Forward rate calculator
If the 1-year spot rate is 4% and the 2-year spot is 5%, the curve already locks in 6.00961538% for the one-year period starting a year from now. Check it against an FRA or a deposit rollover. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Spot rate 1
- 4
- Years 1
- 1
- Spot rate 2
- 5
- Years 2
- 2
- Years forward
- 1
- Forward rate
- 6.00961538
- Forward rate decimal
- 0.0600961538
The implied forward rate is the break-even interest rate between two later dates that is already locked in by today's spot (zero) curve. Given a spot rate for a nearer tenor and a spot rate for a longer tenor, no-arbitrage compounding says that investing to the long date at the long spot must earn the same as investing to the short date and rolling at the unknown forward. This forward rate calculator accepts those two spot rates as percents together with their year fractions, applies the textbook identity, and returns the annually compounded forward.
What an implied forward rate means and how two spots pin it
An implied forward rate is the future interest rate, between two later dates, that is already priced into today's spot (zero) curve. Spot rates are entered as percents: four means four percent, not 0.04. A worked case of a four percent one-year spot and a five percent two-year spot therefore yields f equal to 1.05 squared over 1.04, minus one, about 6.00961538 percent for the one-year rate starting in one year.
Tenors are year fractions in the same unit as the compounding period of the spots you supply (one is one year, 0.5 is six months). This is not a currency forward, a Fisher real rate, or an implied yield from a present and future value: those pages take different inputs and target different searches.
What you can do with it
Yield-curve FRA and futures checks
Turn two published zero rates and two tenors into the annually compounded forward a trader compares with a FRA or a futures strip before booking a hedge.
Deposit rollover and ALM planning
See what rate the curve already locks in between two future dates when rolling a deposit or planning a refinancing, without a full bootstrap library.
Classroom implied-forward homework
Mark problems that ask students to compute f from two spots and two tenors, including the inverted-curve case, with a deterministic oracle.
FAQ
What happens if a spot rate is −100% or less?
At −100% or below, 1 + rate/100 is not positive, so the compounding power is undefined.
How is the implied forward rate calculated?
Grow one unit at the long spot rate to the long date, divide by its growth at the short spot rate to the short date, take the root for the years between them and subtract one. That is the rate that makes both paths earn the same.
Why must the second tenor be longer than the first?
Because the forward covers the window between the two dates. If the second tenor is not longer, the window has no length and there is no rate to find, so the calculation is refused.
Can I use tenors shorter than a year?
Yes. Enter tenors as year fractions, such as 0.5 for six months, in the same unit as the compounding period of the spot rates you supply. The first tenor must be greater than zero.
Does it handle continuous compounding or other day-count rules?
No. It applies the annually compounded identity only. If your desk uses actual over 360 or continuous zero rates, convert the inputs or the result with your own convention.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/fin/forward-rate \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"spot_rate_1":4,"years_1":1,"spot_rate_2":5,"years_2":2}'const res = await fetch("https://api.kit.forhosting.com/fin/forward-rate", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"spot_rate_1": 4,
"years_1": 1,
"spot_rate_2": 5,
"years_2": 2
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/fin/forward-rate",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"spot_rate_1": 4,
"years_1": 1,
"spot_rate_2": 5,
"years_2": 2
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/fin/forward-rate", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"spot_rate_1":4,"years_1":1,"spot_rate_2":5,"years_2":2}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"spot_rate_1":4,"years_1":1,"spot_rate_2":5,"years_2":2}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/fin/forward-rate", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"spot_rate_1": 4,
"years_1": 1,
"spot_rate_2": 5,
"years_2": 2
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "fin.forward_rate",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
When either spot rate is minus one hundred percent or less, one plus the decimal rate is not positive and the power is undefined; the task fails with invalid_input instead of returning infinity.
What an implied forward rate means and how two spots pin it
This endpoint applies that identity only.
Input contract, response shape, and error behaviour
Pair the result with your own day-count and compounding convention if a desk uses actual over three-sixty or continuous zeros; this calculator measures the annually compounded spot-to-forward identity only. Each field may arrive as a JSON number or as a numeric string. Missing fields, empty strings, booleans, and non-finite values fail with invalid_input naming the field and are not billed. If years_1 is not strictly positive, or years_2 is not strictly larger than years_1, the forward window has no positive length and the request is likewise invalid_input rather than a divide-by-zero. On success the body echoes the four inputs, returns years_forward as t2 minus t1, returns forward_rate as a percent rounded half-up to eight decimal places, returns forward_rate_decimal as the same quantity in decimal form, and includes a formula string restating the annually compounded identity.
Where a forward rate calculator earns its keep
Asset-liability teams rolling a deposit or planning a refinancing use the same figure to see what rate the curve already locks in between two future dates, without standing up a full bootstrap library. Content teams can contrast this implied forward with a currency CIP outright or a Fisher real rate so readers see why those three numbers answer three different questions. Failed validation does not consume balance. Integrators wire the endpoint into notebooks, n8n flows, or edge workers to pin goldens whenever a valuation sheet changes a two-year zero. Keep both spots strictly above minus one hundred percent, keep the long tenor strictly longer than the short tenor, pin the rounded forward_rate field in tests, and you get reproducible implied forwards for widgets, classrooms, and production without standing up a swap library of your own.
Technical questions
How is the implied forward rate calculated?
The annually compounded identity is (1 + r2)^t2 = (1 + r1)^t1 × (1 + f)^(t2 − t1), so f = [(1 + r2)^t2 / (1 + r1)^t1]^(1/(t2 − t1)) − 1. This calculator takes the two spots as percents (4 means 4%) and the two tenors as year fractions.
Are the spot rates entered as percents or decimals?
spot_rate_1 and spot_rate_2 are percents (4 means 4%, 5 means 5%). years_1 and years_2 are year fractions (0.5 is six months). The response reports forward_rate in percent as well.
Why must the second tenor be longer than the first?
The forward window is t2 minus t1. If years_2 is not strictly greater than years_1 the exponent 1/(t2 − t1) is undefined, so the request is rejected as invalid_input rather than a divide-by-zero.
What does the forward rate calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.