Currency Converter

The mid-market rate, and why it is a reference rather than a price

At any moment a currency pair has two prices, not one. The bid is what the market will pay you for the base currency; the ask is what it will charge you to buy it. The ask is always the higher of the two, and the gap between them is the spread. The mid-market rate is simply the midpoint of those two numbers - add the bid and the ask, divide by two - and its defining property is that nobody transacts at it. It is a reference point, the honest centre of the market, and everything a provider charges you is measured as a distance from it.

That makes the mid the right benchmark and the wrong expectation. It is the right benchmark because it strips out every provider's margin and lets you compare two offers on a single scale. It is the wrong expectation because if you walk into a bank quoting the mid and ask to be dealt at it, you will not be. Even the wholesale interbank market deals on a bid and an ask; the mid is a construct that sits between them.

The spread itself is not a fixed number. It widens when liquidity thins - during the Asian session for European crosses, in the minutes around a major economic release, on public holidays in one of the two currencies' home markets, and always over the weekend when the market is shut and the last posted mid is simply the Friday close sitting there going stale. A rate you check on a Sunday is a rate from Friday.

This calculator quotes indicative mid-market rates for reference. It is a way to see what a conversion should cost before anyone adds anything to it, not a quote you can execute against, and it is not connected to any dealing venue.

Cross rates: how any pair is built from two dollar quotes

The US dollar sits on one side of the great majority of currency trades, which means most currencies have a deep, continuously quoted price against USD and a much thinner one against each other. Rather than quote every possible pair directly, the market derives the rest: a cross rate is any exchange rate constructed from two dollar quotes, and this calculator does exactly that internally by routing every conversion through USD.

The rule depends on which side of the dollar each currency sits, and there are only three cases. If both currencies are quoted as X/USD - EUR/USD and GBP/USD, where the dollar is on the right - you divide one by the other. If one is quoted X/USD and the other USD/Y - EUR/USD and USD/JPY - you multiply. If both are quoted USD/Y, with the dollar on the left, you divide again but in the other order. Getting the case wrong produces a number that is out by a factor of several hundred, which is at least easy to spot.

Underneath, there is one formula that covers all three cases and never needs a decision. Express every currency as units per one US dollar, then the rate from one currency to another is simply the target's units-per-dollar divided by the source's. The multiply-or-divide rules above are just that identity rewritten in whichever quoting convention the market happens to use for each leg.

In practice, liquid crosses like EUR/GBP and EUR/JPY are also quoted directly by banks, and the direct quote can differ very slightly from the synthetic one derived through the dollar. That difference is what triangular arbitrage exists to close, and in normal conditions it is small enough that either route gives the same answer to the precision anyone spending money cares about.

Assumed quotes (illustrative only, not live rates)
  EUR/USD 1.0850     GBP/USD 1.2700
  USD/JPY 156.00     USD/CHF 0.9000     USD/CAD 1.3600

Case 1 - both quoted X/USD  ->  DIVIDE
  EUR/GBP = EUR/USD / GBP/USD = 1.0850 / 1.2700 = 0.8543307
  Inverse: GBP/EUR = 1.2700 / 1.0850            = 1.1705069
  Check:   1 / 0.8543307                        = 1.1705069   OK

Case 2 - one X/USD, one USD/Y  ->  MULTIPLY
  EUR/JPY = EUR/USD x USD/JPY = 1.0850 x 156.00 = 169.26
  GBP/JPY = GBP/USD x USD/JPY = 1.2700 x 156.00 = 198.12

Case 3 - both quoted USD/Y  ->  DIVIDE (other order)
  CAD/CHF = USD/CHF / USD/CAD = 0.9000 / 1.3600 = 0.6617647
  Check:   1.3600 x 0.6617647                   = 0.9000000  OK
  (Multiply back through the DISPLAYED 0.66176 and you get
   0.8999936 - the missing digit is the display rounding, which
   is exactly why the calculation carries the full rate.)

The one rule behind all three
  units-per-USD:  EUR 1/1.0850 = 0.921659
                  GBP 1/1.2700 = 0.787402
  Rate(EUR -> GBP) = 0.787402 / 0.921659 = 0.854331   same answer

Reading a quote the right way round

A quote like USD/JPY 156.00 means one unit of the first currency buys 156.00 units of the second. The first currency is the base, the second is the quote currency, and the number is always how much quote currency one unit of base is worth. Multiply when you are converting from the base into the quote currency; divide when you are going the other way. Half of all conversion errors are this one operation performed backwards.

The reason it trips people up is that the market's quoting conventions are not consistent. EUR, GBP, AUD and NZD are conventionally quoted with the dollar second - EUR/USD, GBP/USD - while JPY, CHF, CAD and most other currencies are quoted with the dollar first. So EUR/USD 1.0850 and USD/JPY 156.00 look like the same kind of number and mean structurally opposite things. There is no logic to remember here; it is convention, and the only defence is to read the pair label rather than the number.

The good news is that the sanity check is almost free. Before you accept any converted figure, ask whether the result should be bigger or smaller than what you started with. Going from a currency where one unit is worth a lot into one where a unit is worth little should produce a much bigger number, and vice versa. An answer that is out by a factor of 156 announces itself immediately.

This is also where the calculator's inverse rate row earns its place. If you can read the conversion in both directions at once, an inverted rate becomes obvious rather than plausible - which matters most on exactly the pairs where the two directions look least alike.

Assumed illustrative quote:  USD/JPY = 156.00
Reads as: 1 USD = 156.00 JPY   (USD is the base, JPY is the quote)

Base -> quote currency: MULTIPLY
  500 USD x 156.00                        = 78,000 JPY

Quote -> base currency: DIVIDE
  78,000 JPY / 156.00                     = 500 USD

The error, and why it is easy to catch
  78,000 JPY x 156.00                     = 12,168,000
  A few hundred dollars of yen cannot be twelve million dollars.

Sanity rule
  Converting into a currency with many units per dollar (JPY, HUF,
  KRW) should make the number much LARGER.
  Converting into a currency worth more per unit (EUR, GBP, KWD)
  should make it SMALLER.

Inverse rates as a check
  1 USD = 156.00 JPY   <->   1 JPY = 1 / 156.00 = 0.006410 USD

What the conversion actually costs: turning a rate into a percentage

Most currency conversion is not sold with a visible price. There is often no line item, no commission, and marketing that says fee-free - and yet the conversion cost something, because the rate you were given was not the mid. The only way to see it is to measure the offered rate against the mid-market rate at the same moment and express the gap as a percentage. That single number is comparable across every provider, which is precisely why so few of them show it to you.

The arithmetic is short. Take the mid, subtract the rate you were offered, divide by the mid. On the worked example below, a mid of 1.0850 against an offered 1.0580 is a gap of 0.0270, which is 2.49% of the mid - and on 2,000 EUR that is 54.00 USD that simply did not arrive. Crucially, you get the identical 2.49% whether you compute it from the two rates or from the two cash amounts, which is a useful check that you have compared like with like.

Fixed fees change the shape of the cost, not just its size. A flat charge is a large percentage of a small transfer and a trivial one of a large transfer, while a rate markup scales with the amount. The example shows a provider charging 2.49% embedded plus a 5.00 flat fee, and another charging 0.4% plus 3.00 - on 2,000 EUR the difference is 47.32 USD, but the ranking between two such providers can flip entirely at a different transfer size. Always compute the total cost at the amount you are actually sending.

Two things to keep in mind when comparing. Compare against the mid at the same moment, since rates move and yesterday's mid proves nothing. And compare the amount that lands, not the rate quoted - the receiving-side fees that some routes deduct never show up in the rate at all.

Assumed illustrative mid-market rate: EUR/USD = 1.0850
Amount to convert: 2,000 EUR

At the mid (nobody actually deals here)
  2,000 x 1.0850                             = 2,170.00 USD

Provider A - rate 1.0580, plus a 5.00 flat fee
  2,000 x 1.0580                             = 2,116.00 USD
  less fee                                   =     5.00
  received                                   = 2,111.00 USD

  Rate markup = (1.0850 - 1.0580) / 1.0850   = 2.4885%
  Cross-check = 54.00 / 2,170.00             = 2.4885%   OK
  Total cost  = 2,170.00 - 2,111.00          =    59.00 USD
              = 59.00 / 2,170.00             = 2.72%

Provider B - 0.4% markup, plus a 3.00 flat fee
  rate = 1.0850 x (1 - 0.004)                = 1.080660
  2,000 x 1.080660                           = 2,161.32 USD
  less fee                                   =     3.00
  received                                   = 2,158.32 USD

  Total cost  = 2,170.00 - 2,158.32          =    11.68 USD
  Cross-check = 0.004 x 2,170 + 3.00 = 8.68 + 3.00 = 11.68  OK
              = 11.68 / 2,170.00             = 0.54%

Difference on this one transfer: 59.00 - 11.68 = 47.32 USD.
Both providers can honestly advertise no commission.

Why two providers quote different rates at the same moment

Two things move the rate you are offered away from the mid: the margin the provider takes, and the cost the provider itself faces. A retail bank converting a card transaction is doing something structurally different from a broker filling a wholesale order, and the gap between their rates is mostly explained by volume, timing and who carries the risk of the rate moving before the payment settles.

Timing is a bigger factor than most people expect. Spot foreign exchange conventionally settles two business days after the trade date, and some pairs such as USD/CAD settle one. A provider giving you a rate now for money that will not move for two days is pricing a small amount of risk into that rate. Weekend and holiday conversions add more of the same, because the market that would let them hedge is closed.

Then there are the costs that never appear in the rate at all. Card networks and terminals may offer dynamic currency conversion, which converts at the point of sale at a rate the merchant's processor sets rather than your card issuer's - accepting it almost always costs more than declining it and being billed in the local currency. ATM operators add their own charge on top of whatever your bank does. Correspondent banks in a payment chain can each deduct a handling fee before the money arrives. None of these show up when you compare quoted rates.

Finally, not every currency is equally cheap to trade. Major pairs are the most liquid instruments in the world and carry tiny wholesale spreads; emerging and restricted currencies carry much wider ones, and some are subject to capital controls that create a meaningful gap between an official rate and the rate actually available. A converter can only report a reference rate; it cannot know which of these apply to your specific transaction.

• Ask for the total the recipient receives, not the rate. The rate is one component of the cost and the easiest one to dress up.
• Decline dynamic currency conversion at a card terminal or ATM unless you have checked the rate against the mid - being billed in the local currency and letting your own issuer convert is usually cheaper.
• Check whether the fee is charged on the sending side, the receiving side, or both. Intermediary bank deductions are common on international wires and are invisible in the quoted rate.
• Weekend and holiday rates are stale. The spot market closes for the weekend, and any rate you see is the last one before it shut.
• Expect wider spreads around major economic releases and in a currency's off-hours, and much wider spreads on thinly traded or restricted currencies.
• Large amounts often qualify for a better rate. Providers who publish a single retail rate frequently negotiate above a threshold.
• A converter shows an indicative reference rate. Only your bank or broker can give you a price you can actually deal at.

Precision, minor units and where rounding shows up

Exchange rates and money amounts round differently, and confusing the two is a genuine source of small, persistent discrepancies. A rate is normally carried to four, five or six significant decimals; an amount is rounded to the currency's minor unit. On a small conversion that distinction is invisible. On a large one it is not: converting a million euros at a rate truncated from 1.084246 to 1.0842 leaves 46.00 USD on the table, purely from dropping the last two decimals of the rate.

Not every currency has two decimal places, either, and assuming so produces nonsense. The Japanese yen has no minor unit at all, so 78,000 JPY is a whole number and quoting it as 78,000.00 is meaningless. The Kuwaiti dinar, Bahraini dinar, Omani rial, Jordanian dinar and Tunisian dinar use three decimals. A converter that formats everything to two decimals will silently misstate both.

Rounding direction matters when a conversion runs both ways. Convert an amount out and back again and you will often land a minor unit or two away from where you started - not because the arithmetic is wrong, but because each leg was rounded to a whole minor unit. This is why the conversion table on this page recalculates each row from the rate rather than scaling a single rounded result.

The practical rule: use full rate precision for the calculation and round only the final amount, once. Rounding an intermediate result and then multiplying it is how a small display convenience becomes a real discrepancy on a large transfer.

Rate precision on a large amount
  Assumed illustrative mid EUR/USD = 1.084246
  1,000,000 EUR x 1.084246          = 1,084,246.00 USD
  1,000,000 EUR x 1.0842 (4 dp)     = 1,084,200.00 USD
  Difference                        =        46.00 USD
  (0.000046 per euro x 1,000,000 - the two decimals dropped)

Minor units are not always two decimals
  JPY   0 decimals   250,000 JPY is a whole number
  USD, EUR, GBP   2 decimals
  KWD, BHD, OMR, JOD, TND   3 decimals

  250,000 JPY / 156.00 = 1,602.564103 -> 1,602.56 USD
  Check: 156.00 x 1,602.56 = 249,999.36 JPY
  The 0.64 JPY gap is the USD rounding, not a rate error.

Rule: carry the full rate through the calculation and round the
final amount once. Rounding an intermediate and then multiplying
it compounds the error.

Converting for trading rather than spending

A trader converts currency in a second, less obvious way: every trade produces a profit or loss denominated in the quote currency of the pair, and that result has to be translated back into the account currency before it means anything. Buy EUR/USD and the profit arrives in dollars; buy EUR/JPY and it arrives in yen. If your account is denominated in something else, a conversion happens whether you asked for one or not.

The size of that effect is easy to underestimate. A one standard lot EUR/USD position that gains 40 pips makes 400 USD - one standard lot is 100,000 euros and one pip is 0.0001, so a pip is worth 10 USD. For a euro-denominated account, that 400 USD is worth 368.66 EUR at an assumed rate of 1.0850, but only 357.14 EUR if the conversion happens at 1.1200. The trade result did not change at all; a 3.2% move in the conversion rate took 3.1% off the outcome.

This is also why pip value is not a constant. For a USD account trading EUR/USD it happens to be a clean 10 USD per standard lot, because the quote currency and the account currency are the same. For the same account trading EUR/JPY, the pip is worth 1,000 JPY per standard lot - 100,000 x 0.01 - and must be divided by USD/JPY to become dollars. The pip value calculator does that step; the position size calculator then uses the result to turn a risk budget into lots.

Two currency-specific risks are worth naming plainly. If your account currency is not the quote currency of what you trade, your realised results carry an exchange-rate exposure you did not choose. And if your account currency is not the currency you actually live in, the balance on your statement and its purchasing power are two different things. Neither is a reason to avoid trading; both are reasons to know which currency your numbers are really in.

Trade: 1 standard lot EUR/USD, +40 pips
  Standard lot = 100,000 EUR, 1 pip = 0.0001
  Pip value = 100,000 x 0.0001            = 10.00 USD per pip
  Profit    = 40 x 10.00                  = 400.00 USD

Account denominated in EUR - the profit must be converted
  At an assumed EUR/USD of 1.0850:  400 / 1.0850 = 368.66 EUR
  At an assumed EUR/USD of 1.1200:  400 / 1.1200 = 357.14 EUR

  Difference = 11.52 EUR on an identical trade
             = 3.1% of the result, from a 3.2% move in the rate

Pip value is not always a round 10
  EUR/JPY, 1 standard lot, JPY pip = 0.01
  Pip value = 100,000 x 0.01              = 1,000 JPY per pip
  In USD, at an assumed USD/JPY of 156.00:
  1,000 / 156.00                          = 6.41 USD per pip

Same lot size, very different risk per pip. Check it before sizing.