Interest Rate Swap Fixed Rate Calculator
The par fixed rate of an interest rate swap is the fixed coupon that makes the swap fair at inception, with zero value to either side. This calculator builds discount factors from a single flat zero rate and computes the par fixed rate over the swap tenor for a chosen payment frequency. It also reports the annuity factor (the sum of discounted accruals) used in the pricing.
Par swap rate formula
Periods n = tenor * frequency, accrual tau = 1 / frequency
Discount factor at period i: DF_i = e^(-zero * i * tau)
Annuity A = tau * sum(DF_i) for i = 1 to n
Par fixed rate = (1 - DF_n) / A
The zero rate is entered as a percentage and converted to a decimal. The float leg of a vanilla swap is worth (1 - DF_n) of notional at par, so dividing by the fixed-leg annuity gives the fixed rate that equates the two legs.
Worked example
Flat zero rate 5%, tenor 5 years, semi-annual (frequency 2). n = 10 periods, tau = 0.5. Discount factors run from e^(-0.05 * 0.5) = 0.97531 down to e^(-0.05 * 5) = 0.77880. The annuity A is 0.5 times the sum of the ten factors, about 4.3689. Par fixed rate = (1 - 0.77880) / 4.3689 = 0.22120 / 4.3689 = 0.05063, or 5.06%, close to the 5% zero rate as expected on a flat curve.
Swap fixed rate: frequently asked questions
What is the par swap rate?
The par (fixed) swap rate is the fixed rate that makes a vanilla interest rate swap worth zero at inception, so neither side pays the other to enter. It equals (1 minus the final discount factor) divided by the sum of discount factors times the accrual fraction across all fixed payment dates.
What assumptions does this calculator make?
It assumes a single flat continuously compounded zero rate used to build discount factors, equal accrual periods set by the payment frequency, and a standard receive-float, pay-fixed vanilla swap. A real swap desk uses a full term structure of dated discount factors; this is a clean teaching and estimation tool.
How does payment frequency affect the rate?
Frequency sets how many fixed payments occur per year and the accrual fraction per period (1 divided by frequency). With a flat yield curve the par swap rate is close to the zero rate; the exact value shifts slightly with frequency because of compounding and discounting conventions.
Sources and method
- U.S. Commodity Futures Trading Commission, education on swaps and derivatives: CFTC: Learn and Protect.
- Method: the standard discount-factor par swap rate identity, (1 - DF_n) / annuity; a public derivatives result. No proprietary data is used.
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. See our methodology.