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CalcMax

Currency Calculator

Range: 0.01 – 1,000,000,000

Range: 0.00 – 1,000,000

Result

100.00

Converted amount

Back the other way
100.00
Inverse rate
1.000000

Almost every currency calculator on the web hands you a rate. This one does not, and that is the point of it. A rate written into a page is wrong the moment the page is published — the published ones change every working day, they differ between sources depending on where and when they were taken, and buying and selling sit on either side of the middle. What can be done exactly is the arithmetic around a rate, and that arithmetic has one genuine trap in it: converting back the other way is a division by the rate you were given, not a multiplication by the rate printed upside down.

Where the published rates come from, and how often each moves

PublisherHow often it is publishedWhat it is
European Central BankEvery working day, at around 16:00 CETEuro foreign exchange reference rates, published with four decimal places for information purposes only — the ECB states that using the rates for transaction purposes is strongly discouraged
Federal Reserve BoardWeekly, on Mondays at 4:15 p.m.Foreign Exchange Rates — H.10: daily bilateral exchange rates and U.S. dollar indexes for the previous business week, released on the following business day when Monday is a Federal holiday
National Bureau of Statistics of ChinaOnce a year, in the annual statistical communiquéThe average exchange rate of the renminbi against the US dollar for the whole year: one figure, published once, and an average over twelve months rather than a rate anything could be transacted at on any particular day

The table is here because the rate field is empty on purpose, and an empty field deserves an answer to the question of where a rate should come from. The rows are publishers rather than rates, and reading down the middle column is the useful part: the three frequencies are not variations on one thing, they are three different kinds of number sharing the word rate. One is published every working day and is a fixing rather than a market, one is published once a week and covers the week that has just ended, and one is published once a year and is an average of the whole year. None of the three is what a card network will settle your transaction at, and the European Central Bank says in as many words that using its reference rates for transaction purposes is strongly discouraged. The last column is what each publisher itself says the figure is for, which is why it is worth reading before copying a number out of any of them into the rate field above.

Formula

Converted amount ＝ amount × rate　｜　Back the other way ＝ amount ÷ rate

baseAmount
The amount you are converting, in whatever unit you are converting from. The page does not ask which unit that is, because the arithmetic is identical in every pair of currencies
exchangeRate
How many units you get for one unit of the amount. It is a number you type in, from a source you have checked, and the page treats it as exact rather than looking one up
convertedAmount
The amount multiplied by the rate, rounded to two decimals. It is the main figure, and the two decimals are a money convention rather than a property of the rate
reverseAmount
The amount divided by the rate — the rate used the other way round. It is a division rather than a multiplication by the reciprocal, and the two differ by more than a rounding step at large amounts
inverseRate
One divided by the rate, to six decimals. It is printed so the inverse rate can be read off, and it takes no part in either money row

Use it when you already have a rate and want to convert an amount and then convert it back, applying the same rate in both directions: a conversion you have looked up and want to check, a receipt in one currency and a budget in another, or a transaction where the amount went one way and you need to see what it comes to coming back. It is not a source of rates, and if you do not have one to type in, the table and the sources cited below say who publishes the official ones and how often each of them changes — which turns out to be three quite different frequencies.

Worked examples

  1. Default case: 100 at a rate of 1

    1. Converted amount: 100 × 1 ＝ 100.00
    2. Back the other way: 100 ÷ 1 ＝ 100.00
    3. Inverse rate: 1 ÷ 1 ＝ 1.000000

    A rate of one is the entry that shows the shape of the panel without any arithmetic in the way: both rows are the amount itself and the inverse rate is one. It is also the honest starting state of the form, because a rate field has to start somewhere and starting at one makes it obvious that the value is a placeholder rather than a rate the page looked up.

  2. A published annual average: 100 at 7.1429

    1. Converted amount: 100 × 7.1429 ＝ 714.29
    2. Back the other way: 100 ÷ 7.1429 ＝ 13.99992…, rounded to two decimals ＝ 14.00
    3. Inverse rate: 1 ÷ 7.1429 ＝ 0.1399991…, rounded to six decimals ＝ 0.139999

    The rate here is a real published figure rather than a convenient one: 7.1429 yuan to the dollar is the average rate for 2025 reported in China's annual statistical communiqué, cited in full below, and it is a yearly average rather than a rate anything could be transacted at on a given day. It is also where the six decimals earn their place. One divided by 7.1429 is 0.1399991, so the printed reciprocal is 0.139999 rather than the rounder 0.14, and a hundred times that reciprocal is 13.9999 against the 14.00 the division gives. Both are defensible readings of the same rate; the division is the one that does not discard the rate's own precision, so the money row uses it and the reciprocal stays a display.

  3. Where dividing beats multiplying by the reciprocal: 1,000,000 at 3

    1. Converted amount: 1000000 × 3 ＝ 3000000.00
    2. Back the other way: 1000000 ÷ 3 ＝ 333333.3333…, rounded to two decimals ＝ 333333.33
    3. Inverse rate: 1 ÷ 3 ＝ 0.3333333…, rounded to six decimals ＝ 0.333333

    This is the case the whole page is built around. Dividing a million by three gives 333,333.33; multiplying a million by the printed reciprocal of 0.333333 gives 333,333.00, which is thirty-three cents short. The reciprocal is a rounded number and the rounding grows with the amount it is multiplied by — six decimals is plenty for a hundred units and not enough for a million. The money row divides, and the reciprocal is shown so that the difference can be seen rather than taken on trust.

  4. A rate below one: 100 at 0.85

    1. Converted amount: 100 × 0.85 ＝ 85.00
    2. Back the other way: 100 ÷ 0.85 ＝ 117.6470…, rounded to two decimals ＝ 117.65
    3. Inverse rate: 1 ÷ 0.85 ＝ 1.1764705…, rounded to six decimals ＝ 1.176471

    A rate below one is the direction people get backwards by hand, because converting at 0.85 and converting back at 1.176471 look like different operations rather than the same one reversed. They are the same rate: 85 is 100 at the first rate, and 117.65 is 100 at the second. Nothing special happens in the arithmetic at the point where the rate crosses one, which is exactly why it is worth having an example sitting on the far side of it.

  5. The smallest rate the field accepts: 500 at 0.000001

    1. Converted amount: 500 × 0.000001 ＝ 0.0005, rounded to two decimals ＝ 0.00
    2. Back the other way: 500 ÷ 0.000001 ＝ 500000000.00
    3. Inverse rate: 1 ÷ 0.000001 ＝ 1000000.000000

    The rate field takes six decimals because real rates need them, and the money rows carry two, because money does. Where the two meet badly, this is what it looks like: five hundred units converted at one millionth come to five ten-thousandths, and the money row reports zero. Nothing has been computed incorrectly — the two rows are simply measured in different units of precision, and the amount is far below one cent in the target currency. Reading 0.00 as an error here would be as wrong as reading it as a balance.

Limitations

The rate is yours, not the page's. Nothing here looks a rate up, checks the one you typed, or knows what day it is, so a stale or mistaken rate produces a confident wrong answer with no warning attached. Published rates also come in more than one flavour: a central bank reference rate is a daily fixing published for information, a card network's rate is set when the transaction settles, and a bureau de change sells at a spread above and buys at a spread below the middle, none of which is the single number this page takes. Two decimals is a money convention and not a property of the exchange rate. The printed amount is rounded to the cent because amounts are money, but the rate itself is used at full precision inside the calculation, and the two rows are computed independently — the converted amount by multiplying and the reverse amount by dividing, rather than one being derived from the other. That independence is deliberate and it has a consequence at large amounts: the six-decimal reciprocal is a rounded number, and multiplying by it is not the same as dividing by the rate. On a million at a rate of three the two differ by thirty-three cents, which is why the reverse row divides. The smallest rate the field accepts is one millionth and the largest is a million, and at the bottom of that range the money rows can round a genuine conversion to nothing: five hundred at one millionth is five ten-thousandths, which the panel reports as zero because it prints two decimals. That is the floor of the display rather than a failure of the conversion. No currency is attached to any figure, and no unit of currency is asked for anywhere: the arithmetic does not depend on which pair is being converted, and the page has no table of currency names to offer. Two amounts in different currencies look identical on this panel, so label your own answer rather than assuming the page did it. Finally, no fee, spread or commission is modelled. What you actually receive will be worse than what this page computes, by whatever the intermediary charges, and that difference is a rate rather than a fixed amount — which means it cannot be subtracted from the result afterwards without changing the rate you entered.

Frequently asked questions

What rate does the page use?
Whichever one you type in, and it does not look one up. That is a deliberate choice rather than a missing feature: published rates change every working day, they differ between sources depending on where and when they were taken, and they carry a spread between buying and selling. A rate frozen into this page would be wrong shortly after publication and there would be nothing on the screen to say so. The exchange rate field is the whole input, and the reference sections cited below describe where the official published rates come from and how often each of them moves.
Why is the reverse direction a division rather than a multiplication by the reciprocal?
Because multiplying by the printed reciprocal loses precision that grows with the amount. On a rate of three the reciprocal shown is 0.333333, which is rounded; a million multiplied by that is 333,333.00, while a million divided by three is 333,333.33 — thirty-three cents apart, and the error scales up with the amount being converted. The reciprocal is rounded to six decimals so that it is readable, and it is printed as information, but the money row divides by the rate so that the full precision of the rate is used.
How many decimals should I enter for the rate?
As many as the source gives you, up to the six the field accepts. Official reference rates are published with four decimals by the European Central Bank, and other sources publish more or fewer, but the field takes up to six so that a rate quoted to six can be entered exactly as published. Rounding the rate before entering it changes the answer: the amount is multiplied by the rate at full precision and only then rounded to the cent, so a rate entered short is not the same as a correct rate rounded in the display.
Why does a legitimate conversion come out as zero?
Because the money rows print two decimals and the answer is smaller than one cent in the target currency. Five hundred units at a rate of one millionth come to five ten-thousandths, which the panel reports as 0.00. Nothing has gone wrong in the arithmetic — the amount really is that small — and the figure to look at in that case is the reverse row, which divides by the same rate and comes back with five hundred million. It is a limit of printing money to the cent rather than a limit of the conversion.
Does the page know which currencies I am converting between?
No, and it does not ask. The arithmetic is identical for every pair of currencies, so the page takes an amount with no unit and a rate with no unit and leaves the labelling to you. The consequence worth knowing is that two amounts in different currencies look the same on the panel: a hundred of one currency and a hundred of another are both printed as 100.00, and nothing distinguishes them. If the answer is going into a document, write the currency in yourself.
Does the conversion include fees or a spread?
No, and it cannot, because a fee is not an amount that can be subtracted from the result. What a bank, card network or bureau de change charges is a margin inside the rate it applies to you, so it changes the rate rather than reducing the answer by a fixed figure. The way to model it here is to enter the effective rate you were actually given — the one implied by the amount that left your account — rather than a mid-market rate with a separate deduction applied afterwards.

References

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