A forward exchange rate is the price agreed today for an exchange of two currencies on a date in the future. It is not a prediction of where the spot rate will be on that date. It is an arithmetic consequence of three things you can observe right now: the spot rate, the interest rate available on the base currency, and the interest rate available on the quote currency. This calculator takes those three inputs, plus a tenor and a day-count convention, and returns the forward rate that leaves no risk-free profit on the table.
Arb Digital builds free tools that keep their assumptions on the surface rather than buried in a black box. This page publishes no exchange rate and no interest rate, because both change continuously and a figure typed from memory would silently corrupt every result computed from it. Every rate on this page is a value you supply from your own quote sheet, and the calculator shows you what those particular numbers imply.
What This Forward Exchange Rate Calculator Does
Enter a spot rate quoted as units of the quote currency per one unit of the base currency, the annualised interest rate on each currency for the tenor you care about, the number of days to settlement, and the day-count basis your deposit quotes use. The hero figure is the implied forward rate under covered interest parity. The supporting grid gives you the forward points — the difference between forward and spot, scaled by the multiplier your dealer quotes in — the annualised premium or discount as a percentage, the quote-currency proceeds the forward would lock in on your notional, and how that compares with settling at today's spot instead.
Two conventions are exposed rather than assumed. The first is the day-count basis: most money markets quote on actual/360, but sterling and several others use actual/365, and using the wrong one shifts the answer by a small but real amount on a large notional. The second is whether interest accrues simply over the period, which is the money-market norm for short tenors, or compounds annually, which is how longer-dated rates are often expressed. Both are supported, and the difference between them widens as the tenor lengthens.
How to Use It
- Enter the spot rate in the direction your quote is written. If your screen shows 1.0850 for EUR/USD, the base is EUR and the quote is USD, so 1.0850 goes in as it stands.
- Enter each interest rate for the matching tenor. The base-currency rate is the one you would earn or pay on the currency you are selling forward; the quote-currency rate is the other side.
- Set the tenor in days and pick the day-count basis that matches how those deposit rates are quoted.
- Choose the rate convention and points multiplier. Simple accrual suits tenors under a year; the multiplier is 10,000 for most pairs and 100 where the quote currency is the yen.
- Add a notional if you want to see the cash effect, then press Calculate to update the forward rate, the points, the annualised premium and the proceeds together.
The Formula and How It Is Calculated
Covered interest parity says that borrowing in one currency, converting at spot, lending in the other, and contracting today to convert back at the forward rate must produce the same result as simply lending in the first currency. If it did not, the difference would be a risk-free profit, and someone would take it until the prices moved. Setting those two paths equal gives the relation the calculator uses.
With S as the spot rate in quote currency per base currency, iq and ib as the quote and base annualised rates, d as days and B as the day-count basis, the simple-accrual form is F = S × (1 + iq × d/B) ÷ (1 + ib × d/B). The compounded form replaces each bracket with (1 + i)d/B.
Work an example by hand. Take a spot of 1.0850, a base rate of 3.25%, a quote rate of 5.00%, a tenor of 90 days and an actual/360 basis. The time fraction is 90 ÷ 360 = 0.25. The numerator is 1 + 0.05 × 0.25 = 1.0125 and the denominator is 1 + 0.0325 × 0.25 = 1.008125. Their ratio is 1.0043409, so the forward rate is 1.0850 × 1.0043409 = 1.08971. The forward points are (1.08971 − 1.0850) × 10,000 = 47.1. The annualised premium is 0.0043409 ÷ 0.25 = 1.736%, which sits just below the 1.75% raw interest differential — the small gap is the denominator effect, and it is not a rounding error. On a one million unit notional, the forward locks in 1,089,710 of quote currency against 1,085,000 at spot, a difference of 4,710.
Why the Higher-Yielding Currency Trades at a Discount
The most common misreading of a forward quote is treating a forward discount as a market forecast that the currency will fall. It is not. If the quote currency pays more interest than the base currency, holding the quote currency for the period earns more, and the forward rate must give back exactly that advantage or the trade becomes a free lunch. The forward price is the mechanism that neutralises the interest differential, not an opinion about the future.
The sign is therefore predictable. Whenever the quote-currency rate exceeds the base-currency rate, the forward sits above spot and the base currency is at a forward premium. Swap the two rate fields and the points change sign while their magnitude barely moves.
The practical implication is that a forward contract does not make an expensive currency cheap. Hedging a high-yield exposure forward costs roughly the interest differential, and shopping between dealers changes only the spread on top.
Where the Textbook Relation Breaks Down
Covered interest parity is an arbitrage relation, and arbitrage relations hold only when the arbitrage is actually executable. Since the financial crisis, persistent deviations have been visible in several major pairs, usually expressed as a cross-currency basis. They exist because the trade that would close them consumes balance sheet, capital and counterparty credit lines, and those are neither free nor unlimited. A bank that could in principle earn a few basis points on the arbitrage may not have the regulatory capacity to do it at quarter-end, which is why the deviations are often widest across reporting dates.
The number this page produces is therefore a benchmark, not a quote. If your dealer's forward differs from it by more than the expected bid-ask spread, the gap is more likely a genuine basis than a mispricing you can exploit.
The Bank for International Settlements' survey of OTC foreign exchange turnover gives a sense of the scale involved: FX swaps and outright forwards make up a very large share of global turnover, which is precisely why small pricing frictions in this market attract so much attention.
Getting the Quote Convention Right
Every error this calculator cannot catch is a convention error. The spot rate must be entered in the same direction as the interest rates are assigned. If you enter 1.0850 meaning US dollars per euro, then euro is the base and its rate belongs in the base field. Enter the same market as 0.9217 dollars-to-euro and the roles swap; put the dollar rate in the base field instead. Get this backwards and the forward comes out on the wrong side of spot, which is a large error dressed up as a plausible number.
If you are deriving the pair itself from two separate quotes against a common third currency, do that first with our cross exchange rate calculator, which handles the spot arithmetic and carries the bid-ask spread through correctly, then bring the resulting spot rate here to move it through time. The two tools deliberately do different jobs: one derives a spot rate across three currencies, this one projects one pair forward using two interest rates.
Forward Points, Swaps and What You Actually Trade
Dealers rarely quote a forward as an outright number. They quote points, added to or subtracted from spot, because the points move far less than spot does and can be held stable through a conversation. That is why the calculator surfaces points as a headline supporting figure. An FX swap — spot one way, forward the other — is priced entirely off those points, and the swap is the instrument most commonly used to roll a hedge rather than to take a view.
The points multiplier is a display convention, not mathematics. Setting it wrongly does not change the forward rate the calculator returns; it only rescales the points figure, which is why it is an input rather than a guess.
How This Fits Alongside Interest Rate Tools
The two interest rates are doing all the work here, so it is worth being deliberate about which ones you use. A policy rate is not a deposit rate, and a headline nominal rate is not what you would earn after inflation — our real interest rate calculator makes that distinction explicit, and the interest rate calculator and compound interest calculator cover the accrual conventions in more depth. For longer tenors, where the compounding choice matters most, the discounting logic behind a bond price calculator is the same machinery viewed from a different angle.
Currency exposure also feeds into cost of capital for any business that earns in one currency and borrows in another, which is where the WACC calculator becomes relevant. Note that the accounting treatment of currency movements is a separate discipline again; IAS 21 The Effects of Changes in Foreign Exchange Rates governs which rate a reporting entity uses and where the resulting differences are presented, and that is a question about financial statements rather than about pricing a contract.
Arb Digital builds tools, calculators and content that earn trust with technical audiences — the same approach used to build this page.
Browse the free tools hub Talk to Arb DigitalCommon Mistakes to Avoid
- Reading the forward as a forecast. It is the rate that removes arbitrage between two interest rates, and it carries no information about where spot will actually be.
- Mixing the quote direction and the rate assignment. The base-currency rate must belong to the currency in the denominator of your spot quote, or the forward lands on the wrong side of spot.
- Using a policy rate instead of a transactable deposit rate. Parity is about rates you can actually borrow and lend at for that tenor, not about a central bank's headline number.
- Ignoring the day-count basis. Actual/360 and actual/365 give different answers, and on a large notional the difference is real money rather than rounding.
- Treating the parity figure as an all-in cost. The dealer's bid-ask spread, any credit or collateral terms, and the cross-currency basis all sit on top of the number this page returns.
Related Free Tools From Arb Digital
Derive a spot pair from two quotes with the cross exchange rate calculator, tidy up how a figure is displayed with the currency format converter, or convert digital assets with the crypto converter. On the rates side, the real interest rate calculator, interest rate calculator and bond price calculator cover the inputs this page consumes, and the full free tools hub lists everything else.
Frequently Asked Questions
No. It is the rate implied by covered interest parity from today's spot rate and the two currencies' interest rates. It is the price that removes a risk-free profit between borrowing in one currency and lending in the other, and it carries no forecast content about where spot will actually trade.
Because holding it earns more interest over the period. The forward rate has to give that advantage back, or an investor could borrow the low-rate currency, lend the high-rate one, and lock in the exchange back at a rate that left a guaranteed gain. The discount neutralises the interest differential rather than expressing a view.
Match whichever basis the deposit rates you entered are quoted on. Actual/360 is the common money-market convention for many currencies, while actual/365 is used for others including sterling. The choice changes the answer slightly, which is why it is an input on this page rather than a fixed assumption.
Forward points are the difference between the forward rate and the spot rate, scaled by a display multiplier — usually 10,000, or 100 for yen-quoted pairs. Dealers quote points rather than outright forwards because points move far less than spot does over the course of a conversation.
Three reasons, usually together: the dealer's bid-ask spread, the credit and collateral terms attached to your relationship, and the cross-currency basis, which is a persistent deviation from parity that exists because the arbitrage consumes balance sheet and capital. The parity figure is a benchmark to question a quote against, not a quote.
The arithmetic extends, but switch the rate convention to annually compounded, because simple accrual understates the effect of interest over longer periods. Longer-dated forwards are also where the cross-currency basis tends to be largest, so the gap between the parity figure and a real quote widens.
The cross rate tool derives a spot rate between two currencies from each one's quote against a common third currency. This page takes a single pair's spot rate and moves it through time using the two currencies' interest rates. One works across currencies, the other across dates.
This tool is an educational and planning aid only. It is not financial, investment or hedging advice, and it publishes no exchange rate or interest rate — every figure is one you supply. Real forward pricing depends on dealer spreads, credit and collateral terms and the prevailing cross-currency basis, and any actual transaction should be discussed with a qualified professional.
