Forward Premium Calculator
Enter a forward exchange rate and the spot rate for the same currency pair and this calculator returns the gap between them as a percentage of spot. A positive result is a forward premium, a negative result is a forward discount, and the size of that percentage is, to a first approximation, the interest rate differential between the two currencies. That is the number treasurers check before hedging a foreign-currency payment and the number behind every forward quote a bank gives you.
Quick Answer
Forward Premium (%) = (Forward Rate – Spot Rate) / Spot Rate x 100. With a forward rate of 1.15 and a spot rate of 1.10, the result is 4.55%: the pair trades at a forward premium for the contract period. The figure is not annualized, and under covered interest parity it mainly reflects the interest rate gap between the two currencies, not a market forecast.
Key takeaways
- Positive means premium, negative means discount, zero means the forward and spot rates are at par.
- The percentage covers the full contract period. Comparing two contracts of different lengths without annualizing is a category error.
- Covered interest parity ties the premium to the interest rate differential; the higher-rate currency normally sits at a forward discount.
- Premium describes the quoted pair. Flip the quote direction and the sign story flips with it.
- Quick Answer
- How to use the forward premium calculator
- The formula, and the parity condition behind it
- Worked example: a 4.55% premium, then checked against parity
- Raw premium versus annualized premium
- Reading the sign: which currency is at a premium?
- What competing calculators miss
- Frequently asked questions
- Add This Calculator to Your Website
- References
How to use the forward premium calculator
Enter the forward rate and the spot rate for the same pair, quoted the same way, then click Calculate. The tool returns one number: the forward rate’s percentage distance from spot.
- Forward exchange rate. The outright forward quote for the delivery date you care about, from your bank, broker or a market data source. If you only have spot and the two interest rates, a forward rate calculator derives the forward rate first; this page starts where that one ends.
- Spot exchange rate. The current rate for the same pair and the same quotation direction. Reference rates published by central banks, such as the Federal Reserve H.10 release or the ECB daily reference rates, are a clean spot source for end-of-day work.
- Read the sign before the size. The badge under the result labels the outcome as a premium, a discount or par, and the note restates the raw rate difference, so a small percentage on a large rate (a yen pair, for example) is not mistaken for a small move.
Quote discipline is the whole game here. Both rates must describe the same pair in the same direction: if spot is 1.10 US dollars per euro, the forward must also be dollars per euro, not euros per dollar. A mismatched pair of quotes produces a confident, precise and completely wrong percentage.
The formula, and the parity condition behind it
The calculation itself is one line: Forward Premium (%) = (F – S) / S x 100, where F is the forward rate and S is the spot rate. What gives that line its meaning is covered interest parity, the no-arbitrage condition that prices forward contracts in the first place.
Covered interest parity says an investor must earn the same return investing in either currency once the exchange is locked in with a forward. Rearranged, it prices the forward rate directly from spot and the two interest rates:
F = S x (1 + iquote x t) / (1 + ibase x t), and dividing through by S gives the approximation every desk actually uses:
(F – S) / S is approximately iquote – ibase for the same period, where i is the interest rate in each currency and t is the contract length in years.
This is the formulation taught in the CFA Institute curriculum learning module on currency exchange rates and tested in the Bank for International Settlements research programme: the BIS working paper series has examined deviations from covered interest parity during the 2007-08 turmoil, and Du, Tepper and Verdelhan documented in their NBER study of deviations from covered interest rate parity that real-world forwards can sit measurably away from the parity price when bank balance sheets are constrained. Two practical consequences follow. First, the currency with the higher interest rate trades at a forward discount, other things equal, because its rate advantage is handed back through the forward price. Second, a premium is not the market predicting appreciation; it is mostly arithmetic about interest rates, which is why reading it as a forecast goes wrong so often.
Worked example: a 4.55% premium, then checked against parity
Suppose a pair is quoted at spot 1.10 and the forward for your delivery date is 1.15. Enter forward 1.15 and spot 1.10, and the calculator returns Forward Premium: 4.55%.
The hand check is short: (1.15 – 1.10) / 1.10 = 0.05 / 1.10 = 0.04545, which is 4.55% rounded to two decimals. The raw rate difference is 0.0500, or 500 forward points at the four-decimal convention dealers use for pairs quoted to four places. Now cross-check it against parity. If the quote-currency interest rate is 5% and the base-currency rate is 2% for a one-year contract, parity implies F = 1.10 x 1.05 / 1.02 = 1.13235, and entering 1.13235 against spot 1.10 in this calculator gives 2.94%, close to the 3% differential the approximation promises (the exact figure is a touch lower because of the 1.02 denominator). A market forward of 1.15 against those same rates would sit well above the parity price, which is exactly the kind of gap the BIS deviation studies measure.
| Forward rate | Spot rate | Result | Reading |
|---|---|---|---|
| 1.15 | 1.10 | 4.55% | Forward premium |
| 1.08 | 1.10 | -1.82% | Forward discount |
| 1.10 | 1.10 | 0.00% | At par |
| 155.40 | 150.00 | 3.60% | Premium on a yen-style quote |
| 0.92 | 0.95 | -3.16% | Forward discount |
| 1.13235 | 1.10 | 2.94% | Parity-implied premium at 5% vs 2% for one year |
Every row reproduces exactly in the calculator, including the parity row. If you are comparing two forward quotes from different banks for the same date, this percentage is also the honest way to compare them, since both are measured against the same spot base. Converting a rate from one quotation direction to the other is a separate step; a cross exchange rate calculator handles that side of the work.
Raw premium versus annualized premium
The tool reports the premium for the contract period, exactly as quoted. Whether that is the number you need depends on what you are comparing.
(F – S) / S x 100 over the actual contract. Use it to price one specific hedge: it is the percentage cost or benefit locked into that one forward contract, and it is what settles.
Raw premium x (360 / contract days) on the money-market basis, or x (12 / months). Use it to compare contracts of different lengths, or to compare the premium against annual interest rates. It describes a rate, not a settlement amount.
Taking the worked example’s 4.55% raw premium (4.5455% before rounding) and annualizing it on a 360-day basis shows how much the tenor changes the story:
| If that premium covered | Multiplier (360 / days) | Annualized premium |
|---|---|---|
| 30 days | 12 | 54.55% |
| 90 days | 4 | 18.18% |
| 180 days | 2 | 9.09% |
| 360 days | 1 | 4.55% |
The tool deliberately does not ask for a tenor and does not annualize for you. A premium figure with no stated period is incomplete information, and bolting an assumed tenor onto someone else’s contract would manufacture precision the inputs do not contain. Annualize by hand with the table’s method when you need the comparison, and state the basis (360 or 365) alongside the result, the same discipline used when comparing any effective interest rate across products.
Reading the sign: which currency is at a premium?
A positive result says the forward rate, as quoted, sits above spot. Translating that into “currency X is at a premium” requires the quote convention, and skipping this step is how premium and discount get swapped in reports.
When a rate is quoted as units of quote currency per one unit of base currency (1.10 dollars per euro, say), a forward above spot means the base currency buys more of the quote currency forward than it does today: the base currency is at a forward premium and the quote currency is, by the same token, at a forward discount. Quote the pair the other way around (euros per dollar) and the same market produces a negative number with the labels reversed. Neither is wrong; they are the same prices read from opposite sides. This is also why the parity rule is stated per quotation: with the rate in dollars per euro, the premium on the euro approximates the US rate minus the euro-area rate, so the euro tends to sit at a premium when US rates are the higher ones, because the higher-rate currency (the dollar, in the quote seat) gives its advantage back through the forward price. Central bank operations desks work with these conventions daily; the Reserve Bank of Australia describes its own use of spot purchases and FX swaps at agreed forward rates in its international market operations overview, a useful reminder that forward pricing is plumbing, not prophecy.
What competing calculators miss
The one-line formula is identical everywhere, so rival tools separate themselves on everything around it. Reviewing the current field for this keyword turned up the same four weaknesses repeatedly.
- Annualization baked in without saying so. Several rival calculators silently multiply by 12/months or 360/days and present an annualized figure under the plain label “forward premium”. A 90-day contract at a real 4.55% premium comes out labelled 18.18%. This page reports the raw contract premium and shows the annualization separately, with its basis stated.
- “Expected to appreciate” as the explanation. Many tools, and the old text on this very page, describe a premium as the market expecting the currency to strengthen. Under covered interest parity the premium is set by the interest differential; treating it as a forecast contradicts the parity evidence from the BIS and the Federal Reserve research literature, including work on how persistent the resulting forecast errors are (the forward premium puzzle surveyed in Avdjiev, Du, Koch and Shin’s BIS symposium paper on the dollar and CIP deviations).
- No quote-direction warning. Tools accept any two numbers and never mention that flipping the pair direction flips the interpretation. The premium belongs to a quotation, not to a currency in the abstract.
- Forward points ignored. Dealers quote points, not outright rates, much of the time. Rivals rarely connect the two; here the results note restates the raw forward-minus-spot difference so the percentage and the points view stay tied together.
Frequently asked questions
A forward premium is the percentage by which a forward exchange rate exceeds the spot rate for the same currency pair: (Forward – Spot) / Spot x 100. A forward rate of 1.15 against spot of 1.10 gives a forward premium of 4.55% for that contract period.
A negative result is a forward discount: the forward rate sits below spot, so the quoted pair is cheaper forward than today. The calculator still labels the number Forward Premium, and the badge under the result marks it as a discount so the sign is not missed.
No. The result is the premium over the whole contract period, because the tool does not ask for a tenor. To annualize it yourself, multiply by 360 divided by the contract days on a money-market basis: a 4.55% premium over 90 days annualizes to about 18.18%.
Mainly the interest rate differential between the two currencies. Covered interest parity requires the forward rate to offset the rate gap, so the higher-interest-rate currency normally trades at a forward discount and the lower-rate currency at a forward premium, with smaller deviations appearing when bank balance sheets are constrained.
No. The premium is set by interest rate differentials under covered interest parity, not by a market vote on the future spot rate. Decades of research, often called the forward premium puzzle, find that forward rates are biased predictors of future spot rates, so treat the premium as a hedging cost measure, not a forecast.
It depends on the quotation. If the rate is quoted as quote-currency units per one base-currency unit, a positive result means the base currency is at a forward premium and the quote currency is at a forward discount. Inverting the pair inverts the labels, so always state the premium together with the pair direction.
Forward points are the raw difference between the forward and spot rates, before dividing by spot. For pairs quoted to four decimal places, dealers express that difference in points by multiplying by 10,000, so a forward of 1.15 against spot of 1.10 is 500 points and a 4.55% premium at the same time.
A spot rate of zero stops the calculation with a message, because the spot rate is the base of the percentage and dividing by zero is undefined. If both rates are equal, the result is 0.00% and the pair is at par, with neither a premium nor a discount.
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References
- CFA Institute. Learning Module: Currency Exchange Rates, Understanding Equilibrium Value (curriculum excerpt on covered interest rate parity). Accessed October 21, 2026.
- Bank for International Settlements. BIS Working Paper No. 267: Interpreting Deviations from Covered Interest Parity During the Financial Market Turmoil of 2007-08. Accessed October 21, 2026.
- Avdjiev, S., Du, W., Koch, C. and Shin, H.S., Bank for International Settlements. The Dollar, Bank Leverage and the Deviation from Covered Interest Parity (BIS symposium paper). Accessed October 21, 2026.
- Du, W., Tepper, A. and Verdelhan, A. Deviations from Covered Interest Rate Parity, NBER Working Paper 23170. Accessed October 21, 2026.
- Du, W., Tepper, A. and Verdelhan, A. Deviations from Covered Interest Rate Parity (American Economic Association paper page). Accessed October 21, 2026.
- Board of Governors of the Federal Reserve System. Foreign Exchange Rates, H.10 Daily Summary. Accessed October 21, 2026.
- European Central Bank. Euro Foreign Exchange Reference Rates. Accessed October 21, 2026.
- Bank of Canada. Daily Exchange Rates. Accessed October 21, 2026.
- Reserve Bank of Australia. International Market Operations. Accessed October 21, 2026.
- Federal Reserve Bank of St. Louis, FRED. U.S. Dollars to One Euro Exchange Rate (DEXUSEU). Accessed October 21, 2026.