Forward Rate Calculator
A forward rate is the interest rate for a future period that is locked into today’s spot curve: enter the near and far spot rates with their maturities and this calculator returns the implied forward rate between them, with a choice of annual effective or continuous compounding and the five-step no-arbitrage check printed underneath. Note this is the interest-rate forward from the term structure of yields, not a currency forward price: no exchange rate is involved anywhere in this tool.
Forward rate:
Quick Answer
With a 2-year spot rate of 3% and a 5-year spot rate of 6%, the implied forward rate for years 2 to 5 is 8.0484% per year on annual effective compounding, or 8.0000% on continuous compounding. The forward sits above both spot rates because the curve slopes upward: $1 growing at 6% for 5 years reaches 1.338226, and only an 8.0484% roll-over rate for the last 3 years gets the 2-year path to the same place.
Key takeaways
- A forward rate is a breakeven rate backed out of two spot rates. It is implied by prices today, not observed in the market and not a forecast.
- Compounding changes the answer on identical inputs: 8.0484% a year annually versus 8.0000% continuously in the worked example. Always match the convention your spot rates were quoted in.
- Curve shape decides where the forward lands: above both spot rates on an upward slope, equal to both on a flat curve, below both on an inverted segment.
- Fractional and negative inputs work: half-year maturities and negative spot rates both return honest forwards, which matters for money-market tenors and negative-yield curves.
- Quick Answer
- How to use the forward rate calculator
- The no-arbitrage formula, in both compounding bases
- Worked example: 3% for 2 years, 6% for 5 years
- What the curve shape does to the forward rate
- Where to get spot rates worth entering
- A forward rate is a breakeven rate, not a forecast
- What forward rates are used for in practice
- What competing calculators miss
- Frequently asked questions
- Add This Calculator to Your Website
- References
How to use the forward rate calculator
Enter two spot rates and their maturities, pick the compounding basis, and click Calculate Forward Rate. The results stay hidden until you calculate.
- Enter the near spot rate and its maturity: the shorter of the two. Spot rate means the zero-coupon yield from today to that date, in percent per year. The worked example pre-fills 3% for 2 years.
- Enter the far spot rate and its maturity: the longer of the two, here 6% for 5 years. The far maturity must be later than the near one, or the calculator stops with an error, because the forward period would not exist.
- Choose the compounding basis: annual effective if your spot rates are effective annual yields, continuous if they are continuously compounded. If you are converting a quoted yield to an effective annual figure first, the effective interest rate calculator does that conversion.
- Read the result in three parts: the headline forward rate, the forward period it covers (here 3.00 years, from year 2 to year 5), and the five-step check showing both growth paths landing on the same number. The badge under the result names the curve segment: upward-sloping, flat or inverted.
One honest limit: in annual mode, a spot rate of exactly -100% wipes out the growth factor and the tool reports an infinite forward rate rather than a usable number. Rates anywhere near that level do not occur in real yield data, but the tool does not hide the breakdown if you type it in.
The no-arbitrage formula, in both compounding bases
The forward rate is the roll-over rate that makes two routes to the far date worth exactly the same. Route one invests $1 for the full t2 years at the far spot rate. Route two invests $1 for t1 years at the near spot rate, then rolls the proceeds forward at the forward rate f for the remaining t2 minus t1 years. No-arbitrage says the two end values must match, and solving that equation for f gives the formula.
Continuous: f = (r2·t2 − r1·t1) / (t2 − t1)
The continuous version is a weighted average unwound: the total return r2·t2 minus the return already earned r1·t1, spread over the forward window. Any forward rate other than the one these formulas produce would let a trader borrow along one path and lend along the other for a riskless profit, and market trading closes that gap quickly. That arbitrage logic, rather than anyone's opinion about future rates, is what pins the number down.
Worked example: 3% for 2 years, 6% for 5 years
The pre-filled example prices the 3-year forward period that starts in year 2. Run it in annual mode and the calculator prints the whole chain, so every step can be checked by hand.
Switch the same inputs to continuous compounding and the answer is exactly 8.0000%: growth factors become e0.03×2 = 1.061837 and e0.06×5 = 1.349859, and the forward factor 1.271249 annualizes to 8.0000% on a continuous basis. The 0.0484-point gap between the two modes is pure convention, not disagreement: the inputs describe slightly different growth paths once the compounding basis changes.
The same calculator, run on five more spot pairs, gives the verified results below. Every row is a real run of the tool above, so you can re-enter any row and get the same figure back to four decimals.
| Case | Near spot | Far spot | Forward rate |
|---|---|---|---|
| One-year rate, one year forward (annual) | 3.5% for 1 year | 4% for 2 years | 4.5024% per year |
| Flat curve (annual) | 4% for 1 year | 4% for 3 years | 4.0000% per year |
| Inverted segment (annual) | 5% for 1 year | 4% for 3 years | 3.5036% per year |
| Half-year tenors (annual) | 2.5% for 0.5 years | 3.25% for 1.5 years | 3.6271% per year |
| Negative far rate (annual) | 1% for 2 years | -0.5% for 5 years | -1.4876% per year |
What the curve shape does to the forward rate
The forward rate always lands outside the two spot rates, on the side the curve is heading, unless the curve is flat. That is arithmetic, not opinion: the far spot rate is an average of the near rate and the forward, so the forward has to sit beyond it to pull the average up or down.
| Spot pattern | Forward lands | Usual reading |
|---|---|---|
| Far spot above near spot | Above both spot rates | Normal upward slope: rising-rate expectations, term premium, or both |
| Far spot equal to near spot | Equal to both | Flat segment: no net move priced over the window |
| Far spot below near spot | Below both spot rates | Inverted segment: markets pricing rate cuts; the pattern recession watchers track |
The calculator flags the third case in words: when the far spot rate is below the near one, the note under the result says the forward is below both and names it an inverted segment, and the badge turns red. Inversion gets attention because the gap between long and short Treasury yields has preceded US recessions often enough that the Federal Reserve Bank of New York maintains a yield curve FAQ on its recession-probability work. A single inverted segment between two maturities is a weaker signal than a full-curve inversion, but the arithmetic flag is the right place to start looking.
Where to get spot rates worth entering
Enter zero-coupon spot yields for the two maturities when you can get them, because the formula assumes each rate compounds untouched to its own date. The two standard free sources are the US Treasury daily par yield curve rates and the Federal Reserve H.15 statistical release, which publishes constant-maturity Treasury yields daily.
Par yields and constant-maturity yields are yields on coupon bonds, so they are close cousins of true spot rates rather than the thing itself. For textbook problems and most practical work the difference is small, and bootstrapped spot curves from data services such as the FRED constant-maturity series close most of the remaining gap. What matters more is consistency: both rates from the same curve, the same day, and the same compounding basis. Mixing a nominal annual yield with a continuously compounded one silently corrupts the forward by more than any rounding in this tool.
A forward rate is a breakeven rate, not a forecast
The forward rate is the roll-over rate at which a forward contract struck today would have zero value. It blends genuine rate expectations with term premia, the extra yield investors demand for locking money up longer, plus smaller convexity and liquidity effects. That blend is why realized rates routinely arrive above or below the forward that was priced years earlier.
Keep the two currency and rates meanings apart as well. An FX forward rate is a future exchange rate built from a spot exchange rate and two interest rates, and its premium over spot is a separate calculation covered by the forward premium calculator in this same batch of tools. This page never touches exchange rates: two yields in, one implied yield out. Search results blur the two topics constantly, and half the confusion around the phrase "forward rate" starts there.
What forward rates are used for in practice
Forward rates price contracts that start later: that is the whole job. A forward rate agreement (FRA) settles on exactly the rate this page computes, an interest rate swap stacks a strip of these forwards into a fixed-versus-floating exchange, and a bond desk reads them to judge carry and roll-down before buying a maturity.
- FRAs and futures: the FRA fixed rate is set at the implied forward so the contract starts at zero value. Eurodollar and SOFR futures strip out into the same forward curve, with a small convexity adjustment futures desks apply on top.
- Swaps: each floating payment in a swap is forecast from the forward curve, then discounted back along it. The equity swap calculator shows the same fixed-for-floating structure on the equity side.
- Bond strategy: a bond priced off the spot curve earns its yield only if forwards are realized; comparing the forward path with your own rate view is the core of carry-and-roll-down analysis, and forwards feed the discounting behind measures such as effective duration.
- Reading policy expectations: central bank watchers back forwards out of overnight-index-swap curves to see how many cuts or hikes are priced. The levels move with term premium too, which is why the after-tax yield on the bonds behind the curve can tell a different story from the headline forward.
What competing calculators miss
Forward rate tools split into camps, and each leaves a gap this page closes:
- Single-convention tools (Brave Calculator, BearSavings, Ryan O'Connell Finance): clean annual-compounding calculators with useful curve commentary, but no continuous mode. Derivatives and textbook problems quoted on a continuous basis get a silently wrong answer from them, by 0.0484 points against the worked example in the section above.
- Continuous-only tools (Akyno): present the linear formula f = (r2·t2 − r1·t1) / (t2 − t1) as if it were the general formula. It is exact only under continuous compounding, and the page never says so: its own multi-year example would come out differently under the annual convention most bond markets quote.
- FX forward tools wearing the same name (Omni currency forward, TradeAnswers): competent currency calculators that answer a different question, spot exchange rate in, forward exchange rate out. Nothing on them computes the interest-rate forward between two maturities.
- Broken formula pages (FormulaDen): its FX forward evaluator uses a garbled formula with a logarithm of a rate difference, which fails basic sanity checks. A reminder to verify any calculator against a hand-worked no-arbitrage check, which is why this tool prints all five steps of its own proof.
- The gap this page fills: both compounding bases in one tool, the growth-factor proof printed with every result, an explicit inverted-segment flag, fractional maturities and negative rates accepted, and the not-a-forecast warning attached to the answer itself rather than buried in fine print.
Frequently asked questions
A spot rate is the yield on money committed today for a set term, such as the 2-year or 5-year Treasury yield. A forward rate is the rate for a period that starts in the future, such as years 2 to 5, worked out from the two spot rates so that both paths grow $1 to the same amount. It is calculated from market prices, not quoted directly.
Match the rates you were given. Yields quoted as annual effective rates belong in the annual mode, which is how most textbooks and bond problems state spot rates. Continuous compounding is the default in derivatives pricing and much academic work. On the same inputs the two modes can differ: 3% for 2 years and 6% for 5 years give 8.0484% a year annually and 8.0000% continuously.
No. A forward rate is a breakeven rate implied by today's spot curve under no-arbitrage. It blends market expectations with term premia and other risk adjustments, so the rate that actually arrives usually differs. Traders use it to price contracts and hedges, not as a forecast they expect to come true.
Yes. If the far spot rate sits far enough below the near one, the implied forward falls below zero. With a 2-year spot rate of 1% and a 5-year spot rate of -0.5%, this calculator returns -1.4876% a year. Negative forwards appeared in euro and yen curves when policy rates were below zero.
An FX forward rate is an exchange rate for swapping currencies on a future date, built from the spot exchange rate and the interest rates of the two currencies. This page works with interest rates only: it takes two spot yields and returns the implied forward yield between their maturities. Currency forwards are a separate tool with a separate formula.
Yes. Maturities are plain numbers of years, so half years and quarters work: a 0.5-year spot rate of 2.5% with a 1.5-year spot rate of 3.25% gives a forward rate of 3.6271% a year for the year in between. Keep both maturities in years and on the same compounding basis.
Use zero-coupon spot yields for the two maturities when you can find them. The US Treasury publishes daily par yield curve rates and the Federal Reserve publishes the H.15 release, both linked in the References section below. Coupon bond yields to maturity are close cousins, not true spot rates, so results built from them are approximations.
The forward period is the gap between the two maturities, t2 minus t1. If the far maturity were equal or earlier, the gap would be zero or negative, there would be no future period to price, and the annual formula would divide by zero. The calculator stops with an error message in that case.
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References
- Board of Governors of the Federal Reserve System. Statistical Release H.15: Selected Interest Rates. Accessed October 21, 2026.
- US Department of the Treasury. Daily Treasury Par Yield Curve Rates. Accessed October 21, 2026.
- Federal Reserve Bank of St. Louis (FRED). Market Yield on US Treasury Securities at 2-Year Constant Maturity (DGS2). Accessed October 21, 2026.
- Federal Reserve Bank of St. Louis (FRED). Market Yield on US Treasury Securities at 10-Year Constant Maturity (DGS10). Accessed October 21, 2026.
- Federal Reserve Bank of St. Louis (FRED). 10-Year Treasury Constant Maturity Minus 2-Year Treasury Constant Maturity (T10Y2Y). Accessed October 21, 2026.
- Bank of England. UK Yield Curves. Accessed October 21, 2026.
- Federal Reserve Bank of New York. The Yield Curve as a Leading Indicator: Frequently Asked Questions. Accessed October 21, 2026.
- Gurkaynak, R., Sack, B. and Wright, J. Board of Governors of the Federal Reserve System. The US Treasury Yield Curve: 1961 to the Present (FEDS 2006-28). Accessed October 21, 2026.
- Bank for International Settlements. OTC Derivatives Statistics. Accessed October 21, 2026.
- US Securities and Exchange Commission, Investor.gov. Compound Interest Calculator and Compounding Explainer. Accessed October 21, 2026.