Year Fraction Calculator

A year fraction, called the day count fraction or accrual factor in contract language, is the dimensionless quantity tau that converts an annualized rate into the interest actually earned over a period: Interest equals Notional times Rate times tau. Every convention is a pair of choices, how to count the days in the numerator and what to use as the year basis in the denominator. Actual methods count real calendar days; the 30/360 family replaces the numerator with (Y2-Y1) times 360 plus (M2-M1) times 30 plus (D2-D1), forcing every month to contribute exactly 30 days so that each semiannual coupon is precisely half a year. US 30/360 truncates a day-31 start to 30 and truncates a day-31 end to 30 only when the start was already the 30th; 30E/360 truncates both unconditionally, so the two diverge only when the end date lands on the 31st and the start does not. The magnitudes are small per unit but material on size. A full 365-day year priced Actual/360 gives tau equal to 1.01389, so a borrower pays about 1.39 percent more than the quoted rate implies; on a 10 million dollar loan at 6 percent that is roughly 8,333 dollars of extra annual interest. Actual/Actual under the ISDA method splits the period at year boundaries and divides each part by 365 or 366, which is why a leap-year period returns 1.000000 rather than 1.002740. Two caveats matter. First, Actual/Actual has several incompatible variants; the ISDA version implemented here is not the ICMA bond version, which divides by the coupon period times the coupons per year. Second, the convention is a contractual term, not a physical fact, and is fixed by the prospectus, credit agreement, or ISDA confirmation rather than chosen by the analyst.

The 360-day year is older than any of the instruments that now use it. Twelve 30-day months descend from the bankers year of medieval and early modern commercial arithmetic, a device that made interest computable by hand when logarithms and calculating machines did not exist. That habit persisted into the modern US bond market, where 30/360 kept coupon payments identical from period to period, and into US money markets and commercial lending, where Actual/360 became the default. As instruments proliferated the informal rules produced genuine settlement disputes, and the Securities Industry Association responded by publishing Standard Securities Calculation Methods, compiled by Jan Mayle, which set out unambiguous algorithms for accrued interest and yield across US instrument types. The derivatives market forced a second round of standardization. The International Swaps and Derivatives Association, founded in 1985, codified day count fractions in its successive definitional booklets, culminating in the 2006 ISDA Definitions, which spell out Actual/365 Fixed, Actual/360, Actual/Actual, 30/360, 30E/360 and their variants in the text that swap confirmations incorporate by reference. ISDA also circulated a paper in the late 1990s distinguishing the three Actual/Actual methods then in circulation, the ISDA, ICMA and AFB versions, because dealers were quoting the same trade with different accruals. The convention question resurfaced during the LIBOR transition of 2021 to 2023, since the replacement risk-free rates carry their own bases, with SOFR quoted on Actual/360 and SONIA on Actual/365, so legacy contracts required explicit day count language when they were amended.