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Currency

How To Convert Currency

A currency conversion is a single multiplication once you know the rate, but finding the right rate is the hard part. The rate depends on direction, on the day, and on whether you are looking at the mid-market figure or the one your bank actually gives you.

Quick Answer

Amount in target = amount x (rate of target per USD / rate of source per USD)

Amount
The amount in the source currency
Source rate
Units of the source currency per US dollar
Target rate
Units of the target currency per US dollar

At a reference rate of 0.892438 euros per US dollar, 1,000 dollars is 892.44 euros. The inverse rate is 1.12052 dollars per euro, and the two always multiply to one.

What Is How To Convert Currency?

An exchange rate is the price of one currency in terms of another. Quoting it as a single number always implies a direction: 0.89 euros per dollar is a different statement from 1.12 dollars per euro, even though they describe the same market.

Conversion itself is trivial once the rate is known. Multiply the amount by the number of target units that one source unit buys. Everything difficult about currency conversion is in choosing the rate rather than in the arithmetic.

Rates are conventionally quoted against a base currency, most often the US dollar. Storing every currency as units per dollar reduces the whole problem to one multiplication and one division, because the dollar cancels out in the middle.

The inverse rate is the reciprocal of the rate. If one dollar buys 0.892438 euros, then one euro buys 1 divided by 0.892438, which is 1.12052 dollars. The two figures always multiply to exactly one, which makes the inverse a useful check.

The mid-market rate, also called the interbank rate, is the midpoint between the buy and sell prices in the wholesale market. It is the rate you see on a news site, and it is the rate this calculator uses as its reference.

The rate you actually get will be worse. Banks and card networks add a spread, and exchange bureaux and airport kiosks add a much larger one. A spread of three percent on a thousand dollars costs thirty dollars, which is often more than a visible commission.

Because of that spread, the honest way to use any converter is to enter your own rate. If your card statement shows the rate you were charged, putting that number in gives a result that matches your account exactly rather than approximately.

A rate quoted today applies to a trade today. Settlement may take two business days, and the rate can move in between, which is why businesses that invoice across borders hedge or lock a rate forward.

Currency pairs are quoted to different numbers of decimal places depending on the size of the rate. Pairs near parity are quoted to four or five decimals, while a rate like the yen per dollar is quoted to two or three.

The reference rates here are a snapshot rather than a live feed, because a static site cannot query a market continuously. They are accurate enough to size a purchase or check an order of magnitude, and the override field covers everything that needs more.

Inflation is the reason a currency conversion is not a purchasing-power comparison. Converting at today's rate tells you what an amount buys abroad today, not whether it is a good price relative to what the same money buys at home.

Fees sit on top of the rate. A card may charge a foreign transaction fee of three percent in addition to the spread, and a transfer service may charge a flat fee plus a percentage. Compare the total landed cost rather than the headline rate.

The calculator takes an amount, a source currency and a target currency, and shows the converted amount, the rate used, its inverse, and the value in US dollars. Setting the override field to any non-zero number replaces the reference rate with your own.

Formula

Target = amount x (target per USD / source per USD)

Both currencies are expressed against the dollar, so the dollar cancels and only the ratio of the two rates survives.

SymbolMeaning
A_sAmount
r_sSource rate
r_tTarget rate

Inverse rate = 1 / rate

Reversing the direction of a quote takes the reciprocal, and the product of a rate and its inverse is always one.

SymbolMeaning
rRate

How To Calculate How To Convert Currency

  1. 1

    Find the rate for the direction you need

    Rates are directional. If you are buying euros with dollars you need euros per dollar, not dollars per euro.

  2. 2

    Multiply the amount by the rate

    One thousand dollars at 0.892438 euros per dollar is 892.44 euros. That is the whole calculation when the rate is already in the right direction.

  3. 3

    Take the reciprocal if the direction is wrong

    If you only have dollars per euro, divide by it instead of multiplying, or take the reciprocal first and then multiply.

  4. 4

    Adjust for the spread you will actually pay

    Subtract the bank or card spread from the mid-market rate before converting. A three percent spread on the mid-market rate is a good default for cards.

  5. 5

    Add any flat fees

    Transfer fees and fixed charges are separate from the rate. Add them to the converted total to get the real landed cost.

Examples

Example 1: 1,000 US dollars to euros at the reference rate

Amount
1000
From currency
USD
To currency
EUR
Custom rate (0 = use reference)
0
StepCalculationResult
Reference rate (EUR per USD)0.892438 / 10.892438
Converted amount1000 x 0.892438892.44
Inverse rate (USD per EUR)1 / 0.8924381.12052

Result: At the reference rate of 0.892438 EUR per USD, 1,000.00 USD is 892.44 EUR. The inverse rate is 1.12052 USD per EUR.

Example 2: 100 US dollars to yen at a custom rate

Amount
100
From currency
USD
To currency
JPY
Custom rate (0 = use reference)
160
StepCalculationResult
Reference rate (JPY per USD)158.287265 / 1158.287265
Custom rate appliedoverride 160 replaces the reference160
Converted amount100 x 16016000.00

Result: With a custom rate of 160 JPY per USD, 100.00 USD is 16,000.00 JPY. The reference rate would have given 15,828.73.

Calculator

Converted amount

892.438

Rate used
0.892438
Inverse rate
1.12052602
Value in USD
1,000

Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.

Prefer a full-width tool? Open the How To Convert Currency calculator page.

Common Mistakes

  • Multiplying when the rate is quoted the other way

    A rate of 1.12 dollars per euro cannot be multiplied by an amount in dollars. Either divide by it or take the reciprocal first.

  • Assuming the mid-market rate is what you get

    Banks and cards add a spread, and kiosks add a large one. A three percent spread on a thousand dollars is thirty dollars that the mid-market figure hides.

  • Ignoring the foreign transaction fee

    Many cards charge a percentage on top of the spread. The two together are the real cost, and they are quoted separately.

  • Rounding the rate too aggressively

    Rounding 0.892438 to 0.89 introduces an error of about 0.3 percent, which matters on large amounts. Keep the full rate until the final step.

  • Comparing currencies as if they measured value

    A conversion tells you the price today, not whether something is expensive. Purchasing power and local prices are a separate question.

  • Using a stale rate for a large transfer

    Rates move continuously. For anything sizeable, lock the rate with your provider rather than relying on a figure from a day ago.

  • Adding the fee before converting

    Flat fees and percentage spreads apply at different stages. Apply the rate first, then add flat fees, so the two are not confused.

FAQ

What is the mid-market rate?

The midpoint between the wholesale buy and sell prices for a currency pair. It is the rate shown on news sites and the fairest single reference, but consumers rarely get it exactly.

Why does my bank give a worse rate?

The difference is the spread, which is how the provider earns money on the conversion. Card networks typically add around one percent and banks more, before any separate transaction fee.

How do I convert in the opposite direction?

Take the reciprocal of the rate. One divided by 1.12052 dollars per euro gives 0.892438 euros per dollar, and the two multiply to one.

Are the rates in this calculator live?

No. They are a dated reference snapshot, because a static page cannot query the market continuously. Set the custom rate field to your own figure for an exact result.

How many decimal places should I keep?

Keep the full rate through the calculation and round only the final amount, to the smallest unit of the target currency. Rounding the rate first is where most small errors come from.

Does converting currency tell me if something is cheap?

No. It tells you the price at today's rate. Whether that is good value depends on local prices, which is a purchasing-power question rather than an exchange-rate one.

References

  1. [1]ExchangeRate-API, ExchangeRate-API — https://www.exchangerate-api.com/
  2. [2]Investopedia, Exchange Rates: What They Are and How They Work — https://www.investopedia.com/terms/e/exchangerate.asp
  3. [3]Board of Governors of the Federal Reserve System, Foreign Exchange Rates (H.10) — https://www.federalreserve.gov/releases/h10/