How to calculate pip value

What the number has to do 

A price moves. The movement is counted in pips, which is a unit of the price rather than a unit of money. The account, meanwhile, is denominated in one currency and reports everything in it. Between those two facts sit two more: how much of the underlying one contract covers, and what the currency the instrument is quoted in is worth in the currency the account is kept in. Pip value is the amount of money one pip is worth for a stated contract size, expressed in the account currency. It belongs to a combination, not to an instrument, and the same pair has a different pip value in two accounts denominated differently.

The calculation has three steps and the third one is conditional. Read once in order, it never changes, whatever is being priced:

1. Take the size of one pip as a number, read off the decimal structure of the quote itself. For most currency pairs that is a unit in the fourth decimal place, and for pairs quoted to two decimals it is a unit in the second.
2. Multiply it by the number of units of the underlying the contract covers. The result is the value of one pip in the quote currency, because the quote currency is what the rate counts.
3. Convert that amount into the account currency at the prevailing rate between the two. Where the quote currency and the account currency are already the same, this step disappears and the calculation is two steps long.

Nothing in those three steps refers to the direction of a position, and nothing refers to whether a position is open. Pip value is a property of size and currency alone. It prices a movement of one pip identically whether that movement is favourable or adverse, which is why the same figure appears on both sides of every calculation below.

When the quote currency is the account currency 

This is the case most textbook examples use, and it is worth being precise about why it is the easy one. When an account is denominated in the currency written second in the pair, the amount produced by the multiplication is already in the currency the account reports in, so there is nothing left to convert.

The last three rows are the whole of what contract size does to the calculation. Pip value scales in exact proportion to the number of units covered, so a contract a tenth of the size prices the same movement at a tenth of the money. That proportionality applies to an adverse move exactly as it applies to a favourable one, in the same figure, at the same moment: there is only one pip value in a calculation and both sides of it use that one number.

One further property of this case is easy to miss. The value per pip does not change as the pair moves, because no step of the calculation refers to the level of the rate at all. That is a peculiarity of the no conversion case rather than a general truth, and the next section is where it stops holding.

When the quote currency is not the account currency 

The first two steps are unchanged. The multiplication produces an amount in the quote currency, and that amount is correct and complete: it is simply denominated in a currency the account does not report in. The third step is a currency conversion like any other, and it is arithmetic rather than a special rule about pips.

What trips people is which way round the conversion runs, and there is a reliable way to read it. The conversion pair states how many units of its quote currency one unit of its base currency costs. When the account currency sits on the quote side of that pair, the amount is multiplied by the rate. When the account currency sits on the base side, the amount is divided by it. The two cases are worked separately below because reading them side by side is the only thing that makes the direction obvious.

The dividing case arrives whenever the account currency is written first in the conversion pair, and there is a common instance of it where the pair being traded is also the pair doing the converting. A dollar denominated account trading the US dollar against the yen is exactly that: the multiplication lands in yen, the rate that converts yen back into dollars is the pair on the screen, and the account currency sits on its base side.

A one dollar move in gold 

Metals are not natively quoted in pips. Gold against the US dollar is quoted as a price per troy ounce, its smallest quoted increment is a cent, and the contract covers a number of ounces rather than a number of currency units. The word most desks use for one increment here is a tick or a point rather than a pip. None of that changes the structure of the calculation: an increment is multiplied by a quantity, and the result is converted if the quote currency and the account currency differ.

Two habits of language cause most of the confusion here. The first is that a point means the last decimal place of the quote to one source and a whole unit of the price to another, so a figure described as the value of a point can differ by a factor of a hundred between two documents that are each internally consistent. The second is that the quantity is physical, so the contract size carries its unit with it and a stated value per dollar of movement means nothing detached from the number of ounces behind it. The specification is the authority for both.

A point on an index 

An index has no physical unit at all, and index contracts are conventionally written to say so directly: the specification states an amount of money per index point, which means the first multiplication has already been performed by whoever wrote the contract. What remains is a count of contracts, a distance in points, and the conversion step where the index is quoted in a currency the account is not denominated in.

Why pip value does not stay still 

Where a conversion is involved, pip value inherits everything that happens to the conversion rate. The amount in the quote currency is fixed by pip size and contract size and never moves. What moves is what that amount is worth, and the effect is large enough to be worth seeing at three levels of the same rate.

The direction of that relationship depends on which side of the conversion pair the account currency sits, and it is the mirror of the rule for setting the calculation up. Where the amount is divided by the rate, a rising rate lowers pip value in the account currency. Where the amount is multiplied by it, a rising rate raises pip value. Neither is a feature of the instrument being traded. It is the account currency strengthening or weakening against the currency the result arrives in, showing up in the only place it can.

Where practitioners disagree 

Three points in this calculation are genuinely unsettled, and each of them changes a total. The first is which rate converts. A conversion can be performed at the bid, at the offer or at the mid rate between them, and firms differ. The gap is small on a single pip and is not small across a large position or a long sequence of them, which is why the choice appears in the terms of a trading arrangement rather than being left to convention.

The second is when the conversion happens. One accounting convention converts each amount as it arises, so a running result in the account currency reflects the conversion rate continuously. Another converts once, when the position closes. Both are defensible and both are in use, and in a market where the conversion rate has moved they produce different totals for identical trading. Neither can be inferred from the platform display, so the arrangement's own terms are the only place the answer is written down.

The third is whether pip value is a constant or a variable. Traditions that plan a position before it is opened treat it as a constant, computed once at the outset, on the grounds that a number recalculated continuously cannot be used to size anything. Accounting treats it as a variable, because that is what it observably is. Both readings are correct about different things, and the disagreement is really about what the number is for rather than about what it equals. The arithmetic is short enough to do by hand, and the cost calculator page performs it for a stated instrument and contract size.