account records commission of GBP 4.50 for a round turn on its sterling MetaTrader offering, GBP 2.25 a side, charged at open. Add the eighty pence of spread and you have GBP 5.30, exactly the all-in intraday cost per standard lot reported for liquid hours. The commission-free equivalent is put at roughly GBP 8 a lot on a one pip spread, and one pip is USD 10, which at 1.25 is GBP 8.00. Three published figures, one implied rate, no contradictions. 

Then divide the other way, because cost in pips is the only form that compares across sizes. GBP 4.50 against a pip worth GBP 8.00 is 0.56 pips. Against a GBP/JPY pip worth GBP 5.26 it becomes 0.86 pips. Careful with that second sum. The GBP 4.50 was recorded on EUR/USD, and whether the schedule charges the same per lot on a yen cross is a question for the schedule, not for me. 

The calculator converts now and the broker converts later 

Here is where the tool and the world come apart. A calculator applies a rate the instant you press the button, prints an answer to two decimals and sits looking settled. Move GBP/USD from 1.25 to 1.35 and the sterling value of a EUR/USD pip falls from GBP 8.00 to GBP 7.41, a drop of 7.4 per cent, and the ten pip stop that risked GBP 80.00 now risks GBP 74.07. A rate you were not trading moved underneath a number you had stopped looking at. 

Where the conversion actually happens 

The deeper trouble is timing rather than accuracy. Profit or loss on a dollar-quoted pair arises in dollars and reaches your account when the position closes, converted at whatever the firm applies then and after whatever it charges for converting. 

None of which makes the static figure sloppy. Hold a dollar-denominated account, trade EUR/USD, and a pip is USD 10 permanently, so the simplification is exactly true for the account currency the tool was built around. A sterling user inherits a design correct somewhere else. 

EUR/GBP is the pair that stays where you left it 

EUR/GBP is the pleasant exception for a sterling account. The quote currency is already your account currency, so there is no second multiplication and no rate to go stale. A standard lot is GBP 10 a pip today, next Tuesday and in March. If you want one instrument where a pip value on a sticky note stays true, that is the one to practise on. 

GBP/JPY moves the pip while you are holding it 

GBP/JPY bends the other way and hardly anybody mentions it. The rate you divide by is GBP/JPY itself, the rate you are trading, so a pip changes value as your position moves. Ride a long from 190 to 200 and each pip was worth GBP 5.26 at the start and GBP 5.00 at the end, so the later pips of a winning trade pay slightly less than the early ones. 

Give the answer a range, the way you would any measurement 

So do the sum three times. Work out the pip value at the rate showing now and at rates ten per cent either side, and write all three down. On a standard lot of EUR/USD that is GBP 8.00 at 1.25, GBP 7.27 at 1.375 and GBP 8.89 at 1.125. Thirty seconds, and you hold a band rather than a point. 

Size against the unfavourable end, and recalculate when the rate has left the band rather than when a month has gone by, since the calendar has no opinion about currencies. 

Then keep the habit that produced the band. Two decimal places are an expression of arithmetic rather than of accuracy, and a figure carried to the penny is only ever as exact as the rate it was divided by.