How-to guidesHow-to

Calculate a cross rate

Derive EUR to JPY from two USD quotes

24 Oct 2026 · 3 min read

To calculate EUR to JPY, divide the JPY per USD rate by the EUR per USD rate. This is a cross rate: a rate between two currencies worked out through a third currency, with USD as the bridge.

Get both rates against USD

Get EUR and JPY rates with USD as the base currency. Both values must describe the same direction: euros per dollar and yen per dollar. EUR per USD means the euros you get for one dollar.

Our API quotes every currency against USD. These two quotes give you the inputs for EUR to JPY. Keep their full precision and use rates from the same moment so the calculation compares matching inputs.

Shell
curl "https://api.exchangerate.dev/v1/latest/USD?symbols=EUR,JPY"

Divide JPY per USD by EUR per USD

The formula is EUR to JPY = (JPY per USD) / (EUR per USD). Put the currency you want to receive in the numerator and the currency you start with in the denominator. The result is yen per euro.

You can also multiply JPY per USD by USD per EUR. To get USD per EUR, take the reciprocal: USD per EUR = 1 / (EUR per USD). Both calculations use the same inputs and produce the same cross rate.

Multiply the euro amount by the cross rate

At 24 Oct 2026, 04:08 UTC, EUR per USD is 0.89255 and JPY per USD is 156.834. Divide 156.834 by 0.89255 to get 175.715 JPY per EUR.

For 1,000 EUR, multiply 1,000 by 175.715. The converted amount is 175,715 JPY, rounded to whole yen.

Multiply the amount in euros by the yen per euro rate. JPY has no minor unit, so round the final amount to whole yen at the end. Keep the input rates and the calculated cross rate at full precision through the multiplication.

StepCalculationResult
EUR per USD1 USD = 0.89255 EUR1 EUR = 1.12039 USD
JPY per USD1 USD = 156.834 JPY1 JPY = 0.006376 USD
EUR to JPY rate156.834 ÷ 0.892551 EUR = 175.715 JPY
1,000 EUR in JPY1,000 × 175.7151,000 EUR = 175,715 JPY

Compare with an EUR base request

Request JPY with EUR as the base. Compare its JPY value with your calculated cross rate, with both results taken at the same moment. The results should agree closely when both requests are made at the same moment, though they may differ in the last digits from rounding.

The response has derived_symbols set to ["JPY"] because the API derives this pair through USD. It also has source, market_session, timestamp and data_updated_at, plus the notice “Indicative rates, not for settlement.”

Check the time fields alongside the rate when you compare results. A quote from another moment changes the inputs to the calculation.

Shell
curl "https://api.exchangerate.dev/v1/latest/EUR?symbols=JPY"

Mistakes that change the result

Dividing EUR per USD by JPY per USD gives the inverse: EUR per JPY.

Check the units before you divide, especially if you have read EUR per USD as dollars per euro.

Mixing a rate from this morning with one from this afternoon combines different quote times.

Rounding each input rate to two decimals before division changes the cross rate before you even convert an amount. Keep the quote direction consistent, match the times and leave rounding until the final amount.

When to calculate it yourself

Calculate the cross rate yourself when you have both USD quotes and want to work out their relationship or check the API result. For a pair without USD, the API already derives the rate through USD. Request EUR as the base and JPY as the symbol to get the pair directly.

Keyless calls allow 10 requests a minute and 100 an hour per IP, with rates 15 minutes late. Free rates are also 15 minutes late; paid plans are live.

The figures are indicative mid-market rates, not for settlement or trading. Banks, cards and transfer services apply their own spread and fees, so a payout differs from the cross rate.

Questions

Which rate goes on top?

For EUR to JPY, put JPY per USD on top and EUR per USD underneath. Dividing them gives JPY per EUR. Reversing the division gives EUR per JPY, the inverse rate.

Can I multiply instead of dividing?

Yes. Multiply JPY per USD by USD per EUR. USD per EUR is the reciprocal of EUR per USD, so this produces the same result as dividing JPY per USD by EUR per USD.

Why does the API mark JPY as derived?

The API quotes every currency against USD. When you request JPY with EUR as the base, it derives that pair through USD and includes JPY in the response's `derived_symbols` list.

Will this equal the amount a transfer pays out?

A payout differs because banks, cards and transfer services apply their own spread and fees. The cross rate uses indicative mid-market figures. These rates are not for settlement or trading.

Keep reading

Get a free API key

Free has 5,000 requests a month and 10 requests a minute. No credit card is required.

Get a free key