Years to Days

In Lending, a Year Is Whatever the Contract Says It Is

Interest is a rate per year applied to a period measured in days, so every loan agreement, bond prospectus and swap confirmation has to state two things before a single figure can be calculated: how the days in the period are counted, and how many days the year is deemed to contain. That pair is the day-count convention, written as a fraction — 30/360, ACT/360, ACT/365 — and the denominator is very often not the number of days the calendar actually delivered.

Conversion factor: this converter uses a fixed year of 365.2425 days, so multiply years by 365.2425. A ten-year term comes to 3 652.425 days — against 3 600 under a 30/360 basis, and 3 652 or 3 653 on a real calendar depending on where the leap days land.

Where the Denominator Comes From

360 is an inheritance, not a mistake

Twelve equal thirty-day months divide cleanly by 2, 3, 4, 6 and 12, which mattered enormously when coupon schedules were worked out on paper. The convention outlived the constraint that produced it.

ACT means count the squares

An "actual" numerator counts real elapsed days, February's shortness and leap days included, so the same nominal rate produces a slightly different figure in different periods.

Numerator and denominator disagree on purpose

ACT/360 counts real days over a 360-day year, so a full year accrues 365/360 of the quoted rate. That is a feature of money-market pricing, not an error to be corrected.

The basis is a negotiated term

Two facilities quoted at the same headline rate can carry different bases, and the documented convention — not the rate on the term sheet — decides what is owed on the payment date.

Sizing a Term Before You Apply a Basis

The converter answers the neutral question — how many days is this many years — which is the figure you then adjust for whichever convention the document specifies.

Enter the term in years

Type 0.25 for a quarterly period, 1.5 for eighteen months or 30 for a long-dated bond. A comma is accepted in place of the decimal point, so 0,25 works the same as 0.25.

Compare it against the contractual basis

Set the mean-year figure beside the 360 or 365 the document uses. The gap between them is exactly the accrual difference you are looking for, before any rate is applied.

Reverse it for a period quoted in days

The swap control (↔) gives days → years, the direction you need when a confirmation states a 182-day or 1 095-day period and you want it expressed as a term.

Copy the raw number into the accrual formula

The copy control returns the figure without the unit or spacing, ready for the cell that multiplies principal by rate by days over basis. Ctrl + C inside the field does the same.

365.2425 is not a day-count basis: the year in this tool is fixed at the Gregorian mean, derived from the 146 097 days in a 400-year cycle. It is deliberately neutral and it matches no convention in the table below — no market accrues on 365.2425. Use it to size a term or sanity-check a period length, then apply the documented basis for anything that settles money.

What One Year at 5 % Pays Under Each Basis

The same principal, the same nominal rate and the same calendar year, run through the conventions a treasury desk meets most often. Interest is 1 000 000 × 5 % × days ÷ basis, rounded to the cent.

Convention	Days ÷ basis for the year	Interest on 1 000 000 at 5 %	Where it turns up
30/360 (US bond basis)	360 ÷ 360	50 000.00	US corporate and agency bonds, many mortgage schedules
30E/360 (Eurobond)	360 ÷ 360	50 000.00	Eurobonds; month-end handled without the US exceptions
ACT/360, ordinary year	365 ÷ 360	50 694.44	USD and EUR money markets, most commercial lending
ACT/360, leap year	366 ÷ 360	50 833.33	Same paper, one extra day of accrual in the period
ACT/365 fixed, ordinary year	365 ÷ 365	50 000.00	GBP, AUD and JPY money markets
ACT/365 fixed, leap year	366 ÷ 365	50 136.99	Sterling loans crossing a 29 February

Two things fall out of that column. A 30/360 basis is immune to the calendar — every period of the same nominal length pays the same, which is precisely why amortisation schedules like it. And ACT/360 systematically pays more than its headline rate suggests: 365 ÷ 360 is 1.3889 % extra, so 5 % on an ACT/360 basis is worth 5.0694 % quoted ACT/365.

What the Pair Does on a Rates Desk

Term lengths without a calendar open

Typing a tenor gives its day length while you type, which is enough to check that a schedule's period count and a stated maturity agree.

Read a stated day count as a tenor

Swapping the pair turns the 1 826 or 3 653 days written on a confirmation back into the five- or ten-year term everyone actually discusses.

Months and quarters from the same field

Both dropdowns search every time unit, so a tenor can be read straight into months or quarters when the schedule pays on that frequency rather than annually.

Fractions survive to eight decimals

Short tenors such as 0.0833 of a year keep enough precision to be worth checking, instead of collapsing to a rounded figure that hides the stub.

Basis Questions That Come Up in Documentation Review

Why do money markets divide by 360 when the year has 365 days?

It began as arithmetic convenience — 360 splits evenly into months, quarters and half-years, and short-dated paper was priced by hand from tables built on that assumption. It survived because it favours the lender in a way both sides now price in: dividing by the smaller number raises the effective yield, so 5 % ACT/360 delivers 50 694.44 on a million over an ordinary year rather than 50 000. Nobody is being caught out; the convention is simply part of the quote, and a borrower comparing an ACT/360 facility with an ACT/365 one has to restate one of them before the rates mean the same thing.

Which basis do government bonds use, and why is it different?

Sovereign issues generally settle on an actual/actual basis — US Treasuries, gilts and most European government paper. The logic is that a coupon is a fixed sum promised on a fixed date, so the accrual method should divide that exact coupon across the exact days of the coupon period rather than impose an idealised year. Under ACT/ACT a leap year simply becomes 366 over 366, and the result is unchanged, which is the behaviour you want when the amount payable was fixed at issue. Corporate paper leans the other way and takes 30/360, because there the priority is a schedule where every period looks identical.

How is a stub period accrued when it does not line up with the schedule?

Exactly like any other period — the convention does not change just because the period is irregular. Take a drawdown running 15 March to 30 June: the calendar gives 107 days, so ACT/360 on a million at 5 % accrues 14 861.11 and ACT/365 gives 14 657.53. A 30/360 basis sees the same window as 105 days, because it counts three notional months of 30 plus 15 days, and accrues 14 583.33. Three defensible answers, roughly 278 apart, from one identical set of dates.

What does a leap day do to an ACT/365 fixed calculation?

It adds a day of interest that the denominator never acknowledges. A sterling loan running through 29 February accrues over 366 days but still divides by 365, so the year pays 50 136.99 per million at 5 % instead of 50 000 — the "fixed" in the name refers to the denominator being pinned at 365 whatever the calendar does. That is the deliberate difference between ACT/365 fixed and ACT/ACT, where the denominator follows the year and the leap day washes out.

How much does applying the wrong basis actually cost?

Around 1.39 % of the interest for the classic ACT/360-versus-ACT/365 mix-up — a small proportion attached to a large number. On a 10 000 000 facility at 5 % that is 6 944.44 in a single ordinary year, repeated every year of the term and compounded into every reconciliation built on it. It rarely surfaces as a dramatic failure; it surfaces as a settlement figure that stubbornly disagrees with the counterparty's by a consistent fraction, which is usually the first clue that the two models were built on different denominators.